Deterministic learning from ISS-modular adaptive NN control of nonlinear strict-feedback systems

Abstract

This paper studies deterministic learning from adaptive neural control for a class of strict-feedback nonlinear systems with unknown affine terms. Firstly, an ISS-modular approach is presented to ensure uniformly ultimate boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. The proposed ISS-modular approach avoids the possible control singularity without the restriction of the derivative of affine terms. Secondly, it will be shown the proposed stable ISS-modular adaptive neural controller is able to learn closed-loop system dynamics. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using previous methods. To overcome these difficulties, the stable closed-loop system in control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation (PE) condition for radial basis function (RBF) neural networks (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals, and a learning ability is implemented during a closed-loop feedback control process. The learned knowledge can be reused in the same or similar control tasks, and avoid the tremendous repeated training process of NNs.