DNN-Based H∞ Control Scheme of Nonlinear Time-Varying Dynamic Systems With External Disturbance and its Application to UAV Tracking Design

The main difficulty in the traditional nonlinear H
_∞
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
_∞
control scheme is proposed to be efficiently trained for nonlinear H
_∞
stabilization and tracking control designs of nonlinear dynamic systems with the external disturbance. The proposed DNN-based H
_∞
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
_∞
control scheme can approach the theoretical result of H
_∞
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
_∞
reference tracking control of nonlinear systems for more practical applications. Finally, two examples, including (i) an H
_∞
stabilization of nonlinear time-varying system and (ii) an H
_∞
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
_∞
method.