Robust Adaptive Output Regulation Of Minimum-phase Uncertain Nonlinear Systems

The complexities and diversities nonlinear phenomena reveal are neither explained by linear system theory nor possibly characterized by unified theory. It is therefore of interest for most of the researchers in nonlinear control literature to delineate classes of nonlinear systems for which certain of analysis and design methods are readily proposed to handle the systems dynamics. The methods and results generally confined to partial nonlinear systems make considerable progress in nonlinear control theory.Uncertainties exist in all practical systems, which possibly arise from modelling simplication, modelling error, external disturbance and measurement noise. Handling over the uncertainties in nonlinear control theory is always the interesting but difficult task. The control law can not achieve the expected performance in real control systems without compensating the uncertainty factors appropriately.The dissertation addresses robust output regulation problem for minimum-phase uncertain nonlinear systems, which is to design a feedback control law to achieve tracking for a class of reference input and/or rejecting for a class of disturbances while maintaining close-loop system overall signals uniform ultimate boundedness. In this formulation, the reference input and the unexpected disturbance, referred to "exogenous signals", are generated by a linear and neutrally stable autonomous differential equation which is called the exosystem. The feedback control law, or alternatively regulator which is generally based on the combination of the internal model and the stabilizer, is required to preserve the expected control performance in the presence of uncertainties contained by both the controlled plant and the exosystem. The study of integrating regulator theory and robust adaptive stabilization techniques and extending the regulator theory in uncertain nonlinear systems is emphasized in this dissertation. An internal model design method is proposed for a class of uncertain output feedback nonlinear system and lower-triangular nonlinear systems. We use the exosystem information and the stabilizing input items designed in stabilizing process to construct the internal model and finally present a feedback control law with the immersion of robust stabilizing techniques. When the exosystem contains uncertain parameters, we can also construct the adaptive law to estimate the unknown frequencies of exosystem and therefore completely compensate the unexpected disturbance.On the other hand, we introduce state observer to solve output feedback output regulation problem and attempt to probe into reducing the coupling of observer design, internal design and stabilizing design.The chapters of the thesis are organized as follows:In chapter 1, we introduce the background of this topic and current research situation followed by motivations, and present system models to be addressed and the main contributions of this dissertation briefly.Chapter 2 reviews some relevant fundamental concepts and main theory including stability, center manifold theory, immersion, high-gain observer and basic knowledge of system output regulation theory.Chapter 3 gives the forms of output feedback nonlinear system, and design state feedback regulator when the unknown nonlinearities are vanishing at the system origin and output feedback regulator when they are non-vanishing separately. The uncertain items are supposed to be bounded by a known smooth function. In the design process, we introduce a new method of constructing internal model such that the regulator obtained can compensate the exogenous unexpected disturbance while maintaining close-loop ultimate boundedness stability in the presence of system uncertainties.Chapter 4 extends the internal model design method described in last chapter to a class of uncertain nonlinear low-triangular systems containing unknown parameters, unknown nonlinearities and unmodeled dynamics and studies robust output regulation problem using state feedback and output feedback. When addressing design of output feedback regulator, we introduce classic state observer and dynamic gain observer based on the different model form to estimate system state, and propose the feedback control law with combination of internal model to achieve control objects.In Chapter 5, we firstly investigates robust output regulation problem of nonlinear low-triangular systems driven by uncertain exosystem. A new adaptive law is presented to estimate the unknown frequencies of exosystem in the regulator design. Then, we address the adaptive disturbance rejection problem for a class of single input strict-feedback nonlinear system subject to uncertain nonlinearity and unknown sinusoidal wave disturbance. The uncertain nonlinearity is supposed to satisfy the matching condition. We construct an adaptive internal model and redesign the system using information of Lyapunov function of the nominal systems to achieve the disturbance rejection in the presence of system uncertain nonlinearity.In chapter 6, we summarize the dissertation and discuss open problems for future research.