Active Target Defense Differential Game with a Fast Defender

This paper addresses the active target defense differential game where an Attacker missile pursues a Target aircraft. A Defender missile is fired by the Target's wingman in order to intercept the Attacker before it reaches the aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the distance between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker tries to minimize said distance. The results shown here extend previous work. We consider here the case where the Defender is faster than the Attacker. The solution to this differential game provides optimal heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker and it also provides the optimal heading angle for the Attacker to minimize the said distance.Comment: 9 pages, 8 figures. A shorter version of this paper will be presented at the 2015 American Control Conferenc

Escape Regions of the Active Target Defense Differential Game

The active target defense differential game is addressed in this paper. In this differential game an Attacker missile pursues a Target aircraft. The aircraft is however aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker simultaneously tries to minimize said distance. This paper focuses on characterizing the set of coordinates such that if the Target's initial position belong to this set then its survival is guaranteed if both the Target and the Defender follow their optimal strategies. Such optimal strategies are presented in this paper as well.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1502.0274

Defender-assisted Evasion and Pursuit Maneuvers

Motivated by the possibilities afforded by active target defense, a 3-agent pursuit-evasion differential game involving an Attacker/Pursuer, a Target/Evader, and a Defender is considered. The Defender strives to assist the Target by intercepting the Attacker before the latter reaches the Target. A barrier surface in a reduced state space separates the winning regions of the Attacker and Target-Defender team. In this thesis, attention focuses primarily on the Attacker\u27s region of win where, under optimal Attacker play, the Defender cannot preclude the Attacker from capturing the Target. Both optimal and suboptimal strategies are investigated. This thesis uses several methods to breakdown and analyze the 3-player differential game

Two-On-One Pursuit with a Non-zero Capture Radius

In this paper, we revisit the Two Cutters and Fugitive Ship differential game that was addressed by Isaacs, but move away from point capture. We consider a two-on-one pursuit-evasion differential game with simple motion and pursuers endowed with circular capture sets of radius l \u3e 0. The regions in the state space where only one pursuer effects the capture and the region in the state space where both pursuers cooperatively and isochronously capture the evader are characterized, thus solving the Game of Kind. Concerning the Game of Degree, the algorithm for the synthesis of the optimal state feedback strategies of the cooperating pursuers and of the evader is presented

Virtual Target Selection for a Multiple-Pursuer Multiple-Evader Scenario

This paper considers an M-pursuer N-evader scenario involving virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team's energy is minimized, and second, choose the virtual targets' locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer's virtual target location and each evader. Using the constructed Apollonius circles, the pursuer's travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer-evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example.Comment: AIAA SciTech 2024 Preprin

The Barrier Surface in the Cooperative Football Differential Game

This paper considers the blocking or football pursuit-evasion differential game. Two pursuers cooperate and try to capture the ball carrying evader as far as possible from the goal line. The evader wishes to be as close as possible to the goal line at the time of capture and, if possible, reach the line. In this paper the solution of the game of kind is provided: The Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is constructed. Under optimal play, the winning team is determined by evaluating the associated Barrier function.Comment: 5 pages, 1 figur

Nonlinear Model Predictive Control Framework For Cooperative Three-Agent Target Defense Game

This paper presents cooperative target defense guidance strategies using nonlinear model predictive control (NMPC) framework for a target-attacker-defender (TAD) game. The TAD game consists of an attacker and a cooperative target-defender pair. The attacker's objective is to capture the target, whereas the target-defender team acts together such that the defender can intercept the attacker and ensure target survival. We assume that the cooperative target-defender pair do not have perfect knowledge of the attacker states, and hence the states are estimated using an Extended Kalman Filter (EKF). The capture analysis based on the Apollonius circles is performed to identify the target survival regions. The efficacy of the NMPC-based solution is evaluated through extensive numerical simulations. The results show that the NMPC-based solution offers robustness to the different unknown attacker models and has better performance than CLOS and A-CLOS based strategies.Comment: 16 page

Personal favor and public influence : Arete, Arsinoe II, and the Argonautica

This interdisciplinary study explores the connection between the Ptolemaic monarchy and the Phaeacian episodes in Homer's Odyssey and the Argonautica of Apollonius Rhodius. In particular, I am interested in what the epic representation of the Phaeacian queen Arete can tell us about the political influence of Arsinoe II Philadelphus, ruler of Egypt with Ptolemy II in the third century B.C.E.Not