摘要
The main difficulty in the traditional nonlinear H&null control design lies in how to solve the nonlinear partial differential Hamilton Jacobi Issac equation (HJIE), especially for nonlinear time-varying systems. In this study, a novel HJIE-embedded DNN H&null control scheme is proposed to be efficiently trained for nonlinear H&null stabilization and tracking control designs of nonlinear dynamic systems with the external disturbance. The proposed DNN-based H&null 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&null control scheme can approach the theoretical result of H&null 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&null reference tracking control of nonlinear systems for more practical applications. Finally, two examples, including (i) an H&null stabilization of nonlinear time-varying system and (ii) an H&null 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&null method.