Research On Stability Analysis And Control Of Several Classes Of Higher Order Nonlinear Systems  Posted on:20170425  Degree:Doctor  Type:Dissertation  Country:China  Candidate:X H Zhang  Full Text:PDF  GTID:1108330485476886  Subject:Applied Mathematics  Abstract/Summary:  PDF Full Text Request  Nonlinear, timedelay and external stochastic disturbance are commonly encountered in real systems. In recent years, the control problems for highorder nonlinear systems have been largely studied, especially, the finitetime stabilization now is the research focus. For several classes of highorder 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 highorder nonlinear systems with highorder and loworder nonlinearities, we consider the problem of output feedback control and focus on solving the following problems:(i) The system nonlinearities include not only highorder but loworder, and both order are relaxed to be any real number in an interval.(ii) Due to the general form of highorder and loworder 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 closedloop system.2. For a class of highorder nonlinear systems with multiple timevarying delays, we study its state feedback asymptotic stabilization. Systems become more general due to both loworder and highorder existing simultaneously in nonlinearities together with the multiple timevarying delays. By introducing a novel LyapunovKrasovskii 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 closedloop system.3. For a class of highorder nonlinear feedback systems with highorder and loworder nonlinearities, based on the finitetime 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 finitetime stabilization of the closedloop system.4. For a class of highorder 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 reducedorder observer and determining the observer gains, the finitetime 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 highorder 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 systemâ€™s solution must exist and be unique is verified completely.6. For a class of stochastic highorder feedforward nonlinear systems, based on stochastic Lyapunov finitetime stability theorem and the homogeneous domination approach, by construction a C2 Lyapunov function and verifying the existence and uniqueness of the solution, a continuous finitetime state feedback stabilized controller in probability is designed.7. For a class of stochastic highorder feedforward nonlinear systems, based on stochastic Lyapunov finitetime stability theorem and the homogeneous domination approach, by constructing a reducedorder observer and verifying the the existence and uniqueness of the solution, a finitetime output feedback stabilized controller in probability is designed.
 Keywords/Search Tags:  Nonlinear systems, stochastic systems, feedforward systems, timevarying delay, finitetime, state feedback, output feedback, reducedorder observer, sign function  PDF Full Text Request  Related items 
 
