| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
| 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.
|
|
