Design of mixed H₂ / H_∞ control systems using algorithms inspired by the immune system

We utilize optimization algorithms inspired by the immune system for treating the mixed H₂ / H_∞ control problem. Both precisely known systems and uncertain systems with polytopic uncertainties are investigated. For the latter, a novel methodology is proposed to compute the worst case norms within the polytope of matrices. This methodology consists in defining the worst case norm computation as an implicit optimization problem with a special structure. We exploit this structure of the problem for its solution. The paper presents both mono and multiobjective optimization algorithms developed from the clonal selection principle. The former is the real-coded clonal selection algorithm (RCSA) and the latter is the multiobjective clonal selection algorithm (MOCSA). The complete design process involves the combination of synthesis and analysis. The RCSA is used for analysis, through the worst case norm computation for a given provided controller. The MOCSA is used for synthesis, working on a population of candidate controllers, until providing an estimate of the Pareto set for the mixed H₂ / H_∞ control problem. The numerical examples illustrate the power and the validity of the proposed approach for robust control design. Moreover, our approach for worst case norm evaluation is compared with other approaches available in literature.