Optimal Robust Control of Electro-Hydraulic System Based on Hamilton–Jacobi–Bellman Solution With Backstepping Iteration

There exist hydraulic parametric uncertainty and unknown external load in electro-hydraulic system (EHS), which inevitably decline the tracking performance and the stability of the closed-loop system. In this study, an optimal robust controller (ORC) is presented to solve this problem. Different from the traditional backstepping control, the ORC constructs the Hamilton–Jacobi–Bellman (HJB) equation based on the tracking error model of EHS to optimize the performance cost function as well as derive the optimal control variable. Furthermore, a critical neural network is adopted to estimate the optimal control solution of HJB equation such that guarantee the system state error of EHS uniformly ultimate boundary. Since the model uncertainty is considered in the HJB solution, the ORC has satisfactory robustness by using the network weight updation rather than direct parametric estimation or disturbance observer. The effectiveness of the proposed controller is verified by comparative simulation and experimental results.