Finitely additive stochastic games with Borel measurable payoffs

Maitra, A.; Sudderth, William D.

doi:10.1007/s001820050071

Cited by 72 publications

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“…As observed in [8], the determinacy result for Blackwell games [20] implies determinacy of a large class of stochastic games. This abstract class includes the games studied in this paper, and thus we obtain the following:…”

Section: Resultsmentioning

confidence: 57%

“…By applying the result of [8], we obtain that SRTGs with DTA objectives have a value, i.e., sup σ inf π P σ,π = inf π sup σ P σ,π , where σ and π range over all strategies of player and player , and P σ,π is the probability of all plays satisfying a given DTA objective. This immediately raises the question whether the players have optimal strategies which guarantee the equilibrium value against every strategy of the opponent.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Brázdil

Krčál

Křetínský

et al. 2010

CONCUR 2010 - Concurrency Theory

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We consider two-player stochastic games over real-time probabilistic processes where the winning objective is specified by a timed automaton. The goal of player is to play in such a way that the play (a timed word) is accepted by the timed automaton with probability one. Player aims at the opposite. We prove that whenever player has a winning strategy, then she also has a strategy that can be specified by a timed automaton. The strategy automaton reads the history of a play, and the decisions taken by the strategy depend only on the region of the resulting configuration. We also give an exponential-time algorithm which computes a winning timed automaton strategy if it exists.

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Section: Resultsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Brázdil

Krčál

Křetínský

et al. 2010

CONCUR 2010 - Concurrency Theory

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show abstract

“…In particular, measurability properties, which are vital for ensuring that the probabilities of interest can be computed by a recursive procedure, are more difficult to establish in a stochastic game setting as compared with a single-player setting (Nowak, 1985). Thus, our dynamic programming arguments require the use of results from the analysis of zero-sum stochastic games (Shapley, 1953;Maitra and Parthasarathy, 1970;Kumar and Shiau, 1981;Nowak, 1985;Rieder, 1991;Maitra and Sudderth, 1998;Gonzalez-Trejo et al, 2002), with adjustments to account for the sum-multiplicative form of our utility function and the asymmetric information pattern in a max-min control problem.…”

Section: Overview and Related Workmentioning

confidence: 99%

Methods for Reachability-based Hybrid Controller Design

Ding¹

2012

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With the increasing complexity of systems found in practical applications, the problem of controller design is often approached in a hierarchical fashion, with discrete abstractions and design methods used to satisfy high level task specifications, and continuous abstractions and design techniques used to satisfy low level control objectives. Although such a separation allows the application of mature theoretical and computational tools from the realms of computer science and control theory, the task of ensuring desired closed-loop behaviors, which results from the composition between discrete and continuous designs, often requires costly and time consuming verification and validation. This problem becomes especially acute in safety-critical applications, in which design specifications are often subject to rigorous industry standards and government regulations. Hybrid systems, which feature state trajectories evolving on a combination of discrete and continuous state spaces, have been proposed as a possible approach to reconcile the analysis and design techniques from the discrete and continuous domains under a rigorous theoretical framework. However, designing controllers for general classes of hybrid systems is a highly nontrivial task, as such a design problem inherits both the difficulty of nonlinear control, as well as the range of theoretical and computational issues introduced by the consideration of discrete switching.This dissertation describes several efforts aimed towards the development of theoretical analysis tools and computational synthesis techniques to facilitate the systematic design of feedback control policies satisfying safety and target attainability specifications with respect to subclasses of hybrid system models. The main types of problems we consider are safety/invariance problems, which involve keeping the closed-loop state trajectory within a safe set in the hybrid state space, and reach-avoid problems, which involve driving the state trajectory into a target set subject to a safety constraint. These problems are addressed within the context of continuous time switched nonlinear systems and discrete time stochastic hybrid systems, as motivated by application scenarios arising in autonomous vehicle control and air traffic management.First, we provide several design techniques and synthesis algorithms for deterministic reachability problems formulated in the setting of switched nonlinear systems, with controlled switches between discrete modes, and bounded continuous disturbances. For scenarios in which the mode transitions proceed in a known sequence, a method is discussed for designing controllers to satisfy 1 sequential reachability specifications, consisting of a temporally ordered sequence of invariance and reach-avoid objectives. In particular, we use continuous time reachable sets to inform choices of feedback control policies within each discrete mode to satisfy both individual reachability objectives and compatibility conditions between successive modes. This technique is illus...

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“…A celebrated theorem due to Martin (1998) and Maitra & Sudderth (1998) (see also Maitra & Sudderth 2003) states that S2Gs with Borel objectives are determined:…”

Section: Given An Initial Vertexmentioning

confidence: 99%

Stochastic Multiplayer Games : Theory and Algorithms

Ummels¹

2010

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Finitely additive stochastic games with Borel measurable payoffs

Cited by 72 publications

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Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Methods for Reachability-based Hybrid Controller Design

Stochastic Multiplayer Games : Theory and Algorithms

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