Linear Systems

Multicriteria minimax problems: localization of the pareto set and suboptimal control design

D. V. Balandin^a, R. S. Biryukov^b, M. M. Kogan<sup>b

a</sup> Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950 Russia
^b Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, 603950 Russia

Abstract: We consider multicriteria minimax optimization problems with criteria in the form of the maxima of functionals given by the induced norms of linear operators taking the system inputs and/or initial state to the outputs. It is shown that replacing the difficult minimization of the linear convolution of such criteria by the minimization of the maximum of the linear convolution of the corresponding functionals leads to suboptimal solutions with an estimate of the degree of suboptimality with respect to Pareto optimal solutions. This approach is applied to Pareto suboptimal control design for linear finite-horizon time-varying and infinite-horizon time-invariant continuous- and discrete-time systems with uncertain initial states and/or disturbances. Numerical simulation results are presented.

Keywords: multicriteria control, Pareto set, generalized $H_\infty$-norm, linear matrix inequality.

Presented by the member of Editorial Board: M. V. Khlebnikov

Received: 27.08.2020
Revised: 15.02.2021
Accepted: 16.03.2021

DOI: 10.31857/S000523102108002X

 English version: Automation and Remote Control, 2021, 82:8, 1321–1337

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