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1.
  • Agram, Nacira, Associate professor, 1987-, et al. (författare)
  • Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control
  • 2023
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:3, s. 1472-1493
  • Tidskriftsartikel (refereegranskat)abstract
    • The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffu-sions, for short). To this end, we first prove a stochastic Fokker-Planck equation for the conditional law of the solution of such equations. Combining this equation with the original state equation, we obtain a Markovian system for the state and its conditional law. Furthermore, we apply this to formulate a Hamilton-Jacobi-Bellman equation for the optimal control of conditional McKean-Vlasov jump diffusions. Then we study the situation when the law is absolutely continuous with respect to Lebesgue measure. In that case the Fokker-Planck equation reduces to a stochastic par-tial differential equation for the Radon-Nikodym derivative of the conditional law. Finally we apply these results to solve explicitly the linear-quadratic optimal control problem of conditional stochastic McKean-Vlasov jump diffusions, and optimal consumption from a cash flow.
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2.
  • Almér, Stefan, et al. (författare)
  • Dynamic Phasor Analysis Of Pulse-Modulated Systems
  • 2012
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 50:3, s. 1110-1138
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper considers stability and harmonic analysis of a general class of pulse-modulated systems. The systems are modeled using the dynamic phasor model, which explores the cyclic nature of the modulation functions by representing the system state as a Fourier series expansion defined over a moving time window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case. The paper also shows how the dynamic phasor model can be used to derive a frequency domain input-to-state map which is analogous to the harmonic transfer function.
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3.
  • Aurell, Alexander, et al. (författare)
  • Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics
  • 2018
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 56:1, s. 434-455
  • Tidskriftsartikel (refereegranskat)abstract
    • We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.
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4.
  • Bahlali, Seid, et al. (författare)
  • The relaxed stochastic maximum principle in singular optimal control of diffusions
  • 2007
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 46:2, s. 427-444
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper studies optimal control of systems driven by stochastic differential equations, where the control variable has two components, the first being absolutely continuous and the second singular. Our main result is a stochastic maximum principle for relaxed controls, where the first part of the control is a measure valued process. To achieve this result, we establish first order optimality necessary conditions for strict controls by using strong perturbation on the absolutely continuous component of the control and a convex perturbation on the singular one. The proof of the main result is based on the strict maximum principle, Ekeland's variational principle, and some stability properties of the trajectories and adjoint processes with respect to the control variable.
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5.
  • Bodin, Per, et al. (författare)
  • Selection of best orthonormal rational basis
  • 2000
  • Ingår i: SIAM Journal on Control and Optimization. - 0363-0129 .- 1095-7138. ; 38:4, s. 995-1032
  • Tidskriftsartikel (refereegranskat)abstract
    • This contribution deals with the problem of structure determination for generalized orthonormal basis models used in system identification. The model structure is parameterized by a prespecified set of poles representing a finite-dimensional subspace of H2. Given this structure and experimental data, a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated parameters, one objective is to find coordinates, or a basis, for the finite-dimensional subspace giving as compact or parsimonious a system representation as possible. In this paper, a best basis algorithm and a coefficient decomposition scheme are derived for the generalized orthonormal rational bases. Combined with linear regression and thresholding this leads to compact transfer function representations. The methods are demonstrated with several examples.
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6.
  • Bodnariu, Andi, et al. (författare)
  • Local Time Pushed Mixed Equilibrium Strategies for Time-Inconsistent Stopping Problems
  • 2024
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 62:2, s. 1261-1290
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider the game-theoretic approach to time-inconsistent stopping of a onedimensional diffusion where the time-inconsistency is due to the presence of a nonexponential (weighted) discount function. In particular, we study (weak) equilibria for this problem in a novel class of mixed (i.e., randomized) stopping times based on a local time construction of the stopping intensity. For a general formulation of the problem we provide a verification theorem giving sufficient conditions for mixed (and pure) equilibria in terms of a set of variational inequalities, including a smooth fit condition. We apply the theory to prove the existence of (mixed) equilibria in a recently studied real options problem in which no pure equilibria exist.
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7.
  • Boskos, Dimitris, et al. (författare)
  • ABSTRACTIONS OF VARYING DECENTRALIZATION DEGREE FOR REACHABILITY OF COUPLED MULTIAGENT SYSTEMS
  • 2019
  • Ingår i: SIAM Journal of Control and Optimization. - : SIAM PUBLICATIONS. - 0363-0129 .- 1095-7138. ; 57:5, s. 3471-3495
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we present a decentralized abstraction framework for multiagent systems with couplings in their dynamics, which arise in their popular coordination protocols. The discrete models are basexl on a varying decentralization degree, namely, the agents' individual abstractions are obtained by using discrete information up to a tunable distance in their network graph. Deriving these models at the agent level is essential to address scalability issues which appear in the discretization of systems with a high state dimension. The approach builds on the appropriate discretization of the agents' state space and the selection of a transition time step, which enable the construction of a nonblocking transition system for each agent with quantifiable transition possibilities. The transitions are based on the design of local feedback laws for the manipulation of the coupling terms, which guarantee the execution of the transitions by the continuous systems. For a class of nonlinear agent interconnections, the derivation of such abstractions is always guaranteed, based on sufficient conditions which relate the agents' dynamics and the space/time quantization.
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8.
