Conic surveillance evasion

Lewin, Joseph; Olsder, Geert Jan

doi:10.1007/bf00933329

Cited by 36 publications

(24 citation statements)

References 4 publications

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“…Lewin [18] (performed as well under the supervision of J. Breakwell), in the joint paper by J. Breakwell and J. Lewin [19], and also in the paper by J. Lewin and G. J. Olsder [20], both dynamics and constraints on the controls of the players are the same as in Isaacs' setting but the objectives of the players differ from those in the classic statement. Namely, player E tries to decrease the time of reaching the target set M by the state vector, whereas player P strives to increase that time.…”

Section: Surveillance-evasion Gamementioning

confidence: 99%

Homicidal Chauffeur Game: History and Modern Studies

Patsko¹,

Turova²

2010

Annals of the International Society of Dynamic Games

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Section: Surveillance-evasion Gamementioning

confidence: 99%

Homicidal Chauffeur Game: History and Modern Studies

Patsko¹,

Turova²

2010

Annals of the International Society of Dynamic Games

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“…In both cases, the surface M is followed by a surface M − 0 , through which the characteristic flow goes outside, and then comes a surface M + 0 with singular characteristics on it and with corresponding boundary-value problem. Such configuration also appear in many other problems (see, e.g., [9]). …”

Section: 2mentioning

confidence: 70%

Boundary singularities and characteristics of Hamilton–Jacobi equation

Melikyan

Olsder

2010

J Dyn Control Syst

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Abstract. Boundary-value problems for first order PDEs are locally considered, when the classical sufficient condition for the solution existence does not hold, but a solution still exists, possibly defined on one or both sides of the boundary surface. We note three situations when such a surface (locally) arises: (1) the part of the boundary surface with the given boundary value; (2) the part of the boundary surface with no value initially specified on it, while such a value arises during the constructions; (3) a singular surface arising during the constructions in the internal part of the domain. In the latter two cases, which are typical for the problems of optimal control and differential games, the solution value on the surface is specified due to singular characteristics. Although the character of the singularity of the solution is well known, we show in this paper that it is completely determined by the signs of two multiple Poisson brackets naturally arising in the equations of singular characteristics. We recall the notion of regular and singular characteristics and formulate a new sufficiency condition for the existence and uniqueness in the irregular case. This condition is in invariant form based on Poisson (Jacobi) bracket, which is convenient in applications. We give several examples with irregular solutions and boundary characteristics.

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“…A complete solution to the problem is given in works by J. V. Breakwell and A. W. Merz (see [4]; [15]). Some other variants of differential games with the homicidal chauffeur dynamics are investigated in [12]; [5]; [13]; [2]; [6]. In many papers (see, e.g., [1], [19]), the homicidal chauffeur game is used as a test problem for evaluating the efficiency of algorithms for the computation of the value function and optimal strategies.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer

Patsko

Turova

2009

Annals of the International Society of Dynamic Games

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The paper is devoted to the investigation of a time-optimal differential game in which the pursuer possesses increased control capabilities comparing to the classical homicidal chauffeur problem. Namely, the pursuer steers not only the angular velocity of turn but can additionally change the magnitude of his linear velocity. For such a new variant of the dynamics with non-scalar control of the pursuer, a complete description of families of semipermeable curves is given and the dependence of the structure of level sets of the value function on a parameter that defines the bound on the magnitude of the pursuer's velocity is explored by numerical methods.

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Conic surveillance evasion

Cited by 36 publications

References 4 publications

Homicidal Chauffeur Game: History and Modern Studies

Homicidal Chauffeur Game: History and Modern Studies

Boundary singularities and characteristics of Hamilton–Jacobi equation

Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer

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