Pareto-Based Guaranteed Cost Control of the Uncertain Mean-Field Stochastic Systems

Yaning Lin () and Weihai Zhang ()
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Yaning Lin: Shandong University of Technology, School of Mathematics and Statistics
Weihai Zhang: Shandong University of Science and Technology, College of Electrical Engineering and Automation

Chapter Chapter 6 in Essays on Pareto Optimality in Cooperative Games, 2022, pp 85-113 from Springer

Abstract: Abstract Pareto-based GCC of the uncertain mean-field stochastic systems is investigated. First, Pareto game of the nominal mean-field stochastic systems is discussed in infinite horizon. Based on the convexity of the cost functionals, all Pareto-efficient strategies can be derived by solving a weighted sum optimal control problem. Then, Pareto-based GCC problem is settled by the GCC of the weighted sum cost functional. Employing the Karush–Kuhn–Tucker (KKT) conditionsKarush-Kuhn-Tucker (KKT) conditions, necessary conditions for the existence of Pareto-based guaranteed cost controllers are derived. In particular, it turns out that all controllers can be expressed as linear feedback forms involving the state and its mean based on the solutions of the cross-coupled stochastic algebraic Riccati equations (CSAREs)Cross-coupled Stochastic Algebraic Riccati Equations (CSAREs). In addition, an LMI-based approach is presented to reduce greatly the computational complexity in the controller design. Finally, three examples are given to show the effectiveness of the proposed results.

Date: 2022
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DOI: 10.1007/978-981-19-5049-0_6

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