Global Robust Output Regulation for Nonlinear Output Feedback Systems and Its Applications.

摘要

The thesis is concerned with the global robust output regulation for nonlinear systems in the output feedback form by using output feedback control. For the nonlinear output feedback systems, we mainly study three typical output regulation problems. The first one is the output regulation problem with unknown control directions and input-to-state stable (ISS) inverse dynamics using a direct approach. The second one is the adaptive output regulation problem with an uncertain exosystem and ISS inverse dynamics. The third one is a case study on the solvability of the systems with integral input-to-state stable (iISS) inverse dynamics.;The nonlinear output regulation is a central control problem that involves nonlinear stabilization, tracking control and disturbance rejection as special cases. The control objective is to find a feedback controller to achieve asymptotic tracking and/or disturbance rejection while maintaining closed-loop stability. The output regulation study has experienced rapid developments in the past two decades or so. It is now well known that the problem can be systematically approached according to the general framework of tackling nonlinear output regulation that is composed of the following two steps. The first step is the problem conversion: from nonlinear output regulation to stabilization. The output regulation is generally more complicated than the stabilization problem. Therefore the problem conversion indeed reduces the complexity and makes it possible to be handled. In this step, the output regulation is converted into the stabilization of an augmented system consisting of the original plant and a suitable dynamic compensator called internal model. The second step is the stabilization of the augmented system whose solvability implies solvability of the output regulation problem.;In the past ten years or so, the output regulation of the strict output feedback systems has attracted a lot of attention. In contrast with the strict output feedback systems, the output feedback systems is more general since it not only involves the nonlinearity of the system output but also the unmodeled dynamics. Therefore, the usual design method is not applicable, which motivates us to develop some new methodology for the output regulation design of the output feedback systems.;The main results of the thesis are outlined as follows. i) A direct approach is proposed for the output regulation of the systems with ISS inverse dynamics and unknown control directions. The internal model is first designed for the control input. The output feedback control design is further achieved based on a type of partial state observer which is designed for the transformed augmented system. The Nussbaum function technique is successfully incorporated in the stabilization design to deal with the case of unknown control directions.;The result is applied to solve a tracking control problem associated with the well known Lorenz system and a class of generalized fourth-order Lorenz systems. By certain system decomposition, it is proved that the Lorenz system contains certain ISS inverse dynamics and the output feedback control is successfully realized.;ii) An adaptive output regulation design is proposed for the systems with ISS inverse dynamics and an uncertain exosystem. When the exosystem contains uncertain parameters, the direct approach can not be implemented any longer. To deal with this issue in the general case, by introducing an observer, we first derive an extended system composed of the plant and the observer. Then the output regulation problem of the extended system is solved. It is further shown that the unknown parameter vector of the exosystem can be exactly estimated if a controller containing a minimal internal model is employed.;The application of the result leads to the solution of several interesting control problems such as the global disturbance rejection of the FitzHugh-Nagumo (FHN) system and the robust output synchronization of the generalized third and fourth-order Lorenz system and the Harmonic system.;iii) A sufficient solvability condition of the global output regulation for the systems with iISS inverse dynamics is proposed. Since the concept of iISS is strictly weaker than the ISS one, the result allows us to handle a much larger class of nonlinear systems.;One of the motivations of the case study is to deal with the output regulation problem of a shunt-connected DC motor whose inverse dynamics is iISS but not ISS. As an illustration, a disturbance rejection problem of the shunt-connected DC motor is solved.