LAUSR

The main difficulty in the traditional nonlinear $H_{\infty }$ control design lies in how to solve the nonlinear partial differential Hamilton-Jacobi-Isaacs equation (HJIE), especially for nonlinear time-varying systems. In this study, a novel HJIE-embedded DNN $H_{\infty }$ control scheme is proposed to be efficiently trained for nonlinear $H_{\infty }$ stabilization and tracking control designs of nonlinear dynamic systems with the external disturbance. The proposed DNN-based $H_{\infty }$ control approach not only capitalizes on the availability of theoretical partial differential HJIE but also reduces the amount of empirical data and the complexity to train HJIE-embedded DNN. We have shown that the proposed DNN-based $H_{\infty }$ control scheme can approach the theoretical result of $H_{\infty }$ robust control when the training error approaches zero and the asymptotic stability is also guaranteed if the nonlinear time-varying system is free of external disturbance. The proposed method could be easily extended to DNN-based $H_{\infty }$ reference tracking control of nonlinear systems for more practical applications. Finally, two examples, including $({i})$ an $H_{\infty }$ stabilization of nonlinear time-varying system and $(ii)$ an $H_{\infty }$ unmanned aerial vehicle (UAV) reference tracking control system, are proposed to illustrate the design procedure and to demonstrate the effectiveness of our DNN-based $H_{\infty }$ method.