Abstract
Dynamic games for a class of linear time-delay systems with Markovian jumping parameters are investigated. Both Nash games and Pareto optimization problems are considered for systems in which controls-dependent noise is included. Sufficient conditions for the existence of the Nash strategies and the Pareto strategies in terms of matrix inequality are established by using a classical Lyapunov-Krasovskii method and a non-convex optimization approach, respectively. In order to obtain the Nash strategy sets and the Pareto strategy sets, new cross-coupled stochastic algebraic equations (CSAEs) are derived respectively based on the Karush-Kuhn-Tucker (KKT) conditions. Furthermore, it is shown that the state feedback strategies can be obtained by iteratively solving linear matrix inequalities (LMIs). Finally, a modified practical numerical example is given to demonstrate the validity and potential of the proposed numerical method.
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Mukaidani, H., Xu, H., Dragan, V. (2016). Dynamic Games for Markov Jump Stochastic Delay Systems . In: Witrant, E., Fridman, E., Sename, O., Dugard, L. (eds) Recent Results on Time-Delay Systems. Advances in Delays and Dynamics, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-26369-4_11
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DOI: https://doi.org/10.1007/978-3-319-26369-4_11
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