Optimal Fighter Pursuit-Evasion Maneuvers Found via Two-Sided Optimization

An optimal pursuit-evasion fighter maneuver is formulated as a differential game and then solved by a recently developed numerical method, semidirect collocation with nonlinear programming. In this method, the optimal control for one player is found numerically, that is, by the optimizer, but that for the other player is based on the analytical necessary conditions of the problem. Because this requires costate variables for one player, the method is not a direct method. However, the problem can be placed in the form of conventional collocation with nonlinear programming. Thus, it is referred to it as a semidirect method. A genetic algorithