Switching Adaptive Feedback Control For Several Classes Of Uncertain Nonlinear Systems

Feedback control for uncertain nonlinear systems has become a hot research issue in control theory,which can be used for aerospace,electricity,petrochemical industry,robotics and other fields.On one hand,unlike linear systems,nonlin-ear systems possess essentially nonlinear phenomena,such as finite escape time,multiple isolated equilibria,chaos and so on.Besides,the definitions of control-lability,observability and stabilizability of nonlinear systems are fundamentally different from those of linear cases.For example,controllability implies feedback stabilizability for linear systems,which,however,is not valid for nonlinear ones.On the other hand,the presence of serious uncertainties in the systems means that certain deficiencies of the existing measurement/modeling methods would be admitted,and the pressure from fully modeling and accurate measurement could be reduced.Furthermore,with the deepening of understanding and remaking the world,new uncertainty types constantly emerge,which makes it urgent to develop new design strategies to obtain a feedback control/feedback compensate strategy with wide applicability and strong fault tolerance.Therefore,it is of great significance to study feedback control of uncertain nonlinear systems.This paper is devoted to the global feedback control of several classes of uncer-tain nonlinear systems.Multiple serious uncertainties,such as unknown control directions,unknown powers,non-parametric uncertainties are allowed in the con-sidered systems,which make the existing schemes no longer applicable.By comb-ing the traditional nonlinear control design methods(e.g.,backstepping,adding a power integrator,the domination and output-feedback design methods)with the switching mechanism,this paper developed new switching adaptive feedback control strategies,and respectively presented feedback stable controllers for these nonlinear systems.The research contents of this paper include the following four aspects:(?)Switching adaptive output-feedback control for nonlinear systems with unknown relative degreeThis part is Chapter 3 of this paper,and addrsses the switching adaptive control via output-feedback for a class of nonlinear systems with unknown relative degree,dynamics uncertainties,unknown control directions and non-parametric nonlinearities.Noting that there is no known upper bound for the unknown relative degree,this renders us a research for a filter with varying dimension instead of the ones with over dimensions in the existing literature.To realize global stabilization,a switching adaptive output-feedback scheme is designed via switching mechanism together with varying-dimensional filter.In this scheme,two switching sequences are designed,which separately generate the gains and the varying dimensions of the filter.(?)Switching adaptive output-feedback control for power integrator systems with unknown control directionThis part is Chapter 4 of this paper,and considers the switching adaptive output-feedback control for power integrator systems with unknown control di-rection.The existence of inherent nonlinearities(i.e.,the systems with uncon-trollable and unobservable linearization)makes the strategy based on Nussbaum function rather difficult(even impossible)to compensate the unknown controldirection.To simultaneously dominate the inherent nonlinearities and unknown control direction,a switching adaptive output-feedback strategy is developed by combing the design of dynamic output-feedback controller and switching mecha-nism.First,a special case with known control direction is considered to obtain a basic controller structure and the dependence of the design parameters on the unknown control coefficient.Then,we investigate the case with unknown control direction by tuning the design parameters online based on a switching logic.(?)Switching adaptive control for the nonlinear systems with un-certainties from unknown system powersThis part is Chapter 5 of this paper,and considers the switching adaptive control for a class of nonlinear systems with unknown system powers,unknown control directions and non-parameterized system nonlinearities.Unlike the results in the existing literature,the powers in the studied system axe unknown and there is no known upper bound.By flexibly combing the domination,adding a power integrator and switching mechanism,we develop a controller with the design parameters which are tuned online based on a switching logic.The obtained controller would be operative as long as finite switchings happen and will not lead to Zeno phenomenon for the closed-loop system.(?)Switching adaptive control for more general nonlinear systems with uncertainties from unknown system powersThis part is Chapter 6 of this paper,and studies the switching adaptive con-trol of more general nonlinear systems with unknown system powers.Noting the restriction p1>p2>…? on the system powers in the last chapter,we are devoted to entirely remove it.We design a switching adaptive feedback controller with more design parameters which play a very distinct role in compensation.Because of the introduction of these parameters,new switching sequences with significantly different nature and another Lyapunov function in the analysis pro-cess axe developed,which bring more complexity in the theoretical analysis of global stabilization and highlight the contribution of this part.