An Implicit Function-Based Adaptive Control Scheme for Noncanonical-Form Discrete-Time Neural-Network Systems

This article proposes a new implicit function-based adaptive control scheme for the discrete-time neural-network systems in a general noncanonical form. Feedback linearization for such systems leads to the output dynamics nonlinear dependence on the system states, the control input, and uncertain parameters, which leads to the nonlinear parametrization problem, the implicit relative degree problem, and the difficulty to specify an analytical adaptive controller. To address these problems, we first develop a new adaptive parameter estimation strategy to deal with all uncertain parameters, especially, those of nonlinearly parameterized forms, in the output dynamics. Then, we construct a key implicit function equation using available signals and parameter estimates. By solving the equation, a unique adaptive control law is derived to ensure asymptotic output tracking and closed-loop stability. Alternatively, we design an iterative solution-based adaptive control law which is easy to implement and ensure output tracking and closed-loop stability. The simulation study is given to demonstrate the design procedure and verify the effectiveness of the proposed adaptive control scheme.

I. Introduction

Neural network (NN) and T–S fuzzy systems have been widely used for adaptive control of the uncertain nonlinear systems. They are generically used to approximately parameterize the characterizable uncertainties existing in the controlled plants. Adaptive approximation control of uncertain nonlinear systems has been extensively and systematically studied and a large number of remarkable results have been reported in [1]–[20] [continuous-time (CT) case], in [21]–[27] [discrete-time (DT) case], and in [28]–[30] (stochastic case).