Adaptive Neural Network Control for Uncertain Nonlinear Systems with Asymptotic Stability Guarantees

A neuroadaptive control framework for the nonlinear uncertain dynamical systems is developed in this paper. The proposed framework is Lyapunov-Based and unlike standard neural network (NN) controllers guaranteeing ultimate bounded ness, the framework guarantees asymptotic stability of the closed-loop system The neuroadaptive controllers are constructed without requiring explicit knowledge of the system dynamics, a recurrent neural network (NN) is used to approximate the unknown nonlinear plant. To provide good accuracy in identification of unknown model parameters, an online adaptive law is proposed to adapt the consequent part of the NN. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

I. Introduction

One of the main motivation for developing neural networks (NN) adaptive control algorithms is their capability to approximate a large class of continuous nonlinear maps from the collective action of very simple, autonomous processing units that are connected in simple ways. These processing units involve a weighted interconnection of fundamental elements called neurons, which are functions consisting of a summing junction and a nonlinear operation involving an activation function. In addition, NN shave attracted attention due to their inherently parallel and highly redundant processing architecture that makes it possible to develop parallel weight update laws. This parallelism makes it possible to effectively update an NN online. Consequently, the use of the NNs for system identification and control of complex highly uncertain dynamical systems has become an active area of research [1]–[9]. Unlike adaptive controllers which guarantee asymptotic stability of the closed-loop system states associated with the system plant states, standard NN adaptive controllers guarantee ultimate boundedness of the closed-loop system states[10]. This fundamental difference between adaptive control and neuroadaptive control can be traced back to the modeling and treatment of the system uncertainties. In particular, adaptive control is based on constant, linearly parameterized system uncertainty models of a known structure but unknown variation, while neuroadaptive control is based on the universal function approximation property, wherein any continuous system uncertainty can be approximated arbitrarily closely on a compact set using an NN with appropriate weights.