  • Boskos, Dimitris, et al. (författare)
  • Robustness and invariance of connectivity maintenance control for multiagent systems
  • 2017
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 55:3, s. 1887-1914
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper is focused on a cooperative control design Which guarantees robust connectivity and invariance of a multiagent network inside a bounded domain, under the presence of additional bounded input terms in each agent's dynamics. In particular, under the assumptions that the domain is convex and has a smooth boundary, we can design a repulsion vector field near its boundary, Which ensures invariance of the agents' trajectories and does not affect the robustness properties of the control part that is exploited for connectivity maintenance.
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9.
  • Byrnes, Christopher I., et al. (författare)
  • IMPORTANT MOMENTS IN SYSTEMS AND CONTROL
  • 2008
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 47:5, s. 2458-2469
  • Tidskriftsartikel (refereegranskat)abstract
    • The moment problem matured from its various special forms in the late 19th and early 20th centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception, where the applications have historically been to circuit theory, optimal control, robust control, signal processing, spectral estimation, stochastic realization theory, and the use of the moments of a probability density. Many of these applications are also still works in progress. In this paper, we consider the generalized moment problem, expressed in terms of a basis of a finite-dimensional subspace P of the Banach space C[a, b] and a "positive" sequence c, but with a new wrinkle inspired by the applications to systems and control. We seek to parameterize solutions which are positive "rational" measures in a suitably generalized sense. Our parameterization is given in terms of smooth objects. In particular, the desired solution space arises naturally as a manifold which can be shown to be diffeomorphic to a Euclidean space and which is the domain of some canonically defined functions. The analysis of these functions, and related maps, yields interesting corollaries for the moment problem and its applications, which we compare to those in the recent literature and which play a crucial role in part of our proof.
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10.
  • Byrnes, Christopher, et al. (författare)
  • Identifiability and well-posedness of shaping-filter parameterizations : A global analysis approach
  • 2002
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 41:1, s. 23-59
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we study the well-posedness of the problems of determining shaping filters from combinations of finite windows of cepstral coefficients, covariance lags, or Markov parameters. For example, we determine whether there exists a shaping filter with a prescribed window of Markov parameters and a prescribed window of covariance lags. We show that several such problems are well-posed in the sense of Hadamard; that is, one can prove existence, uniqueness (identifiability), and continuous dependence of the model on the measurements. Our starting point is the global analysis of linear systems, where one studies an entire class of systems or models as a whole, and where one views measurements, such as covariance lags and cepstral coefficients or Markov parameters, from data as functions on the entire class. This enables one to pose such problems in a way that tools from calculus, optimization, geometry, and modern nonlinear analysis can be used to give a rigorous answer to such problems in an algorithm-independent fashion. In this language, we prove that a window of cepstral coefficients and a window of covariance coefficients yield a bona de coordinate system on the space of shaping filters, thereby establishing existence, uniqueness, and smooth dependence of the model parameters on the measurements from data.
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11.
  • Cantoni, Michael, et al. (författare)
  • Robust Stability Analysis For Feedback Interconnections Of Time-Varying Linear Systems
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:1, s. 353-379
  • Tidskriftsartikel (refereegranskat)abstract
    • Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L-2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz-Wiener-Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L-2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier-Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains.
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12.
  • Chasparis, Georgios, et al. (författare)
  • Aspiration Learning in Coordination Games
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 51:1, s. 465-490
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider the problem of distributed convergence to efficient outcomes in coordination games through dynamics based on aspiration learning. Our first contribution is the characterization of the asymptotic behavior of the induced Markov chain of the iterated process in terms of an equivalent finite-state Markov chain. We then characterize explicitly the behavior of the proposed aspiration learning in a generalized version of coordination games, examples of which include network formation and common-pool games. In particular, we show that in generic coordination games the frequency at which an efficient action profile is played can be made arbitrarily large. Although convergence to efficient outcomes is desirable, in several coordination games, such as common-pool games, attainability of fair outcomes, i.e., sequences of plays at which players experience highly rewarding returns with the same frequency, might also be of special interest. To this end, we demonstrate through analysis and simulations that aspiration learning also establishes fair outcomes in all symmetric coordination games, including common-pool games. Read More: http://epubs.siam.org/doi/abs/10.1137/110852462
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13.
  • Chen, Jianqi, et al. (författare)
  • Geometrical Characterization Of Sensor Placement For Cone-Invariant And Multi-Agent Systems Against Undetectable Zero-Dynamics Attacks\Ast
  • 2022
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 60:2, s. 890-916
  • Tidskriftsartikel (refereegranskat)abstract
    • Undetectable attacks are an important class of malicious attacks threatening the security of cyber-physical systems, which can modify a system's state but leave the system output measurements unaffected and hence cannot be detected from the output. This paper studies undetectable attacks on cone-invariant systems and multi-agent systems. We first provide a general characterization of zero-dynamics attacks, which characterizes fully undetectable attacks targeting the nonminimum phase zeros of a system. This geometrical characterization makes it possible to develop a defense strategy seeking to place a minimal number of sensors to detect and counter the zero-dynamics attacks on the system's actuators. The detect and defense scheme amounts to computing a set containing potentially vulnerable actuator locations and nodes and a defense union for feasible placement of sensors based on the geometrical properties of the cones under consideration.
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14.
  • Chen, Wei, et al. (författare)
  • A Phase Theory Of Multi-Input Multi-Output Linear Time-Invariant Systems
  • 2024
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 62:2, s. 1235-1260
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we define the phase response for a class of multi -input multi -output (MIMO) linear time -invariant (LTI) systems whose frequency responses are (semi -)sectorial at all frequencies. The newly defined phase subsumes the well-known notion of positive real systems and is closely related to the notion of negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time -domain interpretations of phase -bounded systems via both energy signal analysis and power signal analysis.
