Finite Horizon Stochastic Optimal Control of Nonlinear Two-Player Zero-Sum Games under Communication Constraint

In this paper, the finite horizon stochastic optimal control of nonlinear two-player zero-sum games, referred to as Nonlinear Networked Control Systems (NNCS) two-player zero-sum game, between control and disturbance input players in the presence of unknown system dynamics and a communication network with delays and packet losses is addressed by using neuro dynamic programming (NDP). The overall objective being to find the optimal control input while maximizing the disturbance attenuation. First, a novel online neural network (NN) identifier is introduced to estimate the unknown control and disturbance coefficient matrices which are needed in the generation of optimal control input. Then, the critic and two actor NNs have been introduced to learn the time-varying solution to the Hamilton-Jacobi-Isaacs (HJI) equation and determine the stochastic optimal control and disturbance policies in a forward-in-time manner. Eventually, with the proposed novel NN weight update laws, Lyapunov theory is utilized to demonstrate that all closed-loop signals and NN weights are uniformly ultimately bounded (UUB) during the finite horizon with ultimate bounds being a function of initial conditions and final time. Further, the approximated control input and disturbance signals tend close to the saddle-point equilibrium within finite-time. Simulation results are included.