Adaptive Neural Inverse Optimal Control for a Class of Strict Feedback Stochastic Nonlinear Systems

This study develops an adaptive neural inverse optimal control method for a class of stochastic nonlinear systems. Neural networks (NN) are used to approximate the unknown nonlinear functions. The designed inverse optimal control strategy avoids the objective of solving the Hamilton-Jacobi-Bellman (HJB) equation and devises an optimal controller, which is related to the meaningful cost functional. Based on adaptive backstepping algorithm and Lyapunov stability theory, it is proved that the proposed control strategy guarantees the asymptotic stability in probability of the control systems and solves the inverse optimal problem.