COORDINATE-WISE INTEGRAL CONSTRAINT PURSUIT GAME OF STATE-TRANSITION MODELLED BY INFINITE SYSTEM OF TWO-COUPLED DIFFERENTIAL EQUATIONS
Abstract
Pursuit-evasion games are pivotal in control theory, robotics, and autonomous systems, modelling adversarial interactions where agents operate under resource constraints. This paper investigates a two-player pursuit game governed by a two-coupled infinite system of first-order ODEs. The pursuer in the game seeks to steer the state trajectory precisely to a prescribed target state in finite time, while the evader works to prevent this outcome. Unlike most existing works, which impose global geometric or integral resource constraints on players’ controls, this study adopts coordinate-wise integral constraints. Under this formulation, for each coordinate, the pursuer’s and evader’s control inputs satisfy per-coordinate energy bounds. It is shown that if, for every coordinate, the pursuer’s energy bound exceeds that of the evader, and if the scaled initial target mismatches are uniformly bounded so that the coordinate-wise pursuit completion times are well-defined and their supremum is finite, then the pursuer possesses a guaranteed winning strategy. An explicit strategy is constructed for the pursuer and its admissibility under the per coordinate integral constraints is proved. Moreover, for every admissible evader control, it is shown that the resulting trajectory reaches the target state exactly at the guaranteed pursuit time, ensuring pursuit completion. An illustrative example is provided to demonstrate the applicability of the obtained results.
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References
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