| In this thesis, we investigate the global robust output regulation problem for nonlinear systems subject to time-varying or nonlinear exosystems.;Output regulation problem, also known as servomechanism problem, is one of the central topics in control theory. The control objective is to design a feedback control law for the given plant so as to achieve asymptotic tracking for a class of reference signals and asymptotic rejection for a class of disturbance signals while maintaining the stability of closed-loop system. The reference or the disturbance signals are assumed to be generated from a dynamical system called the exosystem. Normally, the exosystem is a linear autonomous system, e.g. a harmonic oscillator, and the exogenous signals represent step or ramp signals, or sinusoidal signals contains finite number of harmonics. The extensions of the exosystem, from linear to nonlinear, autonomous to non-autonomous, significantly enlarge the categories of the exogenous signals, and more importantly, such extensions motivate the development of the output regulation theory in both scientific research and practical application.;Paying special attention to the appearance of time-varying or nonlinear exosystems, our research is mainly conducted under the general framework for tackling the output regulation problem. In general, first we convert the output regulation problem of the original plant into the stabilization problem of the augmented system which is composed of the plant and the designed internal model. Second, we achieve the global stabilization of the augmented system by robust and adaptive control approaches, according to both parameter uncertainty and dynamic uncertainty in either plant or the exosystem.;One of the crucial issues in output regulation problem is the design of the appropriate internal model. Internal model is a dynamical compensator which possesses an essential ability of generating all possible steady-state input information asymptotically, and it should not only lead to a well-defined augmented system but also ensure the stabilizability of the augmented system. Besides, stabilization techniques for the augmented system should also be carefully chosen to meet the needs in different scenarios, e.g. the time-varying settings. Efforts are put on both sides throughout the thesis.;The main contributions of the thesis are outlined as follows. 1. A framework for handling the robust output regulation problem for general timevarying nonlinear systems subject to time-varying exosystem is proposed. Especially, certain existence conditions of a time-varying internal model is given, and problem conversion can be achieved. As an application of this framework, we give the solvability conditions of the output regulation problem for the time-varying nonlinear systems in output feedback form. Further, when parameter uncertainties occurred in the time-varying exosystem, we solve the corresponding adaptive robust output regulation problem resorting to some adaptive control methods. These results can also be applied to the time-varying nonlinear systems in lower triangular form. 2. The global robust output regulation problem for nonlinear systems subject to nonlinear exosystem is considered. A new class of internal models is introduced which relaxes the existence conditions of the former one. Also, this class of internal models has the merit that it is zero input globally asymptotically stable which greatly facilitates the global stabilization of the augmented system. Compared with the existing results, the new method solves the global robust output regulation problem without restrictions on the initial conditions or trajectory bounds of the exosystems, and the bound of the parameter uncertainties of the plant is not necessarily known. Moreover, utilizing the Nussbaum gain technique, the unknown control direction case can also be handled by modifying the control law. 3. The theoretical results have been applied to several practical control problems, such as the global disturbance rejection problem for FitzHugh-Nagumo model with Mathieu equation, the synchoniztion of periodically-forced pendulum with Rayleigh equation, etc. |
