Simple-motion pursuit-evasion differential games, part 2: Optimal evasion from proportional navigation guidance in the deterministic and stochastic cases

Pachter, Meir; Yavin, Y.

doi:10.1007/bf00938605

Cited by 10 publications

(2 citation statements)

References 5 publications

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“…GTs with a moving guide can also be found in a problem with a team of unmanned aerial and ground vehicles pursuing another team of evaders [23]. Modeling GTs with a moving guide is important in guidance, homing, and interception in aerospace applications [24]- [26]. An example is a moving object intercepting another moving object.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling

Rezaie¹,

Li²

2021

Preprint

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A trajectory of a destination-directed moving object (e.g. an aircraft from an origin airport to a destination airport) has three main components: an origin, a destination, and motion in between. We call such a trajectory that end up at the destination destination-directed trajectory (DDT). A class of conditionally Markov (CM) sequences (called CML) has the following main components: a joint density of two endpoints and a Markovlike evolution law. A CML dynamic model can describe the evolution of a DDT but not of a guided object chasing a moving guide. The trajectory of a guided object is called a guided trajectory (GT). Inspired by a CML model, this paper proposes a model for a GT with a moving guide. The proposed model reduces to a CML model if the guide is not moving. We also study filtering and trajectory prediction based on the proposed model. Simulation results are presented.

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Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling

Rezaie¹,

Li²

2021

Preprint

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“…In this work, we design feedback control laws that enforce capture of a moving target by a slower pursuer in finite time provided that the pursuer emanates from a set of ‘favorable’ initial conditions, which constitute its winning set . It is well known that a pursuit‐evasion game involving two antagonistic players with simple motion can never be concluded in favor of a slower pursuer provided that both players employ optimal feedback strategies in the sense of Isaacs . In this work, in order to allow for the possibility of capture of the target by a slower pursuer, we will assume that the pursuer has an informational advantage.…”

Section: Introductionmentioning

confidence: 99%

On the finite‐time capture of a fast moving target

Bakolas

2016

Optim Control Appl Methods

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Summary In this work, we propose a feedback control law that enforces capture of a moving target by a slower pursuer in finite time. It is well known that if this problem is cast as a pursuit‐evasion differential game, then the moving target can always avoid capture by taking advantage of its speed superiority, provided that both the target and the pursuer are employing feedback strategies in the sense of Isaacs. Thus, in order to have a well‐posed pursuit problem, additional assumptions are required so that the pursuer can enforce capture of the faster target in finite time provided that it emanates from a set of ‘favorable’ initial positions, which constitute its winning set. In particular, we assume that the target's velocity either is constant and perfectly known to the pursuer (perfect information case) or can be decomposed into a dominant component, which is constant and known to the pursuer, and a second component that is uncertain and unknown to the pursuer (imperfect information case). It turns out that in both cases, the winning sets of the pursuer are pointed convex cones which have a common apex and a common axis of symmetry but different opening angles. We subsequently propose continuous feedback laws that enforce finite‐time capture while the pursuer never exits its winning set before capture takes place, for both cases. Copyright © 2016 John Wiley & Sons, Ltd.

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Optimal Rendezvous with Proportional Navigation Unmanned Aerial Vehicle

Cherkasov

Makieva

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Simple-motion pursuit-evasion differential games, part 2: Optimal evasion from proportional navigation guidance in the deterministic and stochastic cases

Cited by 10 publications

References 5 publications

Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling

Mathematical Modeling of Guidance Trajectory with a Moving Destination Using Conditionally Markov Modeling

On the finite‐time capture of a fast moving target

Optimal Rendezvous with Proportional Navigation Unmanned Aerial Vehicle

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