CMAC neural networks-based adaptive control for discrete-time nonlinear systems with unmatched uncertainties by backstepping

This paper considers adaptive control for a class of SISO discrete-time nonlinear systems with unmatched uncertainties. The discrete-time nonlinear systems with unmatched uncertainties are firstly transformed into a class of new discrete-time nonlinear systems with matched uncertainties, and a CMAC neural network-based controller which linearizes the new discrete-time nonlinear systems is presented. Secondly, the states of the new discrete-time nonlinear systems are estimated using CMAC neural networks by backstepping. A stability proof is given in the sense of Lyapunov using the persistency of excitation (PE) condition. It is shown that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation example is also given.