Studies On Robust Quadratic Optimal Control In LQ Significance And Robust Stable Bounds Of Uncertain Linear System

The analysis and synthesis based on the Lyapunov Theory for uncertain systems, which can deal with the Robust problem of the uncertain system conveniently . which ends in the asking and solving of Riccati equation finally, have therefore received people's great concern, And much research achievement has already been made. The Robust stability and its performance at the same time of uncertain systems and obtaining the maximum Robust stability bounds if possible have all the time been the problem that people hope to solve. The question is also the key problem that the actual project needs to solve urgently when used too. Although there has already been considerable achievement in rhp research of this question, the question needing studying further remains a lot. Though the document [1][2] having made the uncertain system not only robust stable but satisfying some certain performance index and besides, It obtains the helpful results of relatively maximum robust stability bounds ,but the results has certain conservative quality , which embodies mainly on the distribution of closed-loop roots. The document [3] though overcomes these quality of guarding at one, defines robust stability bounds of systems and obtains the system's maximum robust stability bounds subject to restriction of closed-loop roots, But the robust stability of the system has been destroyed, the originally desirable performance index was no longer satisfied . From this, this texts research robust quadratic optimal control and the LQ robust quadratic optimal control as well as its robust stability bounds for some uncertain linear systems Have solved this problem of Robust stability and its performance at the same time for the kind of uncertain linear systems better, At the same time defined its robust stability bounds. And under condition of system closed-loop roots, this robust stability bounds has been optimumed by utilizing the parameters of solution of LQ optimum control inverse problem, thus obtaining the optimum tobust stability bounds. The paper consists of four chapters. The LQ optimum control theory and some relevant concepts have been simply introduced in thefirst Chapter .In the second Chapter .the LQ optimum control inverse problem and parametric condition and parametric form of the inverse problem solution nave been introduced simply. Robust quadratic optimal control of a class of uncertain linear system have been studied, furthermore, the problem of Robust stability and its performance for this kind of control have been discussed con-cretely in the third chapter. In the forth Chapter ,0n the basis of denning Robust quadratic optimal control ,the definition of robust stability bounds has been given out, furthermore, under the condition of system closed-loop roots, translating the problem for maximizing the robust stability bounds to the optimization problem by utilizing parametric solution of the LQ optimum control inverse problem, thus obtaining the maximize of robust stability bounds through optimizing.