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Multi-objective robust generalised H2 control

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  • Dmitry V. Balandin
  • Mark M. Kogan

Abstract

A novel multi-objective robust control problem is studied for systems with norm-bounded structured uncertainty and robust generalised $H_2 $H2 norms as criteria. Necessary conditions for Pareto optimality are formulated from which it follows that Pareto optimal solutions are to be among optimal solutions for scalar multi-objective costs in the form of Germeyer convolution. The upper bounds of the multi-objective costs are used to compute Pareto suboptimal controllers in terms of linear matrix inequalities, while the lower bounds to estimate a ‘difference’ between Pareto suboptimal and unavailable Pareto optimal controllers. Two-criteria robust control problem for a mathematical model of the rotor rotating in active magnetic bearings is considered as an application of this theory.

Suggested Citation

  • Dmitry V. Balandin & Mark M. Kogan, 2020. "Multi-objective robust generalised H2 control," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(10), pages 1873-1882, July.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:10:p:1873-1882
    DOI: 10.1080/00207721.2020.1780512
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