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15.
  • Christensen, Sören, et al. (författare)
  • On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems
  • 2018
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 56:6, s. 4228-4255
  • Tidskriftsartikel (refereegranskat)abstract
    • Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a straightforward way be applied to nonstandard stopping problems without this time-consistent structure. This paper is devoted to the solution of time-inconsistent stopping problems with the reward depending on the initial state using an adaptation of Strotz's consistent planning. More precisely, we give a precise equilibrium definition-of the type subgame perfect Nash equilibrium based on pure Markov strategies. In general, such equilibria do not always exist and if they exist they are in general not unique. We, however, develop an iterative approach to finding equilibrium stopping times for a general class of problems and apply this approach to one-sided stopping problems on the real line. We furthermore prove a verification theorem based on a set of variational inequalities which also allows us to find equilibria. In the case of a standard optimal stopping problem, we investigate the connection between the notion of an optimal and an equilibrium stopping time. As an application of the developed theory we study a selling strategy problem under exponential utility and endogenous habit formation.
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16.
  • Como, Giacomo, et al. (författare)
  • Stability Analysis of Transportation Networks with Multiscale Driver Decisions
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 51:1, s. 230-252
  • Tidskriftsartikel (refereegranskat)abstract
    • Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of nonatomic indistinguishable drivers commuting between a common origin-destination pair in an acyclic transportation network. The drivers' route choices are affected by their relatively infrequent perturbed best responses to global information about the current network congestion levels, as well as their instantaneous local observation of the immediate surroundings as they transit through the network. A novel model is proposed for driver route choice behavior, exhibiting local consistency with their preference toward globally less congested paths as well as myopic decisions in favor of locally less congested paths. The simultaneous evolution of the traffic congestion on the network and of the aggregate path preference is modeled by a system of coupled ordinary differential equations. The main result shows that if the frequency of updates of path preferences is sufficiently small as compared to the frequency of the traffic flow dynamics, then the state of the transportation network ultimately approaches a neighborhood of the Wardrop equilibrium. The presented results may be read as further evidence in support of Wardrop's postulate of equilibrium, showing robustness of it with respect to nonpersistent perturbations. The proposed analysis combines techniques from singular perturbation theory, evolutionary game theory, and cooperative dynamical systems.
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17.
  • Curtain, Ruth, et al. (författare)
  • ON RICCATI EQUATIONS IN BANACH ALGEBRAS
  • 2011
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 49:2, s. 464-475
  • Tidskriftsartikel (refereegranskat)abstract
    • Let R be a commutative complex Banach algebra with the involution .* and suppose that A is an element of R-nxn, B is an element of R-nxm, C is an element of R-pxn. The question of when the Riccati equation PBB*P - PA - A*P - C*C = 0 has a solution P is an element of R-nxn is investigated. A counterexample to a previous result in the literature on this subject is given, followed by sufficient conditions on the data guaranteeing the existence of such a P. Finally, applications to spatially distributed systems are discussed.
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18.
  • De Angelis, Tiziano, et al. (författare)
  • The maximality principle in singular control with absorption and its applications to the dividend problem
  • 2024
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 62:1, s. 91-117
  • Tidskriftsartikel (refereegranskat)abstract
    • Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
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19.
  • Di Bernardo, Mario, et al. (författare)
  • Contraction analysis for a class of nondifferentiable systems with applications to stability and network synchronization
  • 2014
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 52:5, s. 3203-3227
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched nondifferentiable systems satisfying Caratheodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems.
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20.
  • Djehiche, Boualem, et al. (författare)
  • A FINITE HORIZON OPTIMAL MULTIPLE SWITCHING PROBLEM
  • 2009
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 48:4, s. 2751-2770
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider the problem of optimal multiple switching in a finite horizon when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the Snell envelope of processes and reflected backward stochastic differential equations. Finally, when the state of the system is a Markov process, we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles.
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21.
  • Ekström, Erik, 1977-, et al. (författare)
  • How To Detect A Salami Slicer : A Stochastic Controller-And-Stopper Game With Unknown Competition
  • 2022
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 60:1, s. 545-574
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider a stochastic game of control and stopping specified in terms of a process $X_t=-\theta \Lambda_t+W_t$, representing the holdings of Player 1, where $W$ is a Brownian motion, $\theta$ is a Bernoulli random variable indicating whether Player 2 is active or not, and $\Lambda$ is a nondecreasing continuous process representing the accumulated "theft" or "fraud" performed by Player 2 (if active) against Player 1. Player 1 cannot observe $\theta$ or $\Lambda$ directly but can merely observe the path of the process $X$ and may choose a stopping rule $\tau$ to deactivate Player 2 at a cost $M$. Player 1 thus does not know if she is the victim of fraud or not and operates in this sense under unknown competition. Player 2 can observe both $\theta$ and $W$ and seeks to choose a fraud strategy $\Lambda$ that maximizes the expected discounted amount ${\mathbb E} \left [ \left. \int _0^{\tau} e^{-rs} d\Lambda_s \right \vert \theta=1\right ],$ whereas Player 1 seeks to choose the stopping strategy $\tau$ so as to minimize the expected discounted cost ${\mathbb E} \left [\theta \int _0^{\tau} e^{-rs} d\Lambda_s + e^{-r\tau}M\I{\tau<\infty} \right ].$ This non-zero-sum game belongs to a class of stochastic dynamic games with unknown competition and continuous controls and is motivated by applications in fraud detection; it combines filtering (detection), stochastic control, optimal stopping, strategic features (games), and asymmetric information. We derive Nash equilibria for this game; for some parameter values we find an equilibrium in pure strategies, and for other parameter values we find an equilibrium by allowing for randomized stopping strategies.
