Stability And Control Of Kinds Of Uncertain Nonlinear Systems

In practice, physical systems under study possess inherent characteristics of uncertainties and nonlinearities. Therefore, it is important theoretical and practical significant to study on the stability and control of uncertain nonlinear systems. The main contributions of this dissertation are as follows:1. For a class of nonlinear systems with model uncertainties, linear control strategies are proposed based on novel disturbance observers. The basic idea of the proposed strategies is that, since the effects of the model uncertainties must be reflected in the trajectories of the system states once the uncertainties affect the controlled systems, novel linear disturbance observers are constructed to separate the relative information of the model uncertainties from the the state trajectories, and then linear compensators are designed by using the obtained information to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering due to their simple control structure and algorithm.2. For a class of single-input-single-output (SISO) uncertain non-affine nonlinear systems, output feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, to deal with the non-affine appearance of the control input, equivalent transformation is firstly used to transform the controlled system into an affine form; and then novel linear disturbance observers are built to obtain the estimates of the model uncertainties, and linear compensators are presented by using the obtained estimates to compensate the model uncertainties in real-time. Compared with the literature, the proposed strategies are of great significance in engineering due to their simple control structure and algorithm and their relaxed conditions.3. For a class of multi-input-multi-output (MIMO) uncertain non-affine nonlinear systems, feedback control strategies are presented based on novel disturbance observers. The basic idea of the proposed strategies is that, a new multivaluable implicit function theorem is firstly proposed to prove that there exists an ideal controller for the considered multivaluable systems; secondly equivalent transformation is used to transform the controlled system into an affine form, and novel disturbance observers are presented to estimate the model uncertainties, and subsequently full-state feedback controller is developed based on the estimations:when only system outputs are available for feedback, then the state observer is designed to estimate the unmeasurable state, and output feedback controller is presented to compensate the model uncertainties in real-time. The proposed strategies are of great significance in engineering since they possess simple control structure and algorithm and avoid the decoupling problem.4. Novel adaptive neural control strategies are presented for uncertain nonlinear systems. The proposed control strategies are firstly used to sovled a class of SISO affine nonlinear systems with the control coefficients being unknown functions. Control singularity problem possibly exists in the adaptive control when the unknown control coefficients are approximated. To tackle such a problem, the basic idea of the proposed control strategies is that, the control coefficients is firstly divided by equivalent transformation into two iterms:the one iterm that the control coefficients are constants and the other iterm that the control coefficients are unknow functions:based on such a new form, adaptive neural controllers are designed to compensate the model uncertainties, and meanwhile guarantee the iterm that the control coefficients are unknow functions to be non-positive in the derivatives of Lyapunov function candidates, and subsequently avoid the control singularity problem. And then the proposed control strategies are applied to a more general class of MIMO uncertain nonlinear systems in block-triangular form, where all subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. The control strategies can avoid the decoupling problem, the possible control singularity problem and the circular control construction problem.