Control Design For Some Classes Of Nonlinear Systems Based On Backstepping

In the recent several decades, it has developed greatly in control theory research andapplication of control design for nonlinear systems, but there exists no uniform effective researchmethod for the control design of nonlinear systems. Especially with the development oftechnology, many practical engineering systems show strong nonlinearities, and the systemsusually have the characteristics of higher order, complex structure, strict nonlinearity andinterconnection, thus in the control field it is a more difficult problem to design controllers forthese complex systems.Presently there have been lots of theoretic achievements in the control design for thosecomplex nonlinear control systems with especial structures, such as similar systems and stricttriangular in structure or called strict feedback systems. Especially for the strict triangular instructure, in the nineties of last century, Kokotovic P V and his cooperators proposedBackstepping method to design controller. This method has been used widely in the controllerdesign of nonlinear systems with strict triangular in structure directly or indirectly because of thecharacteristics of systematism and structured process. It is noted that the correspondingresearches almost aim to the entire control system that possess correspondingly accurate systemmodel. However, in the practical controlled system modeling, we often derive correspondinglyaccurate system mode of a sub-system but the entire system, so it is important to designcontroller for the entire system by using the known information of the sub-system.In the recent several years, robust adaptive control design of nonlinear systems based onBackstepping has became a highlight problem, but most researches in this aspect focus onsingle-unit, continuous and time-varying nonlinear systems, little refer to the uncertain nonlinearinterconnected systems, and so is the uncertain interconnected systems with nonlinear parameter.Decentralized control is attended greatly at all times, because it can turn the control problem ofinterconnected systems into those of some sub-systems with lower dimensions, thus this cansimplify the control design. So it is deserved to do some researches on robust decentralizedadaptive control design of the uncertain nonlinear interconnected systems with nonlinear parameter.This paper discusses some preliminary research on the control problems of the above twokinds of the nonlinear systems based on Lyapunov stability theory method and Backstepping.The main work is shown as follows:First, for a class of complex nonlinear systems with sub-system that has strict triangularstructure form, the controller of the sub-system is designed by using Backstepping method, thenthe controller is proposed for the entire systems according to the above controller of thesub-system, and it is proved that the controller makes the entire systems asymptotical stability.Second, for a class of the uncertain nonlinear interconnected systems with nonlinearparameter, under more intuitionistic and more common assumptions, the robust decentralizedcontroller and adaptive laws are proposed based on Backstepping, and it is proved that thecontroller and the adaptive laws make the states of systems controlled and parameter estimateerrors uniformly ultimately bounded.Third, the simulation of some examples shows the validity of control algorithm in this paper.