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22.
  • Ekström, Erik, 1977-, et al. (författare)
  • Optimal stopping games for Markov processes
  • 2008
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 47:2, s. 684-702
  • Tidskriftsartikel (refereegranskat)
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23.
  • Ekström, Erik, 1977-, et al. (författare)
  • The de Finetti problem with uncertain competition
  • 2023
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:5, s. 2997-3017
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the ability to extract all the remaining resources in one piece, may exist. This situation is modeled as a nonzero-sum controller-and-stopper game with incomplete information. For this stochastic game we provide a Nash equilibrium with an explicit structure. In equilibrium, the agent and the competitor use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.
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24.
  • Enqvist, Per (författare)
  • A convex optimization approach to arma(n,m) model design from covariance and cepstral data
  • 2004
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 43:3, s. 1011-1036
  • Tidskriftsartikel (refereegranskat)abstract
    • Methods for determining ARMA(n, m) filters from covariance and cepstral estimates are proposed. In [C. I. Byrnes, P. Enqvist, and A. Lindquist, SIAM J. Control Optim., 41 ( 2002), pp. 23-59], we have shown that an ARMA( n, n) model determines and is uniquely determined by a window r(0), r(1),..., r(n) of covariance lags and c(1), c(2),..., c(n) of cepstral lags. This unique model can be determined from a convex optimization problem which was shown to be the dual of a maximum entropy problem. In this paper, generalizations of this problem are analyzed. Problems with covariance lags r(0), r(1),..., r(n) and cepstral lags c(1), c(2),..., c(m) of different lengths are considered, and by considering different combinations of covariances, cepstral parameters, poles, and zeros, it is shown that only zeros and covariances give a parameterization that is consistent with generic data. However, the main contribution of this paper is a regularization of the optimization problems that is proposed in order to handle generic data. For the covariance and cepstral problem, if the data does not correspond to a system of desired order, solutions with zeros on the boundary occur and the cepstral coefficients are not interpolated exactly. In order to achieve strictly minimum phase filters for estimated covariance and cepstral data, a barrier-like term is introduced to the optimization problem. This term is chosen so that convexity is maintained and so that the unique solution will still interpolate the covariances but only approximate the cepstral lags. Furthermore, the solution will depend analytically on the covariance and cepstral data, which provides robustness, and the barrier term increases the entropy of the solution.
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25.
  • Farokhi, Farhad, 1987-, et al. (författare)
  • Decentralized Disturbance Accommodation with Limited Plant Model Information
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:2, s. 1543-1573
  • Tidskriftsartikel (refereegranskat)abstract
    • The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is studied in this paper. We consider discrete-time linear time-invariant systems that are fully actuated and composed of scalar subsystems, each of which is controlled separately and influenced by a scalar disturbance. Each disturbance is assumed to be generated by a system with known dynamics and unknown initial conditions. We restrict ourselves to control design methods that produce structured dynamic state feedback controllers where each subcontroller, at least, has access to the state measurements of those subsystems that can affect its corresponding subsystem. The performance of such control design methods is compared using a metric called the competitive ratio, which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. We find an explicit minimizer of the competitive ratio and show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For step disturbances, it is shown that this structure corresponds to proportional-integral control.
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26.
  • Feyzmahdavian, Hamid Reza, et al. (författare)
  • ASYMPTOTIC STABILITY AND DECAY RATES OF HOMOGENEOUS POSITIVE SYSTEMS WITH BOUNDED AND UNBOUNDED DELAYS
  • 2014
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 52:4, s. 2623-2650
  • Tidskriftsartikel (refereegranskat)abstract
    • There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, we present a necessary and sufficient condition for delay-independent stability of continuous-time positive systems whose vector fields are cooperative and homogeneous. We show that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays. For various classes of time delays, we are able to derive explicit expressions that quantify the decay rates of positive systems. We also provide the corresponding counterparts for discrete-time positive systems whose vector fields are nondecreasing and homogeneous.
  •  
27.
  • Flordal, Hugo, 1977, et al. (författare)
  • Compositional Verification in Supervisory Control
  • 2009
  • Ingår i: SIAM Journal on Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 48:3, s. 1914-1938
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper proposes a compositional approach to verifying whether a large discrete event system is nonblocking. The new approach avoids computing the synchronous product of a large set of finite-state machines. Instead, the synchronous product is computed gradually, and intermediate results are simplified using conflict-preserving abstractions based on process-algebraic results about fair testing. Heuristics are used to choose between different possible abstractions. By translating the problem representation, the same method can also be applied to verify safety properties, in particular, controllability. Experimental results show that the method is applicable to finite-state machine models of industrial scale and brings considerable improvements in performance over other methods for nonblocking verification.
  •  
28.
