Abstract
Coalitional control is studied in this chapter from a static viewpoint. More specifically, a generalized position value that considers centrality measures is obtained for each agent and for a large number of samples of the initial state, for the coalitional game presented in Chap. 3. Then, some statistical indices are calculated and a criterion to decide when an agent should be considered critical for the control network is proposed. These agents may be designed according to higher levels of communication issues, i.e., redundancy, robustness, memory buffer capacity, etc., hence improving the performance of the communication network.
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Notes
- 1.
Note that term \({{\mathbf {x}}_{\mathcal {N}}^{ T }}\big |_{k=0}(\mathbf {P}_\Lambda - \mathbf {P}_{\Lambda _0}){\mathbf {x}}_{\mathcal {N}}\big |_{k=0}\) provides a bound on the cost-to-go starting from initial state \({\mathbf {x}}_{\mathcal {N}}\big |_{k=0}={\mathbf {x}}^0_{\mathcal {N}}\) for each \(\Lambda \).
References
Algaba E, Bilbao JM, van den Brink R (2015) Harsanyi power solutions for games on union stable systems. Ann Oper Res 225(1):27–44
Borm P, Owen G, Tijs S (1992) On the position value for communication situations. SIAM J Discret Math 5(3):305–320
Casella G, Berger RL (2002) Statistical inference, 2nd edn. Duxbury advanced series, Thomson learning, Stamford
Gahinet P, Nemirovskii AS, Laub AJ, Chilali M (1995) LMI control toolbox for use with MATLAB\(^{\textregistered }\). The MathWorks, Inc., Natick
Ghintran A (2013) Weighted position values. Math Soc Sci 65(3):157–163
Haeringer G (2016) A new weight scheme for the Shapley value. Math Soc Sci 52(1):88–98
Muros FJ, Maestre JM, Algaba E, Ocampo-Martinez C, Camacho EF (2015) An application of the Shapley value to perform system partitioning. In: Proceedings of the \(33^{{\rm rd}}\) American control conference (ACC 2015), Chicago, Illinois, USA, pp 2143–2148
Muros FJ, Algaba E, Maestre JM, Camacho EF (2016) Cooperative game theory tools to detect critical nodes in distributed control systems. In: Proceedings of the \(15^{{\rm th}}\) European control conference (ECC 2016), Aalborg, Denmark, pp 190–195
Sun J, Tang J (2011) A survey of models and algorithms for social influence analysis. In: Aggarwal CC (ed) Social network data analytics. Springer, New York, USA, pp 177–214
van den Brink R, Borm P, Hendrickx R, Owen G (2008) Characterizations of the \(\beta \)- and the degree network power measure. Theory Decis 64(4):519–536
van den Brink R, van der Laan G, Pruzhansky V (2011) Harsanyi power solutions for graph-restricted games. Int J Game Theory 40(1):87–110
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Muros, F.J. (2019). Detection of Critical Agents by the Position Value. In: Cooperative Game Theory Tools in Coalitional Control Networks . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-10489-4_7
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DOI: https://doi.org/10.1007/978-3-030-10489-4_7
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