Optimal evasive tactics against a proportional navigation missile with time delay.

Slater, Gary W.; Wells, W. R.

doi:10.2514/3.27759

Cited by 49 publications

(6 citation statements)

References 3 publications

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“…(4). Equations (1)(2)(3)(4)(5)(6)(7)(8) are called EulerLagrange equations. For an extremum, the differential change of the performance index J must be zero for arbitrary differential change of ut: ut, that is, the following condition of optimality has to be satisfied:…”

Section: Equations For Nonlinear Optimal Control Problemsmentioning

confidence: 99%

“…In a oneon-one engagement, and supposing one has achieved an advantageous position to another and has caught the enemy in his lethal cone, he has to employ his missiles most effectively. Many studies have appeared about optimal missile avoidance by an aircraft [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], however, only a few papers have treated avoiding multiple missiles [12,18]. The reason for this could be that it is difficult for an aircraft to avoid even one missile, therefore avoiding two missiles is not realistic.…”

Section: Introductionmentioning

confidence: 99%

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Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Imado

Kuroda

2011

Journal of Guidance, Control, and Dynamics

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The engagement tactics for two missiles to attack an aircraft are studied. A tail chase scenario between two aircraft is assumed where the attacker tries to kill the evader with two missiles, while the evader employs optimal maneuvers for avoiding two missiles. The algorithm to solve this optimal control problem is first developed. For the aircraft, in order to simultaneously maximize the miss distances against two missiles, a special type of performance index is introduced and the problems are solved by the solver based on the steepest ascent method. The result shows that the aircraft optimal maneuvers are divided into three patterns. Next, the optimal timing for the attacker to launch the two missiles, in order to minimize both miss distances against the aircraft is studied. The effect of their taking trajectory shaping is also studied. Nomenclature= missile navigation gain n = power of penalty function p = penalty function for the first missile r = slant range between missile and aircraft r 12 = initial distance between two missiles r 1a = reference value of the slant range between the first missile and aircraft r 1f , r 2f = closest ranges (miss distances) between the aircraft and the first and second missiles, respectively r m = the mean miss distance between two missiles, r 1f :r 2f 1 2 S = reference area T = thrust t = time t e = sustainer burning time t f = interception time t w1 , t w2 = start time and end time of window function u = control vector v = velocity v c = closing velocity w = window function x, y = longitudinal and lateral coordinates x = state vector , 0 = angle-of-attack and zero-lift angle, respectively = adjoint vector = air density , = line-of-sight and azimuth angles, respectively = missile time constant = performance index for minimizing both miss distances = stopping condition = terminal constraints = time derivative Subscripts a = aircraft c = command signal i = ith missile m = missile max, min = maximum and minimum values, respectively

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Section: Equations For Nonlinear Optimal Control Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Imado

Kuroda

2011

Journal of Guidance, Control, and Dynamics

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“…For the PE game problems, the usual method is to linearize the confrontation model, use the method of optimal control [1][2] or the differential game [3] to solve it. Through these algorithms, a certain theoretical solution can be derived.…”

Section: Introductionmentioning

confidence: 99%

The Research on Evasion Strategy of Unpowered Aircraft Based on Deep Reinforcement Learning

Chen

Lei

2022

J. Phys.: Conf. Ser.

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For the pursuit-evasion (PE) game, this paper proposes an evasion strategy with coordinated control of angle of attack, bank angle and body morphing control using deep reinforcement learning. Considering the evasion and ballistic regression of the aircraft, the specified miss distance (SMD) and residual energy are used as the optimization objectives, to acquire the optimal control strategy against the encounter with pursuer in the terminal guidance phase. For the problem of sparse rewards, reward reshaping cannot be performed for this problem, we modify DQN algorithm with the mechanism of Monte-Carlo reinforcement learning to improve the sampling efficiency and realize the end-to-end learning. Finally, the linear analytical solution of the problem based on SMD is analyzed theoretically. With it, the strategy obtained by reinforcement learning is compared and explained.

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“…Therefore, the solutions proposed were obtained by applying different simplifying assumptions and using numerical solution schemes. The typical simplifying assumptions in these studies included: linearization around the collision course [11][12][13]16], two dimensional analysis [11-14, 16, 17], and constant interceptor and target speeds [11][12][13][14]16]. Solving the one-sided optimal control problem numerically, using methods such as steepest descent [10,15], can be done on more realistic models, but does not produce a general evasion strategy like analytical studies.…”

Section: Introductionmentioning

confidence: 99%

“…These target evasion guidance laws can be roughly divided into two categories: those that assume that the target has perfect information on the interceptor's initial conditions and state vector [6][7][8][9][10][11][12][13][14][15][16][17], and those that do not rely on this assumption [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Cooperative Multiple Model Adaptive Guidance for an Aircraft Defending Missile*

Shaferman

Shima

2010

AIAA Guidance, Navigation, and Control Conference

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A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender's missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

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Optimal evasive tactics against a proportional navigation missile with time delay.

Cited by 49 publications

References 3 publications

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

The Research on Evasion Strategy of Unpowered Aircraft Based on Deep Reinforcement Learning

Cooperative Multiple Model Adaptive Guidance for an Aircraft Defending Missile*

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