Journal
AUTOMATICA
Volume 43, Issue 3, Pages 473-481Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2006.09.019
Keywords
adaptive critics; approximate dynamic programming; zero-sum games; policy iterations; H-infinity optimal control; Q-function; Q-learning; adaptive control
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In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x, u, w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft. (C) 2007 Elsevier Ltd. All rights reserved.
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