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Research On Stability Analysis And Control Of Several Classes Of Higher Order Nonlinear Systems

Posted on:2017-04-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:X H ZhangFull Text:PDF
GTID:1108330485476886Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Nonlinear, time-delay and external stochastic disturbance are commonly encountered in real systems. In recent years, the control problems for high-order nonlinear systems have been largely studied, especially, the finite-time stabilization now is the research focus. For several classes of high-order nonlinear(stochastic) systems with different structure, the problems of the controller design and stability analysis are investigated in this paper. The main contributions include:1. For a class of high-order nonlinear systems with high-order and low-order nonlinearities, we consider the problem of output feedback control and focus on solving the following problems:(i) The system nonlinearities include not only high-order but low-order, and both order are relaxed to be any real number in an interval.(ii) Due to the general form of high-order and low-order in the nonlinearities, sign function is introduced in the design procedure.(iii)Based on the Lyapunov stability theorem together with the combined of adding the power integrator and homogeneous domination, an output feedback stabilized controller is designed to guaranteed the globally uniformly asymptotic stability of the closed-loop system.2. For a class of high-order nonlinear systems with multiple time-varying delays, we study its state feedback asymptotic stabilization. Systems become more general due to both low-order and high-order existing simultaneously in nonlinearities together with the multiple time-varying delays. By introducing a novel Lyapunov-Krasovskii functional, a state feedback controller based on the adding a power integrator and sign function methods is designed to guarantee the globally uniformly asymptotic stability of the closed-loop system.3. For a class of high-order nonlinear feedback systems with high-order and low-order nonlinearities, based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilization of the closed-loop system.4. For a class of high-order nonlinear feedforward systems, based on the homogeneous domination method, under a set of coordinate transformations, we first design a output feedback controller for the nominal system. Then by constructing a reduced-order observer and determining the observer gains, the finite-time output feedback controller of the whole system is obtained. Finally, the stability analysis and a simulation example demonstrate the effectiveness of the control method.5. For a class of stochastic high-order nonlinear systems, we further consider the problem of state feedback stabilization. There are two main difficulties:(i) The restriction that the upper bounds of system nonlinearities must have linear parts is removed.(ii) The study precondition that the stochastic system’s solution must exist and be unique is verified completely.6. For a class of stochastic high-order feedforward nonlinear systems, based on stochastic Lyapunov finite-time stability theorem and the homogeneous domination approach, by construction a C2 Lyapunov function and verifying the existence and uniqueness of the solution, a continuous finite-time state feedback stabilized controller in probability is designed.7. For a class of stochastic high-order feedforward nonlinear systems, based on stochastic Lyapunov finite-time stability theorem and the homogeneous domination approach, by constructing a reduced-order observer and verifying the the existence and uniqueness of the solution, a finite-time output feedback stabilized controller in probability is designed.
Keywords/Search Tags:Nonlinear systems, stochastic systems, feedforward systems, time-varying delay, finite-time, state feedback, output feedback, reduced-order observer, sign function
PDF Full Text Request
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