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

• Main Authors: Bor-Sen Chen, Min-Yen Lee, Tzu-Han Lin
• Format: Article
• Language: English
• Published: IEEE 2021-01-01
• Series: IEEE Access
• Subjects: Nonlinear time-varying dynamic system; nonlinear <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ stabilization and tracking control; Hamilton Jacobi Issac equation (HJIE); DNN-based <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ control design; unmanned aerial vehicle (UAV) tracking control
• Online Access: https://ieeexplore.ieee.org/document/9424550/

The main difficulty in the traditional nonlinear <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control scheme is proposed to be efficiently trained for nonlinear <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> stabilization and tracking control designs of nonlinear dynamic systems with the external disturbance. The proposed DNN-based <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control scheme can approach the theoretical result of <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> reference tracking control of nonlinear systems for more practical applications. Finally, two examples, including <inline-formula> <tex-math notation="LaTeX">$({i})$ </tex-math></inline-formula> an <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> stabilization of nonlinear time-varying system and <inline-formula> <tex-math notation="LaTeX">$(ii)$ </tex-math></inline-formula> an <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> unmanned aerial vehicle (UAV) reference tracking control system, are proposed to illustrate the design procedure and to demonstrate the effectiveness of our DNN-based <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> method.