Adaptive Critic Designs for Discrete-Time Zero-Sum Games With Application to $H_{\infty}$ Control
Asma Al-Tamimi, Murad Abu-Khalaf, Frank L. Lewis · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · 2007
In this correspondence, adaptive critic approximate dynamic programming designs are derived to solve the discrete-time zero-sum game in which the state and action spaces are continuous. This results in a forward-in-time reinforcement learning algorithm that converges to the Nash equilibrium of the corresponding zero-sum game. The results in this correspondence can be thought of as a way to solve the Riccati equation of the well-known discrete-time H(infinity) optimal control problem forward in time. Two schemes are presented, namely: 1) a heuristic dynamic programming and 2) a dual-heuristic dynamic programming, to solve for the value function and the costate of the game, respectively. An H(infinity) autopilot design for an F-16 aircraft is presented to illustrate the results.