Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures
In: Mathematics, Jg. 12 (2024-04-01), Heft 8, S. 1132-1132
Online
academicJournal
Zugriff:
This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max–Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the Itô–Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an H∞ control problem applicable to an infinite horizon. Finally, we present the conclusions.
Titel: |
Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures
|
---|---|
Autor/in / Beteiligte Person: | Jia, Zhifu ; Li, Cunlin |
Link: | |
Zeitschrift: | Mathematics, Jg. 12 (2024-04-01), Heft 8, S. 1132-1132 |
Veröffentlichung: | MDPI AG, 2024 |
Medientyp: | academicJournal |
ISSN: | 1208-1132 (print) ; 2227-7390 (print) |
DOI: | 10.3390/math12081132 |
Schlagwort: |
|
Sonstiges: |
|