H_∞ Control For Nonlinear Systems Based On Neural Networks

Uncertainties inevitably and time-delay quite widely exist in all kinds of physi-cal, industrial and engineering systems, and they have a significant e?ect on systemperformance and make the closed-loop system unstable. It is di?cult for the moderncontrol theory, which is based on the exact mathematical model, to make control sys-tems satisfy the desired performance, therefor it is necessary to study. In this thesis,the problem of robust H_∞based on RBF neural network is studied for uncertain non-linear systems with time-delay, and a H_∞controller is designed. The main contentsare listed below:Chapter 1 discussed the basic knowledge of H_∞control theory and neural network.The point working was on the H_∞control based on state observer and the RBF neuralnetwork.H_∞control for a class of uncertainties system with time-delay was investigatedin Chapter 2. Based on the stability theory, by using lyapunov functional and linearmatrix inequality (LMI), the problem of robust H_∞control for time-delay system withuncertainties is investigated. The su?cient condition of H_∞properties for the solutionsto the problem is presented in terms of one LMI. And a state feedback controller isdesigned such that the resulting closed-loop system is asymptotic stable and satisfiesH_∞performance.In Chapter 3, The problem of robust H_∞control for non-a?ne nonlinear systemwith time-delay based on RBF neural networks was investigated. A controller wasdesigned such that the resulting closed-loop system was asymptotic stable and thee?ect of the disturbance on system attenuated to a prescribed level. Firstly, by usingimplicit function theorem, Taylor's formula and mean theorem, the form of the non- a?ne nonlinear system is transformed into the form of a?ne nonlinear systems. Thecontroller consists of an equivalent controller and an H_∞controller. Finally, theoreticalanalysis demonstrates the e?ectiveness of the approach.Based on RBF neural networks , the problem of robust H_∞control for uncer-tain multiple-input multiple-output nonlinear system with time-delay was studied inChapter 4. For a class of unknown external disturbances and internal uncertaintiesof multiple-input multiple-output delay systems, reducing the control to the interfer-ence requirements, based on neural network and interference state observer, a Robusttracking control method is proposed. The controller ensures that all signals uniformlyultimately boundedness and H_∞Performance.And the last ,Chapter 5 is a brief summary and the prospect of this paper.