  • Haasler, Isabel, et al. (författare)
  • Multimarginal optimal transport with a tree-structured cost and the schrödinger bridge problem
  • 2021
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 59:4, s. 2428-2453
  • Tidskriftsartikel (refereegranskat)abstract
    • The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the problem with an entropy term, which connects it to the Schrodinger bridge problem and thus to stochastic optimal control. Moreover, the entropy regularization makes the otherwise computationally demanding optimal transport problem feasible even for large scale settings. This has led to an accelerated development of optimal transport based methods in a broad range of fields. Many of these applications have an underlying graph structure, for instance, information fusion and tracking problems can be described by trees. In this work we consider multimarginal optimal transport problems with a cost function that decouples according to a tree structure. The entropy regularized multimarginal optimal transport problem can be viewed as a generalization of the Schrodinger bridge problem with the same tree-structure, and by utilizing these connections we extend the computational methods for the classical optimal transport problem in order to solve structured multimarginal optimal transport problems in an efficient manner. In particular, the algorithm requires only matrix-vector multiplications of relatively small dimensions. We show that the multimarginal regularization introduces less diffusion, compared to the commonly used pairwise regularization, and is therefore more suitable for many applications. Numerical examples illustrate this, and we finally apply the proposed framework for the tracking of an ensemble of indistinguishable agents.
  •  
29.
  • He, Xingkang, et al. (författare)
  • EVENT-TRIGGERED DISTRIBUTED ESTIMATION WITH DECAYING COMMUNICATION RATE
  • 2022
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 60:2, s. 992-1017
  • Tidskriftsartikel (refereegranskat)abstract
    • We study distributed estimation of a high-dimensional static parameter vector through a group of sensors whose communication network is modeled by a fixed directed graph. Different from existing time-triggered communication schemes, an event-triggered asynchronous scheme is investigated in order to reduce communication while preserving estimation convergence. A distributed estimation algorithm with a single step size is first proposed based on an event-triggered communication scheme with a time-dependent decaying threshold. With the event-triggered scheme, each sensor sends its estimate to neighbor sensors only when the difference between the current estimate and the last sent-out estimate is larger than the triggering threshold. Different sensors can have different step sizes and triggering thresholds, enabling the parameter estimation process to be conducted in a fully distributed way. We prove that the proposed algorithm has mean-square and almost-sure convergence, respectively, under an integrated condition of sensor network topology and sensor measurement matrices. The condition is satisfied if the topology is a balanced digraph containing a spanning tree and the system is collectively observable. The collective observability is the possibly mildest condition, since it is a spatially and temporally collective condition of all sensors and allows sensor measurement matrices to be time-varying, stochastic, and nonstationary. Moreover, we provide estimates for the convergence rates, which are related to the step size as well as the triggering threshold. Furthermore, as an essential metric of sensor communication intensity in the event-triggered distributed algorithms, the communication rate is proved to decay to zero with a certain speed almost surely as time goes to infinity. In addition, we show that it is feasible to tune the threshold and the step size such that requirements of algorithm convergence and communication rate decay are satisfied simultaneously. We also show that given the step size, adjusting the decay speed of the triggering threshold can lead to a tradeoff between the convergence rate of the estimation error and the decay speed of the communication rate. Specifically, increasing the decay speed of the threshold would make the communication rate decay faster but reduce the convergence rate of the estimation error. Numerical simulations are provided to illustrate the developed results.
  •  
30.
  • Heuberger, Peter S. C., et al. (författare)
  • Orthonormal basis functions in time and frequency domain : Hambo transform theory
  • 2004
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 42:4, s. 1347-1373
  • Tidskriftsartikel (refereegranskat)abstract
    • The class of finite impulse response (FIR), Laguerre, and Kautz functions can be generalized to a family of rational orthonormal basis functions for the Hardy space H2 of stable linear dynamical systems. These basis functions are useful for constructing efficient parameterizations and coding of linear systems and signals, as required in, e.g., system identification, system approximation, and adaptive filtering. In this paper, the basis functions are derived from a transfer function perspective as well as in a state space setting. It is shown how this approach leads to alternative series expansions of systems and signals in time and frequency domain. The generalized basis functions induce signal and system transforms (Hambo transforms), which have proved to be useful analysis tools in various modelling problems. These transforms are analyzed in detail in this paper, and a large number of their properties are derived. Principally, it is shown how minimal state space realizations of the system transform can be obtained from minimal state space realizations of the original system and vice versa.
  •  
31.
  • Jacob, Birgit, et al. (författare)
  • Applications of Laplace–Carleson embeddings to admissibility and controllability
  • 2014
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 52:2, s. 1299-1313
  • Tidskriftsartikel (refereegranskat)abstract
    • It is shown how results on Carleson embeddings induced by the Laplace transform can be used to derive new and more general results concerning the weighted (infinite-time) admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. As an example, the heat equation is considered. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterized by means of a new result about weighted interpolation.
  •  
32.
  • Jönsson, Johan, et al. (författare)
  • Finite Horizon Impulse control of Stochastic Functional Differential Equations
  • 2023
  • Ingår i: SIAM Journal of Control and Optimization. - : SIAM Publications. - 0363-0129 .- 1095-7138. ; 61:2, s. 924-948
  • Tidskriftsartikel (refereegranskat)abstract
    • In this work we show that one can solve a finite horizon non-Markovian impulse control problem with control dependent dynamics. This dynamic satisfies certain functional Lipschitz conditions and is path dependent in such a way that the resulting trajectory becomes a flow.
  •  
33.
