Numerical Investigation of the Value Function for the Homicidal Chauffeur Problem with a More Agile Pursuer
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.
KeywordsTime-optimal control pursuit-evasion differential game value function semipermeable curves homicidal chauffeur game numerical construction
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