Full-State Autopilot-Guidance Design Under a Linear Quadratic Differential Game Formulation

Levy, Maital; Shima, Tal; Gutman, Shaul

doi:10.3182/20140824-6-za-1003.01240

Cited by 3 publications

(7 citation statements)

References 19 publications

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“…where the applicable solution is given by (25). We now proceed to obtain the partial derivatives of the term (25) with respect to each element of the state. In order to simplify the notation we define:…”

Section: B Case: N > Mmentioning

confidence: 99%

“…We note that V s (x) is continuous in R P ι * (∈ R P ), where in the optimal assignment ι * there exists at least one evader E j such that µ ij = µ i ′ j = 1, that is, at least one evader is simultaneously captured by two pursuers. Consequently, there exist at least one term (25) contributing to the Value function. From (25) and the definition of D in (26) we conclude that D = 0 only if x i = x i ′ and y i = y i ′ , that is, the centers of the E j P i and E j P i ′ circles coincide.…”

Section: B Case: N > Mmentioning

confidence: 99%

“…Consequently, there exist at least one term (25) contributing to the Value function. From (25) and the definition of D in (26) we conclude that D = 0 only if x i = x i ′ and y i = y i ′ , that is, the centers of the E j P i and E j P i ′ circles coincide. However, in such a case, the circles do not intersect (except when r i = r i ′ ) 1 and E j is captured by only one pursuer.…”

Section: B Case: N > Mmentioning

confidence: 99%

“…However, in such a case, the circles do not intersect (except when r i = r i ′ ) 1 and E j is captured by only one pursuer. This means that for any {x|x i = x i ′ , y i = y i ′ }, then the term (25) does not contribute to the Value function. Thus, D = 0 for any R P ι * .…”

Section: B Case: N > Mmentioning

confidence: 99%

“…The flexibility of the LQDG formulation for addressing target interception problems by tuning the relevant weights was highlighted in [24]. The recent work in [25] developed a method for intercepting a moving target by formulating a linear quadratic differential game. In this vein, an LQDG for intercepting a missile and protecting a target was addressed in [26].…”

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confidence: 99%

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Multiple Pursuer Multiple Evader Differential Games

García¹,

Casbeer²,

Moll³

et al. 2019

Preprint

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In this paper an N -pursuer vs. M -evader team conflict is studied. The differential game of border defense is addressed and we focus on the game of degree in the region of the state space where the pursuers are able to win. This work extends classical differential game theory to simultaneously address weapon assignments and multi-player pursuit-evasion scenarios. Saddle-point strategies that provide guaranteed performance for each team regardless of the actual strategies implemented by the opponent are devised. The players' optimal strategies require the co-design of cooperative optimal assignments and optimal guidance laws. A representative measure of performance is proposed and the Value function of the game is obtained. It is shown that the Value function is continuous, continuously differentiable, and that it satisfies the Hamilton-Jacobi-Isaacs equation -the curse of dimensionality is overcome and the optimal strategies are obtained. The cases of N = M and N > M are considered. In the latter case, cooperative guidance strategies are also developed in order for the pursuers to exploit their numerical advantage. This work provides a foundation to formally analyze complex and high-dimensional conflicts between teams of N pursuers and M evaders by means of differential game theory. I. INTRODUCTION Differential game theory provides the right framework to analyze pursuit-evasion problems and, as a corollary, combat games. Pursuit-evasion scenarios involving multiple agents are important but challenging problems in aerospace, control, and robotics. Pursuit-evasion problems were first formulated in the seminal work [1]. Concerning many players games, reference [2] addressed the interesting dynamic game of a fast pursuer trying to capture in minimal time two slower evaders in succession. Motivated by the work in [2], the paper [3] analyzed the case where the fast pursuer tries to capture multiple evaders. Reach and avoid differential games which include time-varying dynamics, targets and constraints were addressed in [4] by means of a This work has been supported in part by AFOSR LRIR No. 18RQCOR036.

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Section: B Case: N > Mmentioning

confidence: 99%

Section: B Case: N > Mmentioning

confidence: 99%

Section: B Case: N > Mmentioning

confidence: 99%

Section: B Case: N > Mmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Multiple Pursuer Multiple Evader Differential Games

García¹,

Casbeer²,

Moll³

et al. 2019

Preprint

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Full-state autopilot-guidance design under a linear quadratic differential game formulation

Levy

Shima

Gutman

2018

Control Engineering Practice

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Recursive Regret Matching: A General Method for Solving Time-invariant Nonlinear Zero-sum Differential Games

Liao

Wei

Lai

2020

Preprint

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In this paper, a new method is proposed to compute the rolling Nash equilibrium of the timeinvariant nonlinear two-person zero-sum differential games. The idea is to discretize the time to transform a differential game into a sequential game with several steps, and by introducing statevalue function, transform the sequential game into a recursion consisting of several normal-form games, finally, each normal-form game is solved with action abstraction and regret matching. To improve the real-time property of the proposed method, the state-value function can be kept in memory. This method can deal with the situations that the saddle point exists or does not exist, and the analysises of the existence of the saddle point can be avoided. If the saddle point does not exist, the mixed optimal control pair can be obtained. At the end of this paper, some examples are taken to illustrate the validity of the proposed method.

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Full-State Autopilot-Guidance Design Under a Linear Quadratic Differential Game Formulation

Cited by 3 publications

References 19 publications

Multiple Pursuer Multiple Evader Differential Games

Multiple Pursuer Multiple Evader Differential Games

Full-state autopilot-guidance design under a linear quadratic differential game formulation

Recursive Regret Matching: A General Method for Solving Time-invariant Nonlinear Zero-sum Differential Games

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