Neura Neural Network Adaptive Control For Nonlinear Time-delay Systems

Since almost all the systems have nonlinear characteristics, at the same time,time-delay existing phenomenon widely. Time delay is often the root causes systemsinstability or performance deterioration. Control object's uncertainty and time-varyinghave been challenging problems facing to researchers. In this paper, a class ofnonlinear time delay systems controller is designed based on neural network adaptive.By using RBF neural network, adaptive control, Lyapunov stabilization, Younginequality, Error Filtering theory, implicit function theorem, Taylor's formula andmean theorem, and those theories are the basis to design and analysis the closed-loopcontrol systems. The main work of this paper as follows:The first chapter is introducing to the background of neural network and adaptivecontrol as well as basic knowledge.In chapter 2, an adaptive neural network control design approach is proposed fora class of uncertain non-affine nonlinear time-delay systems. By using implicitfunction theorem, Taylor's formula and mean theorem, the form of the non-affinenonlinear systems is transformed into the form of affine nonlinear systems. At thesame time, using the capability of neural networks to approach any nonlinear function,combining with Error Filtering theory, and then using the Young inequality to dealwith the time-delay. According to the Lyapunov theory, a sufficient condition for thestability of the nonlinear system is given. This control guarantees to convergence forthe tracking error; it indicates that the controller is effect.In the chapter3,based on the second chapter, the systems change into non-affinenonlinear time-delay systems with external disturbances, unpredictable state. By usingimplicit function theorem, Taylor's formula and mean theorem, the form of thenon-affine nonlinear systems is transformed into the form of affine nonlinearsystems．The controller designed to on tracking attenuate the effect of externaldisturbance and approximation errors of the neural networks. The unknowntime-delay is compensated by using appropriate Young inequality in the design, theweight update laws based on Lyapunov stability theory can guarantee the systemstability and asymptotic convergence of the tracking error to zero. Theoreticalanalysis and examples results demonstrate the effectiveness of the approach.In chapter 4, neural network-based robust adaptive control is investigated for aclass of nonlinear time-delay systems with unknown nonlinear function andunmodeled dynamics. Use the on-line and RBF neural networks to approximate theunknown nonlinear function and unmodeled dynamics. The unknown time-delay iscompensated by Young inequality. The design method does not require priorknowledge to unknown parameters. It is proved that the proposed control law, the closed-loop system is stable and the good transient tracking performance can beguaranteed while the tracking error, the control signal are all bounded in the presenceof the nonlinear time-delay systems with an unknown nonlinear function andunmodeled dynamics. Theoretical analysis and simulation results demonstrate theeffectiveness of the approach.At the last, chapter 5 is a brief summary and the prospect of this paper.