Control of a class of nonlinear discrete-time systems using multilayer neural networks

Abstract

A multilayer neural-network (NN) controller is designed to deliver a desired tracking performance for the control of a class of unknown nonlinear systems in discrete time where the system nonlinearities do not satisfy a matching condition. Using the Lyapunov approach, the uniform ultimate boundedness of the tracking error and the NN weight estimates are shown by using a novel weight updates. Further, a rigorous procedure is provided from this analysis to select the NN controller parameters. The resulting structure consists of several NN function approximation inner loops and an outer proportional derivative tracking loop. Simulation results are then carried out to justify the theoretical conclusions. The net result is the design and development of an NN controller for strict-feedback class of nonlinear discrete-time systems.

Globally stable adaptive robust tracking control using RBF neural networks as feedforward compensators

“…So far, much work has been done in this area. For example, adaptive neural network control for robotic systems [1][2][3][4]; adaptive backstepping neural (or fuzzy) control for lower-triangular-structured systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17]; neural network-based adaptive control for timedelay systems [18][19][20][21][22][23][24] or discrete-time systems [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], and so on.…”

Stable Adaptive Neural Network Control of Nonaffine Nonlinear Discrete-Time Systems and Application

“…For MIMO nonlinear discrete-time systems, the control problem becomes very difficult due to the difficulty in handling the coupling between different inputs, and only a few results are available. In [7], multilayer NN was used to control a special class of MIMO affine nonlinear discrete-time systems. Direct adaptive neural network control was presented in [8] for a class of MIMO NARMAX systems in affine form.…”

Experimental studies in nonlinear discrete-time adaptive prediction and control

“…Similar to the predictor, we define the error signal (28) where now (29) Finally, is defined as in (21). The direct adaptive control theorem using least squares is very similar to Theorem 1.…”

“…Reference [26] presents an adaptive control method for nonlinear discrete-time systems with input deadzone. In [27], [28] adaptive neural network controllers are presented for a class of single-input-single-output (SISO) strict-feedback discrete time nonlinear systems, and [29] considers the multiple-input-multiple-output (MIMO) case.…”