Robust Invariance Switching Control For Nonlinear Cascade Systems

A nonlinear cascade system consists of two subsystems in cascade structures, whose control enters only one subsystem and properties of the other can be changed by the interconnection which may act either as a control input or as an external disturbance.As many systems with reduced relative degree can be transformed into nonlinear cascade systems, much research attention has been focused on such systems. Invariance control for nonlinear cascade systems can provide theoretical methods and practical support. However, systems in practice have some disturbances and parameters uncertainties because of model errors, measure errors and approximate linearization. Therefore, it is of great significance in both engineering applications and theoretical development to study robust invariance control of nonlinear cascade systems.In additions, a hidden danger in the cascade structure is the intricate peaking phenomenon. Little change on feedback gains may cause explosive forms of instability in some cases. Switching technique may help to overcome the peaking obstacle.In this thesis, we mainly deal with robust invariance control of nonlinear cascade systems by switching. The contents of this paper are as follows.Firstly, related knowledge of nonlinear cascade systems, invariance control, switching control and passivity, etc. is introduced.Secondly, robust invariance switching control problem of a class of nonlinear cascade systems with structural uncertainties is studied. By using methods of passivity and switching control, the linear subsystem is transformed into a robust strictly passive system and it is asymptotically stable independent of the switching policy. After designing invariance region and invariance function, the invariant control is implemented. Under the assumption of stable zero dynamics, the whole system is semi-global asymptotically stable (Semi-GAS).Thirdly, the above-mentioned result is extended to multi-input case. That is, robust invariance switching control of a class of multi-input nonlinear cascade systems...