Adaptive Output Regulation of Nonlinear Systems and Its Applications

非線性系統的自適應輸出調節及其應用

Student thesis: Doctoral Thesis

View graph of relations

Author(s)

  • Meichen GUO

Detail(s)

Awarding Institution
Supervisor(s)
Award date18 Jan 2017

Link(s)

Abstract

In the past decades, output regulation has been an interesting and attractive topic in the control community. Studies on output regulation provide effective solutions to reference tracking and/or disturbance rejection problems for various systems. This thesis focuses on adaptive output regulation of several classes of uncertain nonlinear systems.

The objective of output regulation is to design a controller such that the closed-loop system is stable and the regulated error converges to zero. The reference and/or disturbance signal, described by the exogenous signal, is generated by an exosystem. A suitable internal model is developed so that the output regulation problem for the plant can be converted into a stabilization problem for an augmented system. This is the core idea of the framework for achieving nonlinear output regulation, and it provides an effective tool for solving a series of control problems. In particular, output regulation of uncertain nonlinear systems is a challenging and practical topic in theoretical study as well as industrial applications. Specifically, this thesis concentrates on global adaptive output regulation with uncertain plants and/or uncertain exosystems. In the first part of this thesis, we will investigate global output regulation of some classes of single nonlinear systems with unknown exosystem and unknown control direction. We will start our study from single nonlinear output feedback system, then move on to the more complicated single nonlinear lower triangular system. The main contributions of this part are summarized as follows:

1. The output regulation problem for single nonlinear output feedback system with unknown exosystem and unknown control direction is solved. To the best of our knowledge, there has been only a few existing results on output regulation for non-linear output feedback systems with both exosystem and control direction being unknown. The concurrence of the two unknown parameters makes it impossible to solve the concerned problem by simply combining the existing techniques for each unknown parameter. To overcome this difficulty, besides using the internal model principle and the Nussbaum gain technique, we develop a new estimator for the unknown parameters. Then, to find a proper update law for the estimator, a modified extended matching design method is proposed.

2. The output regulation problem for single nonlinear lower triangular system with unknown exosystem and unknown control direction is solved. We first consider the disturbance rejection problem for a class of nonlinear lower triangular systems. To the best of our knowledge, this problem has not been addressed in previous studies. Specifically, lower triangular systems with single and multiple unknown control directions, are studied respectively. We then consider an output regulation problem for single nonlinear lower triangular system with unknown exosystem and unknown control direction. This problem is more complex and challenging than disturbance rejection of nonlinear lower triangular systems and output regulation of nonlinear output feedback systems. To solve this problem, we adopt a novel internal model candidate, and then integrate it with the backstepping method and the Nussbaum gain technique. The results obtained contain some existing results as special cases.

The second part of this thesis addresses cooperative output regulation of some classes of nonlinear multi-agent systems. Cooperative output regulation provides an effective tool for solving various cooperative control problems for multi-agent systems, for example, leader-following consensus, formation and synchronization. In particular, cooperative control of nonlinear multi-agent systems with unknown control directions has attracted some attentions recently. It is noted that, the existing results were obtained under some restrictive assumptions such as identical unknown control directions, undirected communication graph, and the usage of some special Nussbaum type functions. In this part of the thesis, we intend to remove these assumptions and solve the cooperative output regulation problem under a more general scenario. The main contributions of this part of the thesis are described as follows:

1. The cooperative output regulation problems for some classes of nonlinear multiagent systems with unknown control directions are solved. A dynamic compensator based distributed control scheme is proposed. The advantages of the proposed control scheme include the following aspects. First, the control scheme can use any existing Nussbaum type functions to handle unknown control directions in multi-agent systems. Second, the control scheme allows agents to have non-identical unknown control directions and to use non-identical Nussbaum gains. Third, it is capable of handling multi-agent systems subject to general directed communication graphs. Last but not least, it solves the cooperative output regulation problem for more complex classes of nonlinear multi-agent systems having arbitrary and non-identical relative degrees. The results obtained in this part contain some existing results as special cases.

2. The cooperative output regulation problems for some classes of nonlinear multi-agent systems with unknown exosystem and unknown control directions are solved. To the best of our knowledge, there are very few results on cooperative control of nonlinear multi-agent systems with both exosystem and control directions being unknown. To extend our results in the previous part to a more general problem setting, we integrate the proposed dynamic compensator based distributed control scheme with some novel internal model candidates. As a result, the proposed controllers are able to handle the unknown parameters simultaneously and to solve the concerned problems.

Finally, to show the practical relevance of our work, applications to the ship course control problems are presented. The Norrbin nonlinear model for ships is a practical example of a nonlinear lower triangular system that may contain an unknown control direction. We formulate the ship course control problem into a nonlinear output regulation problem and use it to verify and analyze some of our proposed controllers. The main contribution of this part of the thesis is that the ship course control problems subject to uncertain reference and/or uncertain disturbance is solved. It also shows the effectiveness and performance of our proposed controllers. Moreover, compared with existing results on ship course control, our proposed control method can solve the problem when the desired course of the ship is a class of trajectories generated by an exosystem.