Infinite horizon linear quadratic Pareto game of the stochastic singular systems

Lin, Yaning; Zhang, Tianliang; Zhang, Weihai

doi:10.1016/j.jfranklin.2018.04.025

Cited by 26 publications

(10 citation statements)

References 24 publications

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“…However, notice that ū * determined by (36) is not an precise solution of the indefinite LQ problem P 3 for system (18). In what follows, for purpose of deriving the desired optimal control, which is determined by system (18) and quadratic cost function (21), the corresponding Kalman filter in backwards-time Krein space are invoked.…”

Section: Solution Of the Indefinite Lq Problemmentioning

confidence: 99%

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

2022

Asian Journal of Control

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In this article, the indefinite linear quadratic (LQ) optimal control problem for discrete time-varying rectangular descriptor systems is investigated, in which the indefinite weight matrices are considered in the quadratic cost function. With a suite of equivalent transformations, the indefinite LQ problem for discrete time-varying rectangular descriptor systems can be substituted by an equivalent indefinite LQ problem for standard state space systems. Then, the transformed equivalent indefinite LQ problem is solved by establishing a dual Krein space model, and the optimal control and optimal cost value are obtained by invoking the Kalman filter of Krein space. The form of state feedback optimal control corresponding to the original system is given. Next, to guarantee the dynamic part for the resulting optimal closed-loop system has a unique solution, some necessary and sufficient conditions are proposed. Finally, a numerical example is carried out to demonstrate the availability of established results.

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Section: Solution Of the Indefinite Lq Problemmentioning

confidence: 99%

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

2022

Asian Journal of Control

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“…[14] and Lin et al . [15] studied the linear quadratic (LQ) Pareto game of the stochastic singular systems in finite horizon and infinite horizon, respectively. Lin et al .…”

Section: Introductionmentioning

confidence: 99%

Pareto optimality in the infinite horizon cooperative difference game

Lin

2020

IET Control Theory & Applications

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“…Dynamic game theory has attracted a lot of research attention owing to its practical applications in engineering, economics, management science, and so on, see [1][2][3][4][5][6][7] and references therein. Moreover, LQ Nash games are the focus of these studies because of their importance in both theory and applications.…”

Section: Introductionmentioning

confidence: 99%

Infinite horizon LQ Nash Games for SDEs with infinite jumps

Liu

Hou

2020

Asian Journal of Control

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In this paper, we consider infinite horizon linear-quadratic (LQ) Nash games for stochastic differential equations (SDEs) with infinite Markovian jumps and (x, u, v)-dependent noise. An indefinite stochastic LQ result is first derived for the considered system. Then, under the condition of strong detectability, a necessary and sufficient condition for the existence of a Nash equilibrium is put forward in terms of the solvability of a countably infinite set of coupled generalized algebraic Riccati equations (ICGAREs). Moreover, the mixed H 2 ∕H ∞ control is investigated by Nash game approach as an important application. At last, we present an iterative algorithm to solve the ICGAREs, and a numerical simulation is given to illustrate its efficiency.

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Infinite horizon linear quadratic Pareto game of the stochastic singular systems

Cited by 26 publications

References 24 publications

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

Pareto optimality in the infinite horizon cooperative difference game

Infinite horizon LQ Nash Games for SDEs with infinite jumps

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