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Applied Research Of Linear Matrix Inequality And Evolutionary Algorithm In Multi-objective Control

Posted on:2008-07-28Degree:MasterType:Thesis
Country:ChinaCandidate:W D WangFull Text:PDF
GTID:2178360212490254Subject:Systems Engineering
Abstract/Summary:PDF Full Text Request
In the optimization problems of control system, most of them are multi-objective problems, how to find the Pareto optimal solutions of multi-objective control problem is becoming a hot spot. In this thesis, reduced-order H controller design problem and mixed H2/H control problem are studied based on multi-objective genetic algorithm (MOGA) and linear matrix inequality (LMI) approach.Aimed at the disadvantage that local search ability of genetic algorithm is weak, combining genetic algorithm with local search, a Local Orthogonal Multi-objective Genetic Algorithm is proposed in this thesis. The algorithm first run MOGA in order to obtain approximate Pareto optimal solutions, then a new local orthogonal optimization technique is used to optimize above Pareto solutions for finding better solutions. Simulation results show that the improved algorithm excels prevalent NSGA-II and SPEA in the optimization effect. The analysis of complexity and convergence of improved algorithm show that improved algorithm has the same complexity with NSGA-II and SPEA, and can converge to Pareto optimal solutions set with probability 1.Considering the non-convex restriction condition of controller's order based on LMI approach, a most new design approach of reduce-order H controller base on LMI is used in order to overcome above non-convex problem in this thesis; The improved MOGA can optimize simultaneously controller structure and controller parameters, many controllers having various orders can be found in a single run. In addition, H2 and H performance are competing objectives in control system, so mixed H2 /H control problem is a typical multi-objective problem. LMI and The improved MOGA also are used to handle mixed H2/H control problem respectively in this thesis. The solving processes and optimization effects of two approaches show that improved MOGA's computer cost is bigger, but its optimization effect is better and its conservatism is less, in addition, MOGA can consider more objectives in a single run.
Keywords/Search Tags:Linear matrix inequality, Multi-objective genetic algorithm, Reduced-order H_∞controller, Mixed H2/H∞control, Pareto optimal solution
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