LQ Pareto Game of the Stochastic Singular Systems in Infinite Horizon

Yaning Lin () and Weihai Zhang ()
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Yaning Lin: Shandong University of Technology, School of Mathematics and Statistics
Weihai Zhang: Shandong University of Science and Technology, College of Electrical Engineering and Automation

Chapter Chapter 5 in Essays on Pareto Optimality in Cooperative Games, 2022, pp 69-84 from Springer

Abstract: Abstract This chapter is concerned with the infinite horizon LQ Pareto game of the stochastic singular systems. First, indefinite stochastic singular LQ optimal control problem is discussed in infinite horizon. By the equivalent transformation methodEquivalent transformation method, the primal LQ optimal control problem is transformed into a general stochastic LQ optimization problem. Based on the classical stochastic LQ optimal control theory, necessary and sufficient condition for the attainability is put forward. Next, the infinite horizon LQ Pareto game is studied for the stochastic singular systems. By the discussion of the convexity of the cost functionals, a sufficient condition for the existence of all Pareto-efficient strategies is obtained via the solvability of the corresponding SARE. Finally, an example is given to show the effectiveness of the proposed results.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-19-5049-0_5

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DOI: 10.1007/978-981-19-5049-0_5

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