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.
Research supported in part by the U.S. Department of Energy under Grant DE-FG- 02-88-ER-13939, and in part by the National Science Foundation under Grant NSF ECS 93-12807 and the Joint Services Electronics Program through the University of Illinois.
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Pan, Z., Başar, T. (1995). H∞-Control of Markovian Jump Systems and Solutions to Associated Piecewise-Deterministic Differential Games. In: Olsder, G.J. (eds) New Trends in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 3. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4274-1_4
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DOI: https://doi.org/10.1007/978-1-4612-4274-1_4
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