Neural Learning Control for State Constrained Strict-Feedback Systems: A State Predictor Method

Abstract

This paper concentrates on the neural learning control (NLC) problem for strict-feedback nonlinear systems (SFNSs) despite the presence of time-varying state constraints. A constraint-free system is obtained from the original constrained system through the application of a nonlinear transformed function (NTF). Based on the transformed constraint-free system, a state predictor is constructed for each subsystem. Then, a decoupled neural network weight updating law is developed based on the prediction error instead of the popular used tracking error, which facilitates the convergence of neural weights. Furthermore, by combining the first-order filter and backstepping method, an adaptive neural controller is established to assure the predetermined state constraints. Moreover, different from conventional system decomposition strategy, an effective lemma is given to address the difficulty in verifying the recurrent property of neural inputs, thereby promoting exponential convergence of neural weights. In virtue of the converged neural weights, i.e., learned knowledge, an NLC scheme is constructed, which can not only guarantee the predetermined state constraints, but also upgrade control performance and moderate online computational burden. Finally, simulations are conducted to exhibit the validity and correctness of the presented method. Note to Practitioners—In this paper, we investigate the NLC problem for a kind of SFNSs with time-varying state constraints, and the considered system models have been diffusely applied in the engineering field, such as marine surface vessels, robotic manipulators and so on. Note that two scenarios are widespread in practical applications: 1) system states need to satisfy predetermined constraint conditions; 2) neural weights cannot converge exponentially. Therefore, an NTF is introduced to settle the state constraints problem. Subsequently, an effective neural network weight updating law based on the prediction error, along with a supporting lemma, is developed to facilitate the weights convergence. On that basis, an NLC strategy is proposed by combining the converged neural weights. Simulations show that the developed strategy can efficaciously upgrade control performance and save online computational resources, which has good application prospect.