Adaptive Critic-Based Optimal Control of Input-Constrained Stochastic Systems via Generalized Fuzzy Hyperbolic Models

This article investigates adaptive dynamic programming (ADP)-based optimal control issue of nonlinear stochastic systems with asymmetric input constraints. The solution starts with developing generalized fuzzy hyperbolic model (GFHM) in the stochastic system, which aims to approximate unknown nonlinear terms. By establishing a nonquadratic cost function, the constrained $H_{\infty }$ control problem is converted into zero-sum game and Hamilton–Jacobi–Isaacs equation (HJIE) is derived. To solve the HJIE, the ADP algorithm is developed by constructing a single-network adaptive critic framework. Assisted by GFHM, the updating process obviates the necessity for the dynamics of unknown nonlinear terms. Under the designed controller, the stability of the stochastic system is guaranteed by the Lyapunov method. Two illustrative examples validate the presented method.