Defender-Attacker-Target Game: Open-Loop Solution

TL;DR

This paper models a pursuit-evasion differential game involving a defender and attacker with linear dynamics, deriving an open-loop saddle point solution applicable to controllers of arbitrary order, with practical numerical examples.

Contribution

It provides the first open-loop saddle point solution for a defender-attacker-target game with arbitrary controller orders in pursuit-evasion scenarios.

Findings

Derived open-loop saddle point solution for arbitrary controller orders.

Applied the solution to first-order controllers for defender and attacker.

Presented numerical examples demonstrating the solution's effectiveness.

Abstract

A defender-attacker-target problem with non-moving target is considered. This problem is modeled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional. In this game the pursuer is the defender, while the evader is the attacker. The objective of the pursuer is to minimize the cost functional, while the evader has two objectives: to maximize the cost functional and to keep a given terminal state inequality constraint. The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders. Then, this result is applied to the case of the first order controllers for the defender and the attacker. Numerical illustrating examples are presented.