Book ChapterDOI
H∞-Control of Markovian Jump Systems and Solutions to Associated Piecewise-Deterministic Differential Games
Zigang Pan,Tamer Basar +1 more
- pp 61-94
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TLDR
In this article, a class of linear-quadratic piecewise deterministic soft-constrained zero-sum differential games is formulated and solved, where the minimizing player has access to perfect or imperfect (continuous) state measurements.Abstract:
A class of linear-quadratic piecewise deterministic soft-constrained zero-sum differential games is formulated and solved, where the minimizing player has access to perfect or imperfect (continuous) state measurements. Such systems are also known as jump linear-quadratic systems, and the underlying game problem can also be viewed as an H∞ optimal control problem, where the system and cost matrices depend on the outcome of a Markov chain. Both finite- and infinite-horizon cases are considered, and a set of sufficient, as well as a set of necessary, conditions are obtained for the upper value of the game to be bounded. Policies for the minimizing player that achieve this upper value (which is zero) are piecewise linear on each sample path of the stochastic process, and are obtained from solutions of linearly coupled generalized Riccati equations. For the associated H∞-optimal control problem, these policies guarantee an L 2 gain type inequality on the closed-loop system.read more
Citations
More filters
Journal ArticleDOI
Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems
TL;DR: The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant Hinfin filter for systems where the jumping parameter is not accessible.
Journal ArticleDOI
A bounded real lemma for jump systems
Peter Seiler,Raja Sengupta +1 more
TL;DR: It is shown that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems and reduces to the standard necessary andsufficient condition for discrete-time systems.
Journal ArticleDOI
Decentralized control of power systems via robust control of uncertain Markov jump parameter systems
TL;DR: In this article, the authors considered the problem of decentralized control of interconnected power systems under large changes in real and reactive loads that cause large structural changes in the system model and provided necessary and sufficient conditions for the existence of a decentralized controller which stabilizes the overall system and guarantees its optimal robust performance.
Journal ArticleDOI
Decentralized robust control of uncertain Markov jump parameter systems via output feedback
Li Li,Valery Ugrinovskii +1 more
TL;DR: It is shown that the feasibility of a parametrized collection of mode-dependent coupled algebraic Riccati equations and inequalities are both sufficient and necessary for the existence of a robust decentralized switching controller.
Journal ArticleDOI
Brief paper: Design of H∞ filter for Markov jumping linear systems with non-accessible mode information
TL;DR: A new deterministic filter design procedure is proposed, which shows less conservatism than existing results and can be accomplished by solving a set of linear matrix inequalities (LMIs).
References
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Journal ArticleDOI
H/sup /spl infin//-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach
T. Basar,P. Bernhard +1 more
TL;DR: The authors believe that the H-infinity-optimal control theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs.
Book
Stochastic Stability and Control
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
Book
Markov Models & Optimization
TL;DR: In this article, the authors present a new approach to problems of evaluating and optimizing the performance of continuous-time stochastic systems, based on the use of a family of Markov processes called Piecewise-Deterministic Processes (PDPs) as a general class of stocha- system models.