Some fundamental qualifications of optimal strategies and transition surfaces in differential games

1972 ◽  
Vol 9 (6) ◽  
pp. 399-425 ◽  
Author(s):  
P. L. Yu
Keyword(s):  
Differential Games ◽  
Optimal Strategies

scholarly journals Syntheses of differential games and pseudo-Riccati equations

2002 ◽  
Vol 7 (2) ◽  
pp. 61-83 ◽  
Author(s):  
Yuncheng You
Keyword(s):  
Dynamical Systems ◽  
Saddle Point ◽  
Riccati Equation ◽  
Differential Games ◽  
Regular Solution ◽  
Closed Loop ◽  
Optimal Strategies ◽  
Time Parameter ◽  
Fixed Duration ◽  
Linear Dynamical Systems

For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solutionP(t,x). Then the closed-loop optimal strategies are given byu(t)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(t,x(t)). For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.

scholarly journals Cooperative differential game model with continuous updating

2020 ◽  
Vol 12 (2) ◽  
pp. 82-109
Author(s):  
Ованес Леонович Петросян ◽  
Ovanes Petrosian ◽  
Анна Викторовна Тур ◽  
Anna Tur ◽  
Цзэян Ван ◽  
...  
Keyword(s):  
Differential Games ◽  
Optimal Strategies ◽  
Limited Resource ◽  
Game Model ◽  
Cooperative Solution ◽  
Cooperative Strategies ◽  
The Moment ◽  
Resource Extraction Game ◽  
Cooperative Differential Game ◽  
Cooperative Differential Games

The paper considers and describes the class of cooperative differential games with continuous updating. Such a class of differential games is new, at the moment only the classnoncooperative game models with continuous updating have been studied. This paper describes the process of constructing cooperative strategies, cooperative trajectory, characteristicfunction and cooperative solution with continuous updating. Cooperative case of limited resource extraction game model with continuous updating is considered. Optimal strategies,characteristic function and cooperative solution are constructed. The Shapley vector is used as a cooperative solution. The numerical simulation results are demonstrated in the Matlabenvironment.

scholarly journals PURSUIT-EVASION DIFFERENTIAL GAMES WITH THE GRÖNWALL TYPE CONSTRAINTS ON CONTROLS

2020 ◽  
Vol 6 (2) ◽  
pp. 95
Author(s):  
Bahrom T. Samatov ◽  
Gafurjan Ibragimov ◽  
Iroda V. Khodjibayeva
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Optimal Strategy ◽  
Optimal Strategies ◽  
The State ◽  
Differential Constraints ◽  
Quality Problem ◽  
Pursuit Evasion ◽  
Optimal Pursuit ◽  
Pursuit Strategy

A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (\(\Pi\)-strategy for short) was introduced and used to solve the quality problem for "life-line" games by L.A.Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.

scholarly journals Optimal strategies in event-constrained differential games

1989 ◽  
Vol 18 (1-3) ◽  
pp. 127-131 ◽  
Author(s):  
M. Heymann ◽  
N. Rajan ◽  
M. Ardema
Keyword(s):  
Differential Games ◽  
Optimal Strategies
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