Optimal guidance strategy for the defense of a non‐manoeuvrable target in 3‐dimensions

Weintraub, Isaac E.; García, Eloy; Pachter, Meir

doi:10.1049/iet-cta.2019.0541

Cited by 22 publications

(18 citation statements)

References 23 publications

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“…The game starts at time t 0 , and terminates when capture occurs: x P = x E . While the AC was originally constructed as a circle 2 [4], for notational simplification, we define it to be the closed disc…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

Dorothy¹,

Maity²,

Shishika³

et al. 2021

Preprint

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This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance region, however, it was unclear whether the evader could reach outside the initial AC without being captured. We construct a pursuit strategy that guarantees the capture of an evader within an arbitrarily close neighborhood of the initial AC. The pursuer strategy is derived by reformulating the game into a nonlinear control problem, and the guarantee holds against any admissible evader strategy. Our result implies that the evader can freely select the capture location, but only inside the initial AC. Therefore, a class of problems, including those where the payoff is determined solely based on the location of capture, are now trivial.

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Section: Resultsmentioning

confidence: 99%

“…The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Government, Department of Defense, or its components 1. For a proof of why this locus is a circle see, e.g.,[4,.…”

mentioning

confidence: 99%

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

Dorothy¹,

Maity²,

Shishika³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Recent works by Hayoun et al 11 Shaferman et al 20 and Weintraub et al 21 focus on the missile‐target engagement where the PE problem is formulated as a differential game with an objective of optimizing the linear quadratic cost functional. The work 11 propose bounded maneuverability of the evader to prove the capture in ZS game whereas Weintraub et al 21 consider an engagement scenario by introducing the defense of a non‐maneuverable agent. Further, this work 21 reveals the inclusion of altitude and dynamics in 3‐dimensions, which is more realistic for the modeling of aerial engagements.…”

Section: Introductionmentioning

confidence: 99%

“…The work 11 propose bounded maneuverability of the evader to prove the capture in ZS game whereas Weintraub et al 21 consider an engagement scenario by introducing the defense of a non‐maneuverable agent. Further, this work 21 reveals the inclusion of altitude and dynamics in 3‐dimensions, which is more realistic for the modeling of aerial engagements.…”

Section: Introductionmentioning

confidence: 99%

Optimal game theoretic solution of the pursuit‐evasion intercept problem using on‐policy reinforcement learning

Kartal

Subbarao

Dogan

et al. 2021

Intl J Robust & Nonlinear

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This article presents a rigorous formulation for the pursuit‐evasion (PE) game when velocity constraints are imposed on agents of the game or players. The game is formulated as an infinite‐horizon problem using a non‐quadratic functional, then sufficient conditions are derived to prove capture in a finite‐time. A novel tracking Hamilton–Jacobi–Isaacs (HJI) equation associated with the non‐quadratic value function is employed, which is solved for Nash equilibrium velocity policies for each agent with arbitrary nonlinear dynamics. In contrast to the existing remedies for proof of capture in PE game, the proposed method does not assume players are moving with their maximum velocities and considers the velocity constraints a priori. Attaining the optimal actions requires the solution of HJI equations online and in real‐time. We overcome this problem by presenting the on‐policy iteration of integral reinforcement learning (IRL) technique. The persistence of excitation for IRL to work is satisfied inherently until capture occurs, at which time the game ends. Furthermore, a nonlinear backstepping control method is proposed to track desired optimal velocity trajectories for players with generalized Newtonian dynamics. Simulation results are provided to show the validity of the proposed methods.

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“…Analogous to [7], some guidance laws for the TMD engagement were numerically studied by solving a differential Riccati equation related to the linear quadratic differential game [13,14]. Pachter et al [15] proposed a defence problem considering a zero-sum three-agent pursuit-evasion differential game, and extend the interception model to three-dimensional scenarios [16]. Separating the incoming missile and the target-defender team into winning regions, Liang in [17] presented solutions to a problem of differential game related to the TMD engagement.…”

Section: Introductionmentioning

confidence: 99%

Model predictive guidance for active aircraft protection from a homing missile

Shi

Chen

Zhu

et al. 2021

IET Control Theory & Appl

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This paper proposes a novel guidance law based on model predictive control for protecting an aircraft from a homing missile. Considering that in the target-missile-defender engagement the attacking missile is pursuing the target aircraft by employing a known linear guidance law, a non-linear predictive model for the engagement is established. This predictive model allows converting the three-body engagement to a one-on-one engagement. The time-to-go for the defender towards the future position of the incoming missile is analytically derived, indicating that the optimal time for the defender to intercept the incoming missile is a fixed-point of a real-valued function. As a result, the optimal interception duration can be obtained by a standard fixed-point iteration method, and thus the interception point can be readily predicted via integrating the predictive model. The guidance command is generated by directly leading the defender to the predicted intercept point. Numerical simulations in different scenarios validate the algorithm to be computationally efficient, and demonstrate that the proposed strategy outperforms previous techniques in terms of miss distance, engagement duration, and the control effort.

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Optimal guidance strategy for the defense of a non‐manoeuvrable target in 3‐dimensions

Cited by 22 publications

References 23 publications

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

Optimal game theoretic solution of the pursuit‐evasion intercept problem using on‐policy reinforcement learning

Model predictive guidance for active aircraft protection from a homing missile

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