  • Jönsson, Ulf T. (författare)
  • A SECTOR CONDITION FOR LIMIT CYCLE ROBUSTNESS
  • 2008
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 47:6, s. 2745-2772
  • Tidskriftsartikel (refereegranskat)abstract
    • Robustness of periodic oscillations in autonomous feedback systems is considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude range. The quadratic constraint is generated as a time-periodic sector condition that characterizes the nonlinearity around a nominal periodic solution. The main analysis condition is formulated as an operator inequality involving the nominal dynamics and the sector constraint. This is an infinite dimensional robustness test that must be truncated to be verified numerically. We discuss two possible ways of performing the analysis.
  •  
34.
  • Jönsson, Ulf T. (författare)
  • A small-gain theory for limit cycles of systems on lure form
  • 2005
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 44:3, s. 909-938
  • Tidskriftsartikel (refereegranskat)abstract
    • Local exponential stability and local robustness for limit cycle solutions of ordinary differential equations can be verified using the characteristic multipliers. These well-known results are here generalized to a class of infinite-dimensional systems. Stability and robustness are now verified using certain invertibility conditions on the linear equations that are obtained when the system is linearized along the limit cycle. The new criterion reduces to the classical condition on the characteristic multipliers when we consider a finite-dimensional system which is perturbed by a bounded but possibly infinite-dimensional operator. The computation of a robustness margin, i.e., a bound on the maximally allowed perturbation, is also considered.
  •  
35.
  • Klintberg, Emil, 1989, et al. (författare)
  • Numerical Structure of the Hessian of the Lagrange Dual Function for a Class of Convex Problems
  • 2017
  • Ingår i: SIAM Journal on Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 55:1, s. 574-593
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper considers a structured separable convex optimization problem, motivated by the deployment of model predictive control on multiagent systems that are interacting via nondelayed couplings. We show that the dual decomposition of this problem yields a numerical structure in the Hessian of the dual function. This numerical structure allows for deploying a quasi Newton method in the dual space. For large problems, this approach yields a large reduction of the computational complexity of solving the problem, and for geographically distributed problems a reduction in the communication burden.
  •  
36.
  • Kristalny, Maxim, et al. (författare)
  • Input/Output Stabilization in the General Two-Sided Model Matching Setup
  • 2012
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 50:3, s. 1413-1438
  • Tidskriftsartikel (refereegranskat)abstract
    • The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH infinity. Then, recent results on bilateral Diophantine equations are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which is affine in a single RH infinity parameter. This demonstrates that if the aforementioned assumption is imposed, the general two-sided stabilization problem is similar to its one-sided counterpart in the sense that the constraints imposed by a stability requirement can be resolved without increasing problem complexity.
  •  
37.
  • Lindquist, Anders (författare)
  • On the duality between filtering and Nevanlinna-Pick interpolation
  • 2000
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 39:3, s. 757-775
  • Tidskriftsartikel (refereegranskat)abstract
    • Positive real rational functions play a central role in both deterministic and stochastic linear systems theory, as well as in circuit synthesis, spectral analysis, and speech processing. For this reason, results about positive real transfer functions and their realizations typically have many applications and manifestations. In this paper, we study certain manifolds and submanifolds of positive real transfer functions, describing a fundamental geometric duality between filtering and Nevanlinna Pick interpolation. Not surprisingly, then, this duality, while interesting in its own right, has several corollaries which provide solutions and insight into some very interesting and intensely researched problems. One of these is the problem of parameterizing all rational solutions of bounded degree of the Nevanlinna-Pick interpolation problem, which plays a central role in robust control, and for which the duality theorem yields a complete solution. In this paper, we shall describe the duality theorem, which we motivate in terms of both the interpolation problem and a fast algorithm for Kalman filtering, viewed as a nonlinear dynamical system on the space of positive real transfer functions. We also outline a new proof of the recent solution to the rational Nevanlinna Pick interpolation problem, using an algebraic topological generalization of Hadamard's global inverse function theorem.
  •  
38.
  • Liu, Kun, et al. (författare)
  • Networked control systems in the presence of scheduling protocols and communication delays
  • 2015
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 53:4, s. 1768-1788
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper develops the time-delay approach to networked control systems in the presence of multiple sensor nodes, communication constraints, variable transmission delays, and sampling intervals. Due to communication constraints, only one sensor node is allowed to transmit its packet at a time. The scheduling of sensor information toward the controller is ruled by a weighted try-once-discard or by round-robin protocols. A unified hybrid system model under both protocols for the closed-loop system is presented; it contains time-varying delays in the continuous dynamics and in the reset conditions. A new Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov functionals, is introduced for the stability analysis of the delayed hybrid systems. The resulting conditions can be applied to the system with polytopic type uncertainties. The efficiency of the time-delay approach is illustrated on the examples of uncertain cart-pendulum and of batch reactor.
  •  
39.
  • Lovisari, Enrico, et al. (författare)
  • Resistance-Based Performance Analysis of the Consensus Algorithm over Geometric Graphs
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 51:5, s. 3918-3945
  • Tidskriftsartikel (refereegranskat)abstract
    • The performance of the linear consensus algorithm is studied by using a linear quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting the analogy between Markov chains and electrical resistive networks. Indeed, this allows us to uncover the relation between the LQ performance cost and the average effective resistance of a suitable electrical network and, moreover, to show that if the communication graph fulfills some local properties, then its behavior can be approximated by that of a grid, which is a graph whose associated LQ cost is well known.
  •  
40.
