| 1. |
- Almér, Stefan, et al.
(författare)
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Dynamic Phasor Analysis Of Pulse-Modulated Systems
- 2012
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 50:3, s. 1110-1138
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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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| 2. |
- Cantoni, Michael, et al.
(författare)
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Robust Stability Analysis For Feedback Interconnections Of Time-Varying Linear Systems
- 2013
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:1, s. 353-379
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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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| 3. |
- Chasparis, Georgios, et al.
(författare)
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Aspiration Learning in Coordination Games
- 2013
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 51:1, s. 465-490
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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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| 4. |
- Como, Giacomo, et al.
(författare)
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Stability Analysis of Transportation Networks with Multiscale Driver Decisions
- 2013
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 51:1, s. 230-252
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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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| 5. |
- Curtain, Ruth, et al.
(författare)
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ON RICCATI EQUATIONS IN BANACH ALGEBRAS
- 2011
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 49:2, s. 464-475
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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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| 6. |
- Di Bernardo, Mario, et al.
(författare)
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Contraction analysis for a class of nondifferentiable systems with applications to stability and network synchronization
- 2014
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 52:5, s. 3203-3227
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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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| 7. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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Decentralized Disturbance Accommodation with Limited Plant Model Information
- 2013
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:2, s. 1543-1573
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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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| 8. |
- Feyzmahdavian, Hamid Reza, et al.
(författare)
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ASYMPTOTIC STABILITY AND DECAY RATES OF HOMOGENEOUS POSITIVE SYSTEMS WITH BOUNDED AND UNBOUNDED DELAYS
- 2014
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 52:4, s. 2623-2650
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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.
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| 9. |
- Jacob, Birgit, et al.
(författare)
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Applications of Laplace–Carleson embeddings to admissibility and controllability
- 2014
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 52:2, s. 1299-1313
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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.
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| 10. |
- Kristalny, Maxim, et al.
(författare)
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Input/Output Stabilization in the General Two-Sided Model Matching Setup
- 2012
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 50:3, s. 1413-1438
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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.
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