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Multi-Objective Optimal Theory And Its Application Via Paramater-Dependent Lyapunov Function

Posted on:2008-04-27Degree:DoctorType:Dissertation
Country:ChinaCandidate:L HeFull Text:PDF
GTID:1118360245497376Subject:Control Science and Engineering
Abstract/Summary:PDF Full Text Request
As the emergence of the LMI (Linear matrix inequality) technique, many performance indices of the control system can be translated into LMI formulations. With the excellent synthesis ability, it can easily satisfy multiple performance specifications using a single Lyapunov function, which forms the so called LMI-based multiobjective control problems and keeps prevailing. Due to its utilization a common Lyapunov function for all performance indices, this method has been well recognized as conservative. Some researchers have put forward the concept based on parameter dependent Lyapunov stability theory and its related analysis and synthesis, and has achieved some results on reducing the conservatism in multiobjective control. Based on the previous works of others, this thesis proposed a systematic framework to investigate the problems of the stability and performance analysis, state/output feedback control synthesis, filter design for continuous-time system based on the parameter dependent function by introducing the slack matrix variables. Part of the proposed theory is applied to the multiobjective control of satellite attitude control.Uncertainty appears in many aspects such as aerospace, astronautics and industrial process. Errors are inevitable between the mathematical model and the practical model for it is usually difficult to characterize the controlled object by precise mathematical modeling, thus robust control has been a hot topic in control science for the past years, and is also considered in this dissertation. A novel framework for analysis and synthesis of the continuous-time system is proposed, which gives the relaxed LMI representations of H2, H∞, l1 and domain pole placement using the parameter dependent Lyapunov stability theory.This method has achieved a separation between the system matrix and the Lyapunov matrix variable by introducing slack matrix variables, thus no common Lyapunov function is required and leads to reduction of conservatism. In addition, mixed H2 /H∞state feedback controller and H∞output feedback controller are designed respectively. Moreover, this new method has been extended to the robust control problem for more complicated systems such as continuous time-varying delay system, continuous stochastic system and stochastic time delay system, which shows the ability to reduce conservatism.The multiobjective control problem of precise pole placement blended with Lyapunov type constraints is investigated. By utilizing the parametric representation the eigenstructure assignment and the extended Lyapunov type constraints, the LMI-based multiobjective control which blends eigenstructure assignment and Lyapunov type constraints becomes possible. Based on this, the robust multiobjective control problem is considered. By using state feedback, the resulted closed-lop system satisfies the robust pole placement constraints and the H∞disturbance attenuation, and the condition of the existence of the controller has been converted into the feasibility of the LMIs.The robust mixed H2 /H∞filtering problem for uncertain continuous-time system is studied. A multiobjective filter is designed by utilizing the enhanced parameter dependent Lyapunov performance indices and the filter parameters are derived by solving a convex optimization problem, which guarantees the filtering error system to be asymptotically stable and the prescribed performance indices.Robust stability problem for T-S fuzzy model based uncertain time-delay system is approached. Based on the proposed parameter dependent Lyapunov stability theory, no common Lyapunov function is forced for all matrix inequalities, which can reduce conservatism extremely in the case where the number of rules is large. Then the multiobjective control synthesis for T-S fuzzy systems is considered, the resulting closed-loop system satisfies the domain pole placement requirement and H∞disturbance attenuation.It is discussed that the robust controller design for satellite attitude control with the consideration of multiple constraints as model uncertainty, disturbance torque and control effort. This part constitutes an effort of applying the proposed parameter dependent Lyapunov stability theory to the practical engineering. The simulation shows the validity of the control strategy.
Keywords/Search Tags:Parameter dependent Lyapunov function, Robust filtering, H_∞control, Multiobjective optimization, Linear matrix inequality, Attitude control
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