  • Meng, Z., et al. (författare)
  • Multiagent systems with compasses
  • 2015
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 53:5, s. 3057-3080
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper investigates agreement protocols over cooperative and cooperativeantagonistic multiagent networks with coupled continuous-time nonlinear dynamics. To guarantee convergence for such systems, it is common in the literature to assume that the vector field of each agent is pointing inside the convex hull formed by the states of the agent and its neighbors, given that the relative states between each agent and its neighbors are available. This convexity condition is relaxed in this paper, as we show that it is enough that the vector field belongs to a strict tangent cone based on a local supporting hyperrectangle. The new condition has the natural physical interpretation of requiring shared reference directions in addition to the available local relative states. Such shared reference directions can be further interpreted as if each agent holds a magnetic compass indicating the orientations of a global frame. It is proved that the cooperative multiagent system achieves exponential state agreement if and only if the time-varying interaction graph is uniformly jointly quasi-strongly connected. Cooperative-antagonistic multiagent systems are also considered. For these systems, the relation has a negative sign for arcs corresponding to antagonistic interactions. State agreement may not be achieved, but instead it is shown that all the agents' states asymptotically converge, and their limits agree componentwise in absolute values if and in general only if the time-varying interaction graph is uniformly jointly strongly connected.
  •  
41.
  • Mäkilä, Pertti, et al. (författare)
  • Bounded power signal spaces for robust control and modeling
  • 1999
  • Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 37:1, s. 92-117
  • Tidskriftsartikel (refereegranskat)abstract
    • The nonlinear space of signals allowing Wiener's generalized harmonic analysis (GHA), the linear bounded power signal spaces of Beurling, Marcinkiewicz, and Wiener, and a new linear bounded power space are studied from a control and systems theory perspective. Specifically, it is shown that the system power gain is given by the $H_\infty$ norm of the system transfer function in each of these spaces for a large class of (power) stable finite and infinite dimensional systems. The GHA setup is shown to possess several limitations for the purpose of robustness analysis which motivates the use of the other more general (nonstationary) signal spaces. The natural double-sided time axis versions of bounded power signal spaces are shown to break the symmetry between Hardy space $H_\infty$ methods and bounded power operators; e.g., the system transfer function being in $H_\infty$ does not imply that a causal-linear time-invariant (LTI) system is bounded as an operator on any of the double-sided versions of the studied bounded power signal spaces.
  •  
42.
  • Ninness, Brett, et al. (författare)
  • Generalized Fourier and Toeplitz results for rational orthonormal bases
  • 1998
  • Ingår i: SIAM Journal on Control and Optimization. - 0363-0129 .- 1095-7138. ; 37:2, s. 429-460
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper provides a generalization of certain classical Fourier convergence and asymptotic Toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a special case. These generalized Fourier and Toeplitz results have particular application in dynamic system estimation theory. Specifically, the results allow a unified treatment of the accuracy of least-squares system estimation using a range of model structures, including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole or zero locations.
  •  
43.
  • Prajna, Stephen, et al. (författare)
  • Convex programs for temporal verification of nonlinear dynamical systems
  • 2007
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 46:3, s. 999-1021
  • Tidskriftsartikel (refereegranskat)abstract
    • A methodology for safety verification of continuous and hybrid systems using barrier certi.ficates has been proposed recently. Conditions that must be satisfi.ed by a barrier certi. cate can be formulated as a convex program, and the feasibility of the program implies system safety in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i. e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from the linear programming duality appearing in the discrete shortest path problem, we show in this paper that reachability of continuous systems can also be veri. ed through convex programming. Several convex programs for verifying safety and reachability, as well as other temporal properties such as eventuality, avoidance, and their combinations, are formulated. Some examples are provided to illustrate the application of the proposed methods. Finally, we exploit the convexity of our methods to derive a converse theorem for safety veri. cation using barrier certificates.
  •  
44.
  • Rabi, Maben, 1977, et al. (författare)
  • Adaptive sampling for linear state estimation
  • 2012
  • Ingår i: SIAM Journal on Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 50:2, s. 672-702
  • Tidskriftsartikel (refereegranskat)abstract
    • When a sensor has continuous measurements but sends occasional messages over a data network to a supervisor which estimates the state, the available packet rate fixes the achievable quality of state estimation. When such rate limits turn stringent, the sensor’s messaging policy should be designed anew. What are the good causal messaging policies ? What should message packets contain ? What is the lowest possible distortion in a causal estimate at the supervisor ? Is Delta sampling better than periodic sampling ? We answer these questions for a Markov state process under an idealized model of the network and the assumption of perfect state measurements at the sensor. If the state is a scalar, or a vector of low dimension, then we can ignore sample quantization. If in addition, we can ignore jitter in the transmission delays over the network, then our search for efficient messaging policies simplifies. Firstly, each message packet should contain the value of the state at that time. Thus a bound on the number of data packets becomes a bound on the number of state samples. Secondly, the remaining choice in messaging is entirely about the times when samples are taken. For a scalar, linear diffusion process, we study the problem of choosing the causal sampling times that will give the lowest aggregate squared error distortion. We stick to finite-horizons and impose a hard upper bound N on the number of allowed samples. We cast the design as a problem of choosing an optimal sequence of stopping times. We reduce this to a nested sequence of problems, each asking for a single optimal stopping time. Under an unproven but natural assumption about the least-square estimate at the supervisor, each of these single stopping problems are of standard form. The optimal stopping times are random times when the estimation error exceeds designed envelopes. For the case where the state is a Brownian motion, we give analytically: the shape of the optimal sampling envelopes, the shape of the envelopes under optimal Delta sampling, and their performances. Surprisingly, we find that Delta sampling performs badly. Hence, when the rate constraint is a hard limit on the number of samples over a finite horizon, we should should not use Delta sampling.
