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Slide Mode Control Of Markov Jump Systems

Posted on:2009-06-08Degree:MasterType:Thesis
Country:ChinaCandidate:Z Y TangFull Text:PDF
GTID:2178360272956624Subject:Detection Technology and Automation
Abstract/Summary:PDF Full Text Request
Markov jump linear systems comprise an important class of stochastic time-variant linear systems that have been in great evidence over the last years. Large number of real systems such as manufactory processes, biology and chemistry systems, power systems, network systems as well as economic systems can be properly described by Markov jump linear system model,which subject to sudden environment changes, changes in the interconnections of subsystems, modification of the operating point of a linearized model of a nonlinear system, random failures and repairs of the components and so on. So the study of Markov jump linear system can provide a theoretical foundation to solve the control problem of these systems.Sliding mode control is an effective robust control strategy.After the 1970s,the sliding mode control system received extensive attention of the western researchers for its distinct merits and features and it has been deeply studied from the different aspects with many mathematic methods.Now,the sliding mode control already become a relative independence research branch.Based on the study status of Sliding mode control and the new requirements from the practice for the theory of sliding mode control,some problems are studied and discussed in this paper,also the corresponding results are given.the main contents are as follows:(1) In order to solve the H∞control problem for a class of singular system with markov parameters, a design method based on the memoryless state feedback controller of mode-jumping is proposed. the causal and regular was guaranteed in terms of linear transformation and block matrix. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the systems were admissible was given and proved, and a sub-optimal design approach is presented. The controller was designed and the prescribed H∞performance condition was satisfied. Simulation results demonstrate that the proposed method is valid and the system has strong restraint ability against disturbance.(2) The problem of sliding mode control for a class of jumping system is considered.There are uncertainties in both state matrices and input matrix. Moreover,the uncertainties is mismatched norm bounded.By using Lyapunov theory,a sufficient condition in terms of linear matrix inequalities is derived such as the asympotical stability of the full order sliding mode dynamicsis guaranteed. When the inear matrix inequalities are feasible,the design of both sliding modecontrol law and the integral sliding mode surface can be easily obtain via convex optimization.State trajectories are attracted onto the specified sliding surface.A simulation is given to illustrate the effectiveness of the proposed method.(3) The different sliding mode surface dissipative control problems are discussed for a class of Markov jump nonlinear systems with uncertainties. The systems involve both time-evolving and event-driven mechanisms. In terms of sliding mode theory, different sliding mode surface and controllers are designed for the matched uncertainties. Dissipative control theory and linear matrix inequality are applied to sliding mode surface with nonlinear and unmatched uncertainties. Thereafter, the memoryless state feedback controllers are given. Finally, a sliding mode dissipative controllers are gained. A numerical example demonstrates the effectof the proposed design approach.(4) An sliding mode observers is presented is presented for a class of Markov jump nonlinear systems with uncertainties.By appling the singular value decomposition to decompose the dynamical sytem.An optimizing sliding mode strategy is given which guarantee robustness to uncertainties of systems and disturbance,A particular design of sliding mode observer is presented for which the parameters can be obtained using inear matrix inequalities techniques.Based on the sliding mode observers,fault detection and estimation issues for a class of nonlinear systems with uncertainty is considered.The conclusion and perspective are given in the end of the thesis.
Keywords/Search Tags:jump systems, Sliding mode control, Dissipative, fault detection, singular system, admissible, H_∞control, integral sliding mode surface
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