Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach

Abstract : This letter focuses on the design of decentralized feedback control gains that aims at optimizing individual costs in a multi-agent synchronization problem. As reported in the literature, the optimal control design for synchronization of agents using local information is NP-hard. Consequently, we relax the problem and use the notion of satisfaction equilibrium from game theory to ensure that each individual cost is guaranteed to be lower than a given threshold. Our main results provide conditions in the form of linear matrix inequalities (LMIs) to check if a given set of control gains are in satisfaction equilibrium, i.e., all individual costs are upper-bounded by the imposed threshold. Moreover, we provide an algorithm in order to synthesize gains that are in satisfaction equilibrium. Finally, we illustrate this algorithm with numerical examples.
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Submitted on : Thursday, July 18, 2019 - 2:54:00 PM
Last modification on : Friday, July 19, 2019 - 1:14:21 AM

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Jomphop Veetaseveera, Vineeth Varma, Irinel-Constantin Morarescu, Jamal Daafouz. Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach. IEEE Control Systems Letters, IEEE, 2019, 3 (4), pp.918-923. ⟨10.1109/LCSYS.2019.2919425⟩. ⟨hal-02188433⟩

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