Singular surfaces in multi-agent connectivity maintenance games

Bhattacharya, Sourabh; Başar, Tamer; Hovakimyan, Naira

doi:10.1109/cdc.2011.6160247

Cited by 21 publications

(8 citation statements)

References 21 publications

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“…For example, Bhattacharya, Hutchinson and Başar [25][26][27] concern the visibility based pursuit-evasion game in an environment containing obstacles and present the necessary and sufficient conditions for surveillance and escape. Based on these findings, they construct a value function of the game and obtain optimal trajectories for the players as well as the dispersal surfaces arising in the solutions [28][29]. Shinar et al [30][31][32][33][34] analyze many pursuit-evasion games of kind with different dynamics of missiles and aircrafts, in particular, a hybrid evader who has two possible dynamics considered in [34] is a very interesting viewpoint.…”

Section: Related Workmentioning

confidence: 99%

Construction of Barrier in a Fishing Game With Point Capture

Zha

Chen

Peng

et al. 2017

IEEE Trans. Cybern.

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This paper addresses a particular pursuit-evasion game, called as "fishing game" where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived.

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Section: Related Workmentioning

confidence: 99%

Construction of Barrier in a Fishing Game With Point Capture

Zha

Chen

Peng

et al. 2017

IEEE Trans. Cybern.

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“…Recently, the authors in [2], [3] use the analysis techniques developed by Isaacs to examine a continuous time, visibility based, single-pursuer, single-evader game in an environment containing polygonal obstacles. There have also been several papers that use numerical techniques in order to solve combat games with realistic dynamics [4], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

Generalized Engage or Retreat Differential Game With Escort Regions

Fuchs

Khargonekar

2017

IEEE Trans. Automat. Contr.

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This paper is motivated by the desire to develop optimal defensive control strategies that discourage an attacker from engaging in attack while simultaneously encouraging retreat. We develop a general, two-player, differential game in which one player represents an attacker and the opposing player represents the defender. The attacker possesses superior dynamics such that it is capable of terminating the game either in engagement or retreat as it so chooses. The defender is incapable of directly preventing engagement. Instead, the defender uses the manipulation of the attacker's utility function as a form of indirect control in an attempt to make retreat a more attractive option over engagement. The solution to the overall engage or retreat differential game is found by solving two related optimization problems: the differential game of engagement and the optimal constrained retreat. The equilibrium open-loop control strategies and resulting game values of the attack or retreat game are expressed in terms of the solutions to these subproblems. Within the optimal constrained retreat problem, a value function constraint is imposed in order to prevent the attacker from moving into regions where engagement becomes optimal. This leads to regions of constrained retreat which we refer to as escort regions.

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“…Based on the method of singular characteristics [13], researchers have encountered singular surfaces in pursuitevasion games related to pursuit and capture [14], [15], [9], [16]. In [4], an algorithm is presented to construct the dispersal surfaces [12] for the problem addressed in [6]. To the best of our knowledge, a complete solution to the problem is yet unknown in general environments.…”

Section: Introductionmentioning

confidence: 99%

On the construction of barrier in a visibility based pursuit evasion game

Bhattacharya

Basar

Hovakimyan

2014

2014 European Control Conference (ECC)

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This work addresses a vision-based tracking problem between a mobile observer and a target in the presence of a circular obstacle. The task of keeping the target in the observer's field-of-view is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature. The objective of the observer is to maintain a line-of-sight with the target at all times. The objective of the target is to break the line-of-sight in finite amount of time.Initially, the control of the players on the barrier is computed from a slight modification of the definition of the escape set and the capture set [10]. The barrier is constructed from the boundary of the usable part of the terminal manifold using the retrogressive equation for the normals to it. For a fixed initial position of the observer, a partition of the plane into escape and capture regions for the target is obtained from the construction of the barrier. This technique is extended to provide an approximation for the escape and capture set for a polygonal obstacle. Finally, numerical construction of iso-value surfaces is presented from the optimal strategies for the players in the escape set based on our earlier work in [5].

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Singular surfaces in multi-agent connectivity maintenance games

Cited by 21 publications

References 21 publications

Construction of Barrier in a Fishing Game With Point Capture

Construction of Barrier in a Fishing Game With Point Capture

Generalized Engage or Retreat Differential Game With Escort Regions

On the construction of barrier in a visibility based pursuit evasion game

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