Stochastic nonlinear minimax dynamic games with noisy measurements
AuthorCharalambous, Charalambos D.
SourceProceedings of the IEEE Conference on Decision and Control
Proceedings of the IEEE Conference on Decision and Control
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This paper is concerned with nonlinear stochastic minimax dynamic games which are subject to noisy measurements. The minimizing players are control inputs while the maximizing players are square-integrable stochastic processes. First, the minimax dynamic game is formulated using an information state, which satisfies a stochastic partial differential equation. Subsequently, a separation theorem is derived between the estimation and the control problems. Second, a certainty-equivalence principle is introduced along the lines of Whittle, by defining the future stress, the past stress, the minimum stress and the certainty-equivalence controller. Third, the separation theorem and the certainty-equivalence principle are applied to solve the linear-quadratic-Gaussian minimax game. The optimal control and the certainty-equivalence control are shown to be identical. The results of this paper generalize the L2-gain of deterministic systems to stochastic analogs; they are related to the controller design of stochastic risk-sensitive control and minimax deterministic dynamic games.
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