Solution Techniques for Realistic Pursuit-Evasion Games

Shinar, J.

doi:10.1016/b978-0-12-012717-7.50009-7

Cited by 125 publications

(67 citation statements)

References 23 publications

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“…Note that, due to the SFDG solution (Shinar, 1981;Shima and Shinar, 2002), there exists ϑ 1 ∈ (0, ϑ c1 ) such that H(ϑ 1 , ω e , ω p1 ) = 0 and …”

Section: 3mentioning

confidence: 99%

“…The points (x p , y p ) and (x e , y e ) are current coordinates of the pursuer and the evader, respectively, a p , a e are their lateral accelerations, ϕ p , ϕ e are the respective angles between the velocity vectors and the x-axis (initial line of sight). Based on the small angles assumption (Shinar, 1981;Shima and Shinar, 2002;Shinar et al, 2013), the trajectories of the pursuer and the evader can be linearized with respect to the nominal collision geometry, leading to a constant closing velocity V c . The final interception time t f can be easily calculated for any given initial range r 0 : t f = r 0 /V c .…”

Section: Problem Formulationmentioning

confidence: 99%

“…The solution of such a game is well known (Gutman and Leitmann, 1976;Shinar, 1981;Shima and Shinar, 2002;Gutman, 2006;Shinar et al, 2013). The key elements of this solution are (i) a scalarization of the original game and (ii) a decomposition of the space of the new (scalar) game into two regions, regular and singular.…”

Section: Introductionmentioning

confidence: 99%

“…The game (11)- (13) is called the scalar fixed dynamics game (SFDG). In the next subsection, a brief description of the well-known SFDG solution (Shinar, 1981;Shima and Shinar, 2002) is presented.…”

Section: Problem Scalarization Let Introduce the Functionmentioning

confidence: 99%

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Increasing Pursuer Capturability by Using Hybrid Dynamics

Glizer

Turetsky

2015

International Journal of Applied Mathematics and Computer Science

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A robust interception of a maneuverable target (evader) by an interceptor (pursuer) with hybrid dynamics is considered. The controls of the pursuer and the evader are bounded. The duration of the engagement is prescribed. The pursuer has two possible dynamic modes, which can be switched once during the engagement, while the dynamics of the evader are fixed. The case where for both dynamic modes there exists an unbounded capture zone was analyzed in our previous work. The conditions under which the pursuer can increase its capturability by utilizing the hybrid dynamics were established and the new robust capture zone was constructed. In the present paper, we extend this result to the cases where at least for one dynamic mode of the pursuer the capture zone is bounded. For these instances, conditions of increasing the pursuer's hybrid capturability are derived. Respective capture zones are constructed. Illustrative examples and results of extensive simulation for a realistic non-linear engagement model in the presence of a random wind are given.

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“…Note that, due to the SFDG solution (Shinar, 1981;Shima and Shinar, 2002), there exists ϑ 1 ∈ (0, ϑ c1 ) such that H(ϑ 1 , ω e , ω p1 ) = 0 and …”

Section: 3mentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Problem Scalarization Let Introduce the Functionmentioning

confidence: 99%

See 2 more Smart Citations

Increasing Pursuer Capturability by Using Hybrid Dynamics

Glizer

Turetsky

2015

International Journal of Applied Mathematics and Computer Science

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“…8,11,[14][15][16] Such formulation of a scenario with the assumption of ideal dynamics of two players 17) was investigated and later extended to include first-order pursuer dynamics 18) and evader dynamics. 19) Two formulations 20) are studied for the linear-quadratic differential game associated with a trajectory-shaped interception phase of the interceptor. In recent papers, [7][8][9][10][11] the direct lift was taken into account by using a first-order biproper transfer function (TF).…”

Section: Introductionmentioning

confidence: 99%

Bounded Linear-Quadratic Differential Game Guidance Law for Dual-Thruster Controlled Missiles

Liu

Lü

et al. 2012

Trans. Japan Soc. Aero. S Sci.

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A guidance law tailored for an interceptor missile steered by aerodynamic lift and divert-thruster and with its attitude oriented by forward attitude-thruster (dual-thruster control) is proposed. The bang-bang strategy has the maximal capture zone. However, it leads to control chattering, resulting in excessive control effort. The continuous strategies have smaller capture zones, but can require a smaller control effort. The combination of bang-bang and continuous strategies may lead to a cooperative effect of the capture zone and control effort. In this paper, the guidance law is derived using a linearquadratic differential game formulation and then modified for bounded controls. For the derivation, the interceptor closed-loop dynamics is represented by a first-order biproper transfer function for the attitude-thruster control system and a strictly proper one for the divert-thruster control system, respectively. Analysis based on the proposed guidance law shows that the divert-thruster control system has higher efficiency due to its small time constant and the direct forces that mainly affect the short-term behavior of the missiles. The parameters' effects and the control command distribution are also studied.

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A linear differential game with bounded controls and two information delays

Glizer

Turetsky

2008

Optim Control Appl Methods

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The problem of intercepting a maneuvering target by a guided interceptor is considered. It is assumed that the interceptor gets the information on the relative velocity and the target lateral acceleration with time delays. This problem is formulated as a zero-sum differential game with information delays. By using the uncertainty set concept, this differential game is transformed to a new perfect information differential game with a delayed dynamics. The solution of this game is derived, yielding the interception strategy. Illustrative examples are presented.

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Solution Techniques for Realistic Pursuit-Evasion Games

Cited by 125 publications

References 23 publications

Increasing Pursuer Capturability by Using Hybrid Dynamics

Increasing Pursuer Capturability by Using Hybrid Dynamics

Bounded Linear-Quadratic Differential Game Guidance Law for Dual-Thruster Controlled Missiles

A linear differential game with bounded controls and two information delays

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