Adaptive robust control of the continuous-time two-input systems with unknown disturbance based on Q-function

Considering overshoot and chatter of the multi-input system with unknown interference, this paper studies the adaptive robust optimal controls of continuous-time two-input systems with an approximate dynamic programming (ADP) based Q-function scheme. A complex Hamilton-Jacobi-Issacs (HJI) equation is obtained with the two-input system and the zero-game theory, where a value function is constructed. Solving the HJI equation is a challenging task. Thus, an ADP-based Q-function with a neural network is constructed to learn the saddle point of the HJI equation. Simultaneously, an integral reinforcement signal of the critic networks is introduced such that the system drift and input dynamics in the HJI equation are relaxed when studying the saddle-point intractable solution. Then, the adaptive robust optimal actor and worst disturbance are approximated with another three networks. Finally, an F-16 aircraft plant is used to verify the proposed ADP-based Q-function.