IEEE Access (Jan 2022)
Robust <italic>H<sub>∞</sub></italic> Observer-Based Reference Tracking Control Design of Nonlinear Stochastic Systems: HJIE-Embedded Deep Learning Approach
Abstract
The robust $H_{\infty }$ observer-based reference tracking control design of nonlinear stochastic systems with external disturbance and measurement noise is always a very complicated and difficult problem in the control field. It needs to solve a very difficult control-observer-coupled Hamilton Jacobi Isaacs equation (HJIE) for nonlinear observer and controller in the design procedure. At present, there exists no analytic and numerical way for solving this control-observer-coupled HJIE. A novel HJIE-embedded deep learning approach is proposed as a co-design of deep learning algorithm and $H_{\infty }$ observer-based tracking control scheme to directly solve the nonlinear partial differential control-observer-coupled HJIE of $H_{\infty }$ observer-based reference tracking control design problem of nonlinear stochastic systems. In the off-line training phase, state estimation error and tracking error are inputed to HJIE-embedded deep neural network (DNN) to output the solution of HJIE. If not, the learning error of HJIE is fedback to train DNN to solve HJIE for $H_{\infty }$ tracking control law, observer gain as well as the worst-case external disturbance and measurement noise, which will be sent back to nonlinear stochastic system model to replace the external disturbance and measurement noise and estimation error signal for next step training. The proposed DNN-embedded $H_{\infty }$ observer-based reference tracking scheme can achieve the theoretical $H_{\infty }$ observer-based reference tracking control strategy as the deep learning algorithm converges. If free of external disturbance and measurement noise, the proposed DNN-based $H_{\infty }$ observer-based reference tracking control scheme can approach to the stochastically asymptotical state estimation and reference tracking simultaneously. Finally, a design example of $H_{\infty }$ observer-based reference tracking control for quadrotor UAV system with external disturbance and output measurement noise is provided to illustrate the design procedure and to validate the state estimation and reference tracking performance simultaneously of the proposed HJIE-embedded $H_{\infty }$ DNN-based observer-based reference tracking control scheme of nonlinear stochastic systems.
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