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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| Vydáno v: | IET control theory & applications Ročník 14; číslo 9; s. 1246 - 1254 |
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The Institution of Engineering and Technology
11.06.2020
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Xu, Hua Saravanakumar, Ramasamy Mukaidani, Hiroaki |
| Author_xml | – sequence: 1 givenname: Hiroaki surname: Mukaidani fullname: Mukaidani, Hiroaki email: mukaida@hiroshima-u.ac.jp organization: 1Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 1-4-1 Kagamiyama, 739-8527, Japan – sequence: 2 givenname: Ramasamy orcidid: 0000-0002-4772-1732 surname: Saravanakumar fullname: Saravanakumar, Ramasamy organization: 1Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 1-4-1 Kagamiyama, 739-8527, Japan – sequence: 3 givenname: Hua surname: Xu fullname: Xu, Hua organization: 2Graduate School of Business Sciences, The University of Tsukuba, 3-29-1, Otsuka, Bunkyo-ku, Tokyo, 112-0012, Japan |
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| CitedBy_id | crossref_primary_10_1016_j_jfranklin_2022_11_001 crossref_primary_10_1080_00207721_2021_2005175 crossref_primary_10_1007_s11424_024_2480_1 crossref_primary_10_1002_rnc_7400 crossref_primary_10_1016_j_jfranklin_2022_01_003 |
| Cites_doi | 10.1016/S0005-1098(96)00141-0 10.1007/978-3-030-39789-0_3 10.1109/CDC.2018.8619239 10.1109/LCSYS.2018.2847034 10.1109/TAC.2004.828311 10.1016/0005-1098(95)00178-6 10.1109/TAC.2017.2703924 10.1016/S0377-0427(99)00304-0 10.1049/iet-cta.2017.0105 10.1016/j.automatica.2010.02.001 10.1007/978-3-319-40587-2 10.1016/j.amc.2015.10.038 10.1007/978-1-4614-8663-3 10.1016/0167-6911(94)90096-5 10.1016/j.automatica.2007.07.001 10.1017/S000497271600109X 10.1109/LCSYS.2017.2713879 10.1007/s12190-008-0139-z 10.1023/A:1024887007165 10.1109/SMC.2018.00671 10.1002/rnc.3393 10.1016/S0167-6911(97)00014-5 10.1109/TAC.2014.2305933 |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback |
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