Abstract
This chapter deals with the pursuit games in which players (pursuer, evader, or both) employ impulse control.We consider continuous-time dynamical systems modeled by ordinary differential equations that are affected by jumps in state at discrete instants. The moments of jump comply with the condition for a finite number of jumps in finite time. In so doing, the Dirac delta function is used to describe the impulse control. Such systems represent a special case of hybrid systems. The method of resolving functions provides a general framework for analysis of the above-mentioned problems. This method essentially uses the technique of the theory of set-valued mappings. The following cases are examined in succession: impulse control of the pursuer; impulse control of the evader; impulse control of both players. The problem of approaching a cylindrical terminal set is studied for each case, and the sufficient conditions for its solvability are derived. Obtained results are supported by a model example of the game with simple motion dynamics.
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Chikrii, A.A., Matychyn, I.I., Chikrii, K.A. (2007). Differential Games with Impulse Control. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_2
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DOI: https://doi.org/10.1007/978-0-8176-4553-3_2
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