Dynamic neural learning for state constrained strict-feedback systems based on state transformation method

This article studies the dynamic neural learning issue for strict-feedback nonlinear systems with full state constraints by utilizing the nonlinear transformed function (NTF) method. To handle the issue of state constraints control, a NTF is introduced to convert the original constrained states into the equivalent unconstrained ones. For the transformed system states, a stable adaptive neural control strategy is put forward in combination with the dynamic surface technology. Subsequently, a new lemma, instead of the traditional system decomposition method, is developed to simplify the recurrent verification process of neural network (NN) inputs. Such a new lemma promotes the validation of exponential convergence for NN weight estimates in a steady-state time, and the convergent weights are stored as the learned knowledge. Moreover, a novel corollary is given to verify that the unknown system dynamics under two cases with and without state constraints are almost the same during the steady-state control process, thereby indicating the learned dynamical knowledge from the case with state constraints is also suitable for the case without state constraints. For the two cases, by reusing the learned knowledge, a neural learning controller is established for the better control performance and less online calculations. Simulation studies testify the efficacy of the developed method.