Adaptive control of a class of nonlinear systems using neural networks

Layered neural networks are used in nonlinear adaptive control problems. Both the discrete-time case and the continuous-time case are considered. For the discrete-time case, the plant is an unknown SISO feedback-linearizable discrete-time system with general relative degree, represented by an input-output model; a state space model of the plant is obtained. This model is used to define the zero dynamics, which are assumed to be stable. 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. For the continuous-time case, we work on a SISO relative-degree-one system with zero dynamics, and on a MIMO general relative degree system without zero dynamics. The neural network is used to model the nonlinear functions of the continuous-time systems, instead of modeling the whole system as in the discrete-time case; and the control law for the continuous-time case does not involve an explicit system identification process, as appears in the discrete-time case. The convergence results obtained for both cases are regional in state space, yet local in parameter space