| 1. |
- Bahlali, Seid, et al.
(författare)
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The relaxed stochastic maximum principle in singular optimal control of diffusions
- 2007
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 46:2, s. 427-444
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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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| 2. |
- Byrnes, Christopher I., et al.
(författare)
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IMPORTANT MOMENTS IN SYSTEMS AND CONTROL
- 2008
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 47:5, s. 2458-2469
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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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| 3. |
- Djehiche, Boualem, et al.
(författare)
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A FINITE HORIZON OPTIMAL MULTIPLE SWITCHING PROBLEM
- 2009
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 48:4, s. 2751-2770
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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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| 4. |
- Ekström, Erik, 1977-, et al.
(författare)
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Optimal stopping games for Markov processes
- 2008
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Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 47:2, s. 684-702
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Flordal, Hugo, 1977, et al.
(författare)
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Compositional Verification in Supervisory Control
- 2009
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Ingår i: SIAM Journal on Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 48:3, s. 1914-1938
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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.
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| 6. |
- Jönsson, Ulf T.
(författare)
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A SECTOR CONDITION FOR LIMIT CYCLE ROBUSTNESS
- 2008
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 47:6, s. 2745-2772
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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.
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| 7. |
- Jönsson, Ulf T.
(författare)
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A small-gain theory for limit cycles of systems on lure form
- 2005
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 44:3, s. 909-938
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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.
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| 8. |
- Prajna, Stephen, et al.
(författare)
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Convex programs for temporal verification of nonlinear dynamical systems
- 2007
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 1095-7138 .- 0363-0129. ; 46:3, s. 999-1021
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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.
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| 9. |
- Singh, S. S., et al.
(författare)
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Filters for Spatial Point Processes
- 2009
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Ingår i: SIAM Journal on Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 48:4, s. 2275-2295
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Tidskriftsartikel (refereegranskat)abstract
- We study the general problem of estimating a "hidden" point process X, given the realization of an "observed" point process Y (possibly defined in different spaces) with known joint distribution. We characterize the posterior distribution of X under marginal Poisson and Gauss-Poisson priors and when the transformation from X to Y includes thinning, displacement, and augmentation with extra points. These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of X considered are general enough for many target tracking applications.
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