Multi-objective robust generalised H2 control

Dmitry V. Balandin and Mark M. Kogan

International Journal of Systems Science, 2020, vol. 51, issue 10, 1873-1882

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.

Date: 2020
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DOI: 10.1080/00207721.2020.1780512

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