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

  • Authors:

  • Frederico G. Guimarães;Reinaldo M. Palhares;Felipe Campelo;Hajime Igarashi

  • Affiliations:

  • Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, 31270-010, Belo Horizonte, MG, Brazil;Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, 31270-010, Belo Horizonte, MG, Brazil;Research Group of Informatics for System Synthesis, Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan;Research Group of Informatics for System Synthesis, Graduate School of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Kita-ku, Sapporo 060-0814, Japan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

Quantified Score

Hi-index 0.07

Visualization

Abstract

We utilize optimization algorithms inspired by the immune system for treating the mixed H"2/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 H"2/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.