Journal ArticleDOI
Existence of optimal open-loop strategies for a class of differential games
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In this paper, the class of differential games with linear system equations and a quadratic performance index is investigated for saddlepoint solutions when one or both of the players use open-loop control.Abstract:
In this paper, the class of differential games with linear system equations and a quadratic performance index is investigated for saddlepoint solutions when one or both of the players use open-loop control. For each formulation of the game, a necessary and sufficient condition is obtained for the existence of an optimal strategy pair that generates a regular optimal path. For those cases where a solution exists, the unique saddle-point solution is presented. Also, relationships are established between the time intervals of existence of solutions for the various formulations of the game.read more
Citations
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Journal ArticleDOI
A Leader-Follower Stochastic Linear Quadratic Differential Game
TL;DR: It is shown that the open-loop solution to the two- person leader-follower stochastic differential game admits a state feedback representation if a new stochastically Riccati equation is solvable.
Journal ArticleDOI
Linear–Quadratic Uncertain Differential Game With Application to Resource Extraction Problem
Xiangfeng Yang,Jinwu Gao +1 more
TL;DR: A Max-Min theorem is provided in order to guarantee the saddle-point Nash equilibrium, and when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic, the existence of saddle- point Nash equilibrium is obtained via the solvability of a corresponding Riccati equation.
Journal ArticleDOI
Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points
Jingrui Sun,Jiongmin Yong +1 more
TL;DR: In this paper, the authors considered a linear quadratic stochastic two-person zero-sum differential game, where both players are allowed to appear in both drift and diffusion of the state equation, and the weighting matrices in the performance functional are not assumed to be definite/non-singular.
Posted Content
Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points
Jingrui Sun,Jiongmin Yong +1 more
TL;DR: It turns out that there is a significant difference between open-loop and closed-loop saddle points and there is an essential feature that prevents a linear quadratic optimal control problem from being a special case of linear quadRatic two-person zero-sum differential games.
Concepts and Methods in Multi-Person Coordination and Control
Tamer Basar,Jose B. Cruz +1 more
TL;DR: This paper considers systems defined in discrete-time, and considers the team, Nash and Stackelberg solution concepts under different information structures, and provides an up-to-date survey of the literature.
References
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Journal ArticleDOI
Differential games and optimal pursuit-evasion strategies
TL;DR: In this article, conditions for capture and for optimality are derived for a class of optimal pursuit-evasion problems, and results are used to demonstrate that the well-known proportional navigation law is actually an optimal intercept strategy.
Journal ArticleDOI
Optimal control of linear systems with quadratic costs which are not necessarily positive definite
TL;DR: In this paper, the calculus of variations is applied to the problem of finding the optimal control for linear systems with quadratic costs which are not necessarily positive definite, and a numerical example of a second-order system is solved.
Journal ArticleDOI
Differential games with open-loop saddle point conditions
TL;DR: In this article, the conjugate point condition for zero-sum differential games was investigated and it was shown that the first-order necessary conditions for such problems are identical to the firstorder necessary condition for the usual form of a differential game, where both players use closed-loop control laws.
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