The effects of non‐linear kinematics in optimal evasion

A comparative study of evasive strategies of an aircraft against a missile with fixed, gravity-limited, proportional navigation is conducted for both subsonic and supersonic confrontations. A complete point-mass aircraft model and a variable-mass missile model that includes missile dynamics are used. No linearization is required in the analysis, and all motion is constrained to a horizontal plane. Sequential quadratic programming is used to solve the optimal control problem. Numerical results are presented for an early model of the F-4 fighter aircraft. In particular, the effects of varying the aircraft/missile initial velocity ratio, the missile initial heading angle, and the missile guidance time constant are determined.

Section: Introductionmentioning

confidence: 93%

Optimal planar evasive aircraft maneuvers against proportional navigation missiles

Ong¹,

Pierson

1996

“…(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%

Engagement Tactics for Two Missiles Against an Optimally Maneuvering Aircraft

Imado

Kuroda

2011

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

“…ln order to maximize the closest approach of the pursuers we need to take the results from the 45 degree line on which the two miss~distances are the same. ln removing the third assumption, which allowed us to linearize the state equations, we get either a 'bang-bang' type of solution [2], [4], [8] or a singular behavi0r.ln general, the computations are signiticantly more involved.…”

Section: Problem Formulationmentioning

confidence: 99%

Optimal evasion against a proportionally guided pursuer

Cliff

Ben-Asher

1989

Aerospace and Ocean Engineering (ABSTRACT)We consider the problem of optimal evasion when the pursuer is known to employ fixed gain proportional navigation . The performance index is a mcasure of closest approach. The analysis is done for planar motions at constant speed . The kinematics are first linearized around a nominal eollision course. The dynamics of the opponents are modeled by first order systems and their accelerations may be bounded.Three cases are studied : unconstrained optimal evasion ( where the evader is not subjected to any path constraint ) against a single pursuer, optimal evasion with a terminal path angle constraint for the evader and optimal evasion against more than one pursuer.The optimal controls are shown to be 'bang -bang' with the number of switches depending on the pursuer's navigation gain and on the particular constraints of each case.