Global Robust Adaptive Output Regulation Of Nonlinear Systems And Its Applications

A central control problem in the control community is to design a feedback con-troller to achieve asymptotic tracking for a class of reference inputs and/or rejecting for a class of disturbances while maintaining closed-loop stability. If the reference inputs and the unexpected disturbances are both generated by the same linear autonomous dif-ferential equation which is called as the exosystem, then the control problem is called as the servomechanism problem or the output regulation problem. In recent years, numerous scholars do intensive research on the output regulation problem, especially on the nonlinear output regulation problem. The output regulation problem was first studied for the class of certain linear systems, and then extended to robust output reg-ulation problem of some uncertain nonlinear systems, further extended to robust out-put regulation problem with unknown exogenous signals(the reference inputs and the disturbances). Nevertheless, when it comes to the robust output regulation problem, most work is relevant with the case where the exosystem is linear, thus the exogenous signals that can be handled are a combination of finitely many step functions and si-nusoidal functions, while for the case where the exosystem is nonlinear, the existing work has not received enough attention. While Oscillatory disturbances produced by nonlinear exosystems can easily affect the performance of many engineering systems, such as turbo-machines, motors/generators, flexible structures, and communication cir-cuits. The system's output response of such oscillatory input signals is referred to as nonharmoniously forced vibration, which may cause undesirable effects, e.g., noise, fatigue, precision and durability reduction, unreliability, and unscheduled shutdowns. Reduction/Cancellation of the unwanted vibration is very important for the system's stabilization.This thesis focus on global disturbance rejection problem and global robust output regulation problem of nonlinear systems with the case of nonlinear exosystems. This thesis includes two parts. The first part focuses on establishing the internal model to study the theoretic discussion of the nonlinear robust output regulation problem with nonlinear exosystems, while the second part further studies the applications of the out-put regulation problem. The main achievements contained in this dissertation are as follows:In chapter 1, the research status and advances of output regulation problem have been summarized, analyzed and reviewed, and the main research contents to be solved have been pointed out.In chapter 2, we introduce some relevant fundamental concepts and main theory including the concepts of Lyapunov stability and Lyapunov stability theorems, some adaptive control design tools, basic work of nonlinear output regulation theory, the concept and some properties of immersion.In chapter 3, the global disturbance rejection problem of a general nonlinear sys-tems with nonlinear exosystem is researched. The new nonlinear internal model and state feedback regulator are designed, which ensure that the system's state variables can asymptotically converge to zero. The example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from an uncertain Van der Pol circuit, which is verified the robustness of the proposed controller. Es-pecially, we first design a nonlinear internal model and a state feedback regulator for the Duffing equation, and the numerical simulation showed that the proposed distur-bance rejection algorithm can completely reject the chaotic signals generated from the Duffing equation.In chapter 4, based on Chen and Huang's self-contained concepts of steady-state generator and internal model, we further extend the Chen and Huang's work in the nonlinear exosystems to the global disturbance rejection problem for a class of affine nonlinear system. The new nonlinear internal model and state feedback regulator are designed, which ensure that the system's state variables can asymptotically converge to zero. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol oscillator. Simulation results show the efficacy of the proposed rejection algorithm.In chapter 5, the global disturbance rejection problem of a class of uncertain out- put feedback systems with nonlinear exosystems is considered. The new nonlinear internal model and adaptive output feedback regulator are proposed to ensure that the system's output variables can asymptotically converge to zero. And new adaptive laws are designed to deal with the linearly parameterized unknown parameter in the plant. The example is shown that the proposed algorithm can completely reject the nonhar-monic periodic disturbances generated from an uncertain Van der Pol circuit, which is verified the robustness of the proposed regulator. Especially, we first design a non-linear internal model and an output feedback regulator for the Duffing equation, and the numerical simulation showed that the proposed disturbance rejection algorithm can completely reject the chaotic signals generated from the Duffing equation.In chapter 6, based on Chen and Huang's self-contained concepts of steady-state generator and internal model, we further extend the Chen and Huang's work in the nonlinear exosystems to the global disturbance rejection problem for a class of uncer-tain output feedback systems. The new nonlinear internal model and adaptive output feedback regulator are proposed to ensure that the system's output variables can asymp-totically converge to zero. And new adaptive laws are designed to deal with the linearly parameterized unknown parameter in the plant. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol oscillator. Simulation results show the efficacy of the proposed rejection algorithm.In chapter 7, the robust control of chaos in Modified FitzHugh-Nagumo neuron model under external electrical stimulation is researched. And the external electri-cal stimulation is in the form of F(t)=(A/σ)cos(σt) with A,σthe amplitude and frequency, respectively. Throughout this chapter, the external electrical stimulation is unknown including unknown amplitude, unknown frequency and unknown phases. We first present the solution of the global robust adaptive output regulation problem for an uncertain output feedback systems with an uncertain exosystem. Then we show that the robust control of chaos problem for the MFHN can be formulated as the global robust adaptive output regulation problem of the uncertain output feedback systems. And we apply the obtained result in this chaper to construct a nonlinear adaptive internal model and an output feedback control law for the MFHN to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external elec-trical stimulation, which is also verified the robustness of the proposed output feedback regulator.In chapter 8, the robust control of chaos in Modified FitzHugh-Nagumo neuron model under a class of nonlinear oscillator is considered. We first present the solu-tion of the global robust adaptive output regulation problem for an uncertain output feedback systems with nonlinear exosystems. Then we show that the robust control of chaos in MFHN can be formulated as the global robust adaptive output regulation problem of the uncertain output feedback systems. And we apply the obtained result in this chaper to construct a nonlinear internal model and an adaptive output feedback controller for the MFHN to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation gener-ated from an uncertain Van der Pol circuit, which is also verified the robustness of the proposed output feedback regulator.Finally, the research work of this dissertation is summarized, and the future re-search direction is indicated.