A multi-objective genetic algorithm approach is proposed to design tolerance controllers for uncertain interval systems. Given a set of specifications in terms of acceptability ranges of gain margin (GM) and phase margin (PM), the design objective is to evolutionarily derive controllers such that closed-loop stability and desired dynamic performance are guaranteed. On the basis of extremal design philosophy, the design problem is first formulated as constrained optimisation problems based on deviation between the desired and extremal GM/PM of the resulting loop-transfer function, and subsequently optimised via the proposed genetic algorithm. To ensure robust stability of the closed-loop system, root locations associated with the generalised Kharitonov segment polynomials will be used to establish a constraints handling mechanism, on the basis of which fitness functions can be constructed for effective evaluation of chromosomes in the current population. Because of the cost functions that adopt the concept of centrality, evolution is directed towards derivation of Pareto-optimal solutions of the tolerance controllers with better centrality and limited spreading along the desired region of acceptability, resulting in more consistent system performances and improved robustness of the closed-loop system.
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