Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback

In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are de...

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Veröffentlicht in:	IET control theory & applications Jg. 14; H. 9; S. 1246 - 1254
Hauptverfasser:	Mukaidani, Hiroaki, Saravanakumar, Ramasamy, Xu, Hua
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	The Institution of Engineering and Technology 11.06.2020
Schlagworte:	bilinear matrix inequality Brief Paper CCSALTEs classical Lagrange multiplier technique computational complexity differential equations feedback game theory higher‐order cross‐coupled stochastic algebraic Lyapunov type equations iterative methods Itô differential equations Krasnoselskii–Mann iterative algorithm linear matrix inequalities linear systems Lyapunov methods Markov jump linear stochastic system NP‐hard problem robust control robust incentive Stackelberg strategy robust static output feedback incentive Stackelberg game SOF incentive Stackelberg strategies SOF strategies stochastic systems iterative methods Itô differential equations Krasnoselskii–Mann iterative algorithm bilinear matrix inequality game theory linear systems CCSALTEs differential equations robust incentive Stackelberg strategy feedback SOF strategies NP-hard problem linear matrix inequalities robust static output feedback incentive Stackelberg game Markov jump linear stochastic system stochastic systems robust control higher-order cross-coupled stochastic algebraic Lyapunov type equations SOF incentive Stackelberg strategies classical Lagrange multiplier technique computational complexity Lyapunov methods
ISSN:	1751-8644, 1751-8652
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Zusammenfassung:	In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are derived in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov type equations (CCSALTEs). A classical Lagrange multiplier technique is employed to solve the CCSALTEs; therefore, the solution of the bilinear matrix inequality, which is a common NP-hard problem when designing SOF strategies, is not required. A heuristic algorithm is developed based on the CCSALTEs. In particular, it is shown that a robust convergence is guaranteed by combining the Krasnoselskii–Mann iterative algorithm with a new convergence condition. The performance of the proposed algorithm is discussed and a simple practical example is provided to demonstrate the effectiveness of the proposed algorithm and the SOF incentive Stackelberg strategies.
ISSN:	1751-8644 1751-8652
DOI:	10.1049/iet-cta.2019.0917