Model-free finite-horizon optimal control of discrete-time two-player zero-sum games

Abstract

Conventionally, as the system dynamics is known, the finite-horizon optimal control of zero-sum games relies on solving the time-varying Riccati equations. In this paper, with unknown system dynamics being considered, a Q-function-based finite-horizon control method is introduced to approximate the solutions of the time-varying Riccati equations. First, a time-varying Q-function explicitly dependent on the time-varying control and disturbance is defined. Then the defined time-varying Q-function is utilised to represent the time-varying control and disturbance which are equivalent to the solutions of the time-varying Riccati equations by relaxing the system dynamics. Finally, a model-free method is introduced to approximate the defined time-varying Q-function. Simulation studies are conducted to demonstrate the validity of the developed method.