On pursuit and evasion game problems with Gr$$\ddot{\text {o}}$$nwall-type constraints
Open Access
- 5 February 2023
- journal article
- research article
- Published by Springer Science and Business Media LLC in Quality & Quantity
Abstract
We study a fixed duration pursuit-evasion differential game problem of one pursuer and one evader with Grönwall-type constraints (recently introduced in the work of Samatov et al. (Ural Math J 6:95–107, 2020b)) imposed on all players’ control functions. The players’ dynamics are governed by a generalized dynamic equation. The payoff is the greatest lower bound of the distances between the evader and the pursuers when the game is terminated. The pursuers’ goal, which contradicts that of the evader, is to minimize the payoff. We obtained sufficient conditions for completion of pursuit and evasion as well. To this end, players’ attainability domain and optimal strategies are constructed.Funding Information
- Simons Foundation
- Università degli Studi Mediterranea di Reggio Calabria
This publication has 27 references indexed in Scilit:
- Problems of group pursuit with integral constraints on controls of the players. ICybernetics and Systems Analysis, 2013
- Evasion from many pursuers in simple motion differential game with integral constraintsEuropean Journal of Operational Research, 2012
- On game problems for second-order evolution equationsRussian Mathematics, 2007
- On some sufficient conditions for optimality of the pursuit time in the differential game with multiple pursuersAutomation and Remote Control, 2006
- Optimal Pursuit with Countably Many Pursuers and One EvaderDifferential Equations, 2005
- Control Under Indeterminacy and Double ConstraintsDifferential Equations, 2003
- A problem of group pursuit with phase constraintsJournal of Applied Mathematics and Mechanics, 2002
- A game of optimal pursuit of one object by severalJournal of Applied Mathematics and Mechanics, 1998
- Differential game of optimal approach of two inertial pursuers to a noninertial evaderJournal of Optimization Theory and Applications, 1990
- Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential EquationsAnnals of Mathematics, 1919