Adaptive Neural Network Based Control For A Class Of Nonlinear Systems With Time-delay

It is well known that the time-delays widely exist in the practical control systems. The existence of time-delays has a significant effect on system performance and may make the closed-loop system unstable. The research on control of these systems has important practical significance. There are two methods used to prove the stability of nonlinear system with time-delay. One is based on the Lyapunov-Krasovskii functional, and the other is on Lyapunov-Razumikhin function.In this thesis, the problem of adaptive neural network based control for a class of single-input and single-output (SISO) nonlinear systems with time-delay is studied. The considered systems are in form of low-triangular-structure. The designing of controller is based on the widely used Lyapunov-Krasovskii functional technique. The main results are listed below.I. A novel kind of Lyapunov-Krasovskii functional is constructed. The adaptive Radial Basis Function neural network (RBFNN) and Wavelet neural network (WNN) based controllers are designed for the considered systems. Based on the backstepping, a virtual control is designed at each step and the real control is designed at the last step. Using the Lyapunov-Krasovskii functional stability theorem, it is proved that the proposed controller guarantees the semi-globally uniformly ultimate boundedness of the closed-loop systems.II. Taking a three-order system for an example; an adaptive controller designing method is illustrated for a class of nonlinear system whose time-delays of states are different. The design of controller is based on the same backstepping technique. The virtual WNN based controllers are designed at each step and the adaptive controller is designed at the last step. The effect of different time-delay of each state is dealt with by the Lyapunov-Krasovskii functional chosen at each step. Using the Lyapunov-Krasovskii functional stability theorem, it is proved that the designed controller makes the closed-loop system semi-globally uniformly ultimate bounded. The designing method can be extended to the n-order nonlinear system with multi time-delays.For each designed controller, there is a simulation example provided to illustrate the validity of proposed designing method.