Families of semipermeable curves in differential games with the homicidal chauffeur dynamics

Automatica ◽  
2004 ◽  
Vol 40 (12) ◽  
pp. 2059-2068 ◽  
Author(s):  
Valery S. Patsko ◽  
Varvara L. Turova
Keyword(s):  
Differential Games ◽  
Homicidal Chauffeur

Families of Semipermeable Curves in Differential Games with the Homicidal Chauffeur Dynamics

2001 ◽  
Vol 34 (6) ◽  
pp. 1523-1528
Author(s):  
V.S. Patsko ◽  
V.L. Turova
Keyword(s):  
Differential Games ◽  
Homicidal Chauffeur

Families of semipermeable curves in differential games with the homicidal chauffeur dynamics☆

Automatica ◽  
2004 ◽  
Vol 40 (12) ◽  
pp. 2059-2068 ◽  
Author(s):  
V PATSKO ◽  
V TUROVA
Keyword(s):  
Differential Games ◽  
Homicidal Chauffeur

LEVEL SETS OF THE VALUE FUNCTION IN DIFFERENTIAL GAMES WITH THE HOMICIDAL CHAUFFEUR DYNAMICS

2001 ◽  
Vol 03 (01) ◽  
pp. 67-112 ◽  
Author(s):  
V. S. PATSKO ◽  
V. L. TUROVA
Keyword(s):  
Differential Games ◽  
Level Sets ◽  
Value Functions ◽  
Capture Time ◽  
Evasion Game ◽  
Homicidal Chauffeur ◽  
Turn Radius ◽  
The Value Function ◽  
Maximal Time ◽  
Surveillance Evasion

Three differential games with the dynamics of the homicidal chauffeur are considered. The first problem is the Isaacs' homicidal chauffeur differential game. In this game, a pursuer P minimises the capture time of an evader E. The objective of the evader is to prevent the capture or to maximise the capture time. The magnitude of the velocity is constant for the pursuer, and his maneuverability is bounded through a minimal turn radius. The maneuverability of the evader is not bounded. The pursuer's control is the rate of turn; the evader steers by choosing directions of his velocity. The main difference of the second problem is that the size of the constraint on the control parameter of the evader depends on the position of the game. The idea of such a modification was suggested by Bernhard. The third problem is a conic surveillance-evasion game studied by Lewin and Olsder. In this game, the dynamics is the same as in the Isaacs' problem, but the goals of the players differ from the classic formulation: an evader E minimises the time of escaping from a detection set that is a two-dimensional semiinfinite cone. The detection set is attached to the velocity vector of a pursuer P whose objective is to keep the evader within the detection set for maximal time. The paper describes the computation of level sets of the value functions for these games. The algorithm proposed by the authors is used. An analysis of families of semipermeable curves is carried out. The results of this analysis are used to check the correctness of the computation of level sets and to explain the appearance of holes in victory domains of the pursuer in the second problem.

Near Optimal Strategy for Nonlinear Stochastic Differential Games Based on the Technique of Statistical Linearization

2014 ◽  
Vol 39 (4) ◽  
pp. 390-399
Author(s):  
Ping ZHANG ◽  
Yang-Wang FANG ◽  
Xiao-Bin HUI ◽  
Xin-Ai LIU ◽  
Liang LI
Keyword(s):  
Differential Games ◽  
Optimal Strategy ◽  
Stochastic Differential Games ◽  
Statistical Linearization

A Numerical Method for Solving Time-Optimal Differential Games with a Lifeline

2020 ◽  
Vol 81 (8) ◽  
pp. 1545-1561
Author(s):  
N.V. Munts ◽  
S.S. Kumkov
Keyword(s):  
Numerical Method ◽  
Differential Games ◽  
Time Optimal

Inequalities for Subgradients of a Value Functional in Differential Games for Time-Delay Systems

2020 ◽  
Vol 101 (1) ◽  
pp. 76-79
Author(s):  
N. Yu. Lukoyanov ◽  
A. R. Plaksin
Keyword(s):  
Time Delay ◽  
Differential Games ◽  
Delay Systems ◽  
Time Delay Systems ◽  
A Value ◽  
Value Functional

Differential games of N players in stochastic systems with controlled diffusion terms

2008 ◽  
Vol 69 (5) ◽  
pp. 874-890 ◽  
Author(s):  
Shang Quang Tun ◽  
Sung Xung Li
Keyword(s):  
Differential Games ◽  
Stochastic Systems ◽  
Controlled Diffusion
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