Echo State Network-Based Robust Tracking Control for Unknown Constrained Nonlinear Systems by Using Integral Reinforcement Learning

Abstract

It is necessary to consider the robustness in the tracking problem, which can effectively suppress the external disturbance to ensure the tracking performance. Different from previous tracking control methods, considering the robustness, completely unknown nonlinear system dynamics and constrained controller, we propose a data-based echo state network (ESN) approximated algorithm for a class of robust tracking problems. First, the robust tracking control problem (RTCP) is transformed into the optimal control problem of the according nominal system by designing a elaborate value function. To obtain the optimal control policy, we have to solve a Hamilton-Jacobi-Bellman equation (HJBE) about the augmented nominal system. It is well-known that modelling the accurate dynamics for the practical engineering applications is usually difficult, so the model-free integral reinforcement learning (IRL) algorithm is used to learn the optimal control policy and performance function simultaneously by only using systems data. In this IRL algorithm, a reservoir computing based ESN is used to approximate the performance function and control input. Contrast to other neural networks, ESN need not consider the choice of activation function, which can greatly reduce the difficulty and effort of neural network structure design. The output weights of the ESNs are iteratively updated towards the optimal ones by using least square algorithm and the pre-collected off-line system data. Then, using the converged output weights and ESNs, the tracking control input can be derived without knowing any system dynamic information. Finally, we demonstrate that the given system can be controlled to track the desired trajectory well under the proposed method by using two simulation examples.

Keywords

• Adaptive dynamic programming (ADP)
• echo state network (ESN)
• integral reinforcement learning (IRL)
• robust control
• tracking control