TY - JOUR

T1 - Adaptive Control of a Class of Nonlinear Discrete-Time Systems Using Neural Networks

AU - Chen, Fu-Chuang

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Layered neural networks are used in a nonlinear self-tuning adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. To derive the linearizing-stabilizing feedback control, a (possibly nonminimal) state-space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable, i.e., the system is assumed to be minimum phase. A linearizing feedback control is derived in terms of some unknown nonlinear functions. A layered neural network is used to model the unknown system and generate the feedback control. Based on the error between the plant output and the model output, the weights of the neural network are updated. A local convergence result is given. The result says that, for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball, whose size is determined by a dead-zone nonlinearity. Computer simulations verify the theoretical result.

AB - Layered neural networks are used in a nonlinear self-tuning adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. To derive the linearizing-stabilizing feedback control, a (possibly nonminimal) state-space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable, i.e., the system is assumed to be minimum phase. A linearizing feedback control is derived in terms of some unknown nonlinear functions. A layered neural network is used to model the unknown system and generate the feedback control. Based on the error between the plant output and the model output, the weights of the neural network are updated. A local convergence result is given. The result says that, for any bounded initial conditions of the plant, if the neural network model contains enough number of nonlinear hidden neurons and if the initial guess of the network weights is sufficiently close to the correct weights, then the tracking error between the plant output and the reference command will converge to a bounded ball, whose size is determined by a dead-zone nonlinearity. Computer simulations verify the theoretical result.

UR - http://www.scopus.com/inward/record.url?scp=0029308580&partnerID=8YFLogxK

U2 - 10.1109/9.384214

DO - 10.1109/9.384214

M3 - Article

AN - SCOPUS:0029308580

VL - 40

SP - 791

EP - 801

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 5

ER -