H∞ Constraint Pareto Optimal Strategy for Stochastic LPV Systems

Mostak Ahmed, Hiroaki Mukaidani and Tadashi Shima
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Mostak Ahmed: Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan†Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh
Hiroaki Mukaidani: Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan
Tadashi Shima: Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan

International Game Theory Review (IGTR), 2018, vol. 20, issue 02, 1-20

Abstract: H∞ constraint Pareto optimal strategy for stochastic linear parameter varying (LPV) systems with multiple decision makers is investigated. The modified stochastic bounded real lemma and linear quadratic control (LQC) for the stochastic LPV systems are reformulated by means of linear matrix inequalities (LMIs). In order to decide the strategy set of multiple decision makers, Pareto optimal strategy is considered for each player and the H∞ constraint is imposed. The solvability conditions of the problem are established from cross-coupled matrix inequalities (CCMIs). The efficiency of the proposed strategy set is demonstrated using a numerical example.

Keywords: Gain-scheduled control; Pareto optimal strategy; stochastic linear parameter varying (LPV) system; cross-coupled matrix inequalities (CCMIs); H∞-constraint (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219198917500311

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