Design Of Decentralized Robust Guaranteed Cost Controllers For A Class Of Nonlinear Composite Systems With Uncertainties

There existing no uniform effective research method so far,it is still an open problem synthesizing stable controllers for general nonlinear systems in control region.So are particularly nonlinear composite systems with uncertainties.It is well known that the decentralized control can turn the control problems of composite systems into those of some subsystems with lower dimensions,thus can obtain relatively simple controllers.In practical engineering,since errors in establishing models result inevitably in the existence of the system uncertainties,and composite systems have intrinsic high dimensions and complex structures,the expected control purpose is hardly achieved for the complex systems by using the traditional controllers.Thus research of the decentralized robust control method of nonlinear systems with uncertainties is of important significance.Presently there have been lots of theoretic achievements in the controller designing for composite systems, most of which focus on the system stability s tracking and the alike aspects, the nonlinear interconnected composite systems with their optimization index are seldom referred to. As to nonlinear uncertain composite systems,how to design controllers so as to make the systems controlled not only have robust performance, i.e. , the systems under control can maintain asymptotically stable for all the permitted uncertainties,but also have satisfactory performance index? This kind of problems is the so-called robust guaranteed cost control problems.Recent years,accompanied with the develpment obtained in robust control research of uncertain systems, a good deal of attention has been payed to the robust guaranteed cost control problems of uncertain systems.however,most researches in this aspect focus on single-unit, time-delay and discrete systems,the robust guaranteed cost control problems of uncertain nonlinear composite systems have not been well addressed yet.This paper discusses some preliminary research on this kind of robust guaranteed cost control problems for a class of uncertain nonlinear composite systems based on Lyapunov stability theory method. The main work shown in this paperis as follows:First, for a class of interconnected systems with uncertainties which can be decomposed into matched part and non-matched part,the nonlinear decentralized robust controllers are proposed, the controllers guarantee not only that the given quadratic cost function is bounded based on state errors but also that the close-loop systems controlled are asymptotically stable. Meanwhile, a sufficient condition for the existence of these controllers is proposed in this paper. Finally, a designing algorithm of the controllers is proposed via LMI.Second, for a class of composite systems with uncertainties which have the characteristic of constrained bound, the sufficient conditions for the existence of nonlinear decentralized robust guaranteed cost controllers are proposed respectively under the conditions that the interconnected items are weak and strong, the controllers guarantee not only that the given quadratic cost function has a certain upper bound but also that the close-loop systems are asymptotically stable. Finally, a designing algorithm of the controllers is proposed via LMI.Third, the simulations are given for some dynamical models of practical engineer systems based on the control algorithm proposed in this paper.