Multiobjective Evolutionary Approach to the Design of Optimal Controllers for Interval Plants via Parallel Computation

Chen-Chien James HSU  Chih-Yung YU  Shih-Chi CHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.9   pp.2363-2373
Publication Date: 2006/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.9.2363
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
genetic algorithms,  multi-objective genetic algorithms,  interval systems,  robust controllers,  minimax optimization,  parallel computation,  

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Design of optimal controllers satisfying performance criteria of minimum tracking error and disturbance level for an interval system using a multi-objective evolutionary approach is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem, subsequently solved by a proposed two-phase multi-objective genetic algorithm (MOGA). By using two sets of interactive genetic algorithms where the first one determines the maximum (worst-case) cost function values for a given set of controller parameters while the other one minimizes the maximum cost function values passed from the first genetic algorithm, the proposed approach evolutionarily derives the optimal controllers for the interval system. To suitably assess chromosomes for their fitness in a population, root locations of the 32 generalized Kharitonov polynomials will be used to establish a constraints handling mechanism, based on which a fitness function can be constructed for effective evaluation of the chromosomes. Because of the time-consuming process that genetic algorithms generally exhibit, particularly the problem nature of minimax optimization, a parallel computation scheme for the evolutionary approach in the MATLAB-based working environment is also proposed to accelerate the design process.