  •  
45.
  • Rabi, Maben, et al. (författare)
  • SEPARATED DESIGN OF ENCODER AND CONTROLLER FOR NETWORKED LINEAR QUADRATIC OPTIMAL CONTROL
  • 2016
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 54:2, s. 662-689
  • Tidskriftsartikel (refereegranskat)abstract
    • For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. The encoder outputs are quantized samples, but our results also apply to two other formats for encoder outputs: real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop system. We also show that this separated design need not be optimal when the controller or encoder are to be chosen from within restricted classes.
  •  
46.
  • Ren, Wei, et al. (författare)
  • KRASOVSKII AND RAZUMIKHIN STABILITY THEOREMS FOR STOCHASTIC SWITCHED NONLINEAR TIME-DELAY SYSTEMS
  • 2019
  • Ingår i: SIAM Journal of Control and Optimization. - : SIAM PUBLICATIONS. - 0363-0129 .- 1095-7138. ; 57:2, s. 1043-1067
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper studies stability properties of stochastic switched nonlinear time-delay systems. The stability analysis is based on two extensions of the Lyapunov-based method: the Krasovskii approach and the Razumikhin approach. In terms of the Krasovskii approach, Krasovskiitype stability conditions are derived based on Lyapunov-Krasovskii functions and average dwell-time condition. In terms of the Razumikhin approach, Razumikhin-type stability conditions are obtained via Lyapunov-Razumikhin functions, the small gain condition, and the fixed dwell-time condition. Furthermore, as a widespread phenomenon in switched systems, the asynchronous switching case is studied. Both Krasovskii-type and Razumikhin-type stability conditions are established for the asynchronous switching case. Finally, the developed results are illustrated via two examples from the mechanical rotational cutting process and networked switched control systems.
  •  
47.
  • Ringh, Axel, et al. (författare)
  • MULTIDIMENSIONAL RATIONAL COVARIANCE EXTENSION WITH APPLICATIONS TO SPECTRAL ESTIMATION AND IMAGE COMPRESSION
  • 2016
  • Ingår i: SIAM Journal of Control and Optimization. - : SIAM PUBLICATIONS. - 0363-0129 .- 1095-7138. ; 54:4, s. 1950-1982
  • Tidskriftsartikel (refereegranskat)abstract
    • The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental theoretical questions. In fact, this inverse problem is a key component in many identification and signal processing techniques and plays a fundamental role in prediction, analysis, and modeling of systems and signals. It is well known that the RCEP can be reformulated as a (truncated) trigonometric moment problem subject to a rationality condition. In this paper we consider the more general multidimensional trigonometric moment problem with a similar rationality constraint. This generalization creates many interesting new mathematical questions and also provides new insights into the original one-dimensional problem. A key concept in this approach is the complete smooth parameterization of all solutions, allowing solutions to be tuned to satisfy additional design specifications without violating the complexity constraints. As an illustration of the potential of this approach we apply our results to multidimensional spectral estimation and image compression. This is just a first step in this direction, and we expect that more elaborate tuning strategies will enhance our procedures in the future.
  •  
48.
  • Ringh, Axel, et al. (författare)
  • Multidimensional rational covariance extension with approximate covariance matching
  • 2018
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics Publications. - 0363-0129 .- 1095-7138. ; 56:2, s. 913-944
  • Tidskriftsartikel (refereegranskat)abstract
    • In our companion paper [A. Ringh, J. Karlsson, and A. Lindquist, SIAM T. Control Opton., 54 (2016), pp. 1950-1982] we discussed the multidimensional rational covariance extension problem (RCEP), which has important applications in image processing and spectral estimation in radar, sonar, and medical imaging. This is an inverse problem where a power spectrum with a rational absolutely continuous part is reconstructed from a finite set of moments. However, in most applications these moments are determined from observed data and are therefore only approximate, and the RCEP may not have a solution. In this paper we extend the results of our companion paper to handle approximate covariance matching. We consider two problems, one with a soft constraint and the other one with a hard constraint, and show that they are connected via a homeomorphism. We also demonstrate that the problems are well-posed and illustrate the theory by examples in spectral estimation and texture generation.
  •  
49.
  • Shi, Guodong, et al. (författare)
  • NETWORK SYNCHRONIZATION WITH CONVEXITY
  • 2015
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial and Applied Mathematics. - 0363-0129 .- 1095-7138. ; 53:6, s. 3562-3583
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we establish a few new synchronization conditions for complex networks with nonlinear and nonidentical self-dynamics with switching directed communication graphs. In light of the recent works on distributed subgradient methods, we impose integral convexity for the nonlinear node self-dynamics in the sense that the self-dynamics of a given node is the gradient of some concave function corresponding to that node. The node couplings are assumed to be linear but with switching directed communication graphs. Several sufficient and/or necessary conditions are established for exact or approximate synchronization over the considered complex networks. These results show when and how nonlinear node self-dynamics may cooperate with the linear diffusive coupling, which eventually leads to network synchronization conditions under relaxed connectivity requirements.
  •  
50.
  • Shi, Guodong, et al. (författare)
  • Robust Consensus For Continuous-Time Multiagent Dynamics
  • 2013
  • Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:5, s. 3673-3691
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to L-infinity and L-1 norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions. The results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance. The epsilon-convergence time is obtained for the consensus computation on directed and K-bidirectional graphs.
  •  
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