Robust optimal control of the multi-input systems with unknown disturbance based on adaptive integral reinforcement learning Q-function

Considering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous-time (CT) multi-input systems with an approximate dynamic programming (ADP) based Q-function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q-functions. First, multi-input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton-Jacobi-Issacs (HJI) equation is constructed with the multi-input system and the zero-sum-game-based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q-function. The neural network (NN) is applied to learn the solution of the transformed Q-functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q-function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle-point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed-loop stability of the multi-system with the proposed IRL Q-function scheme is analyzed. Finally, a two-engine driven F-16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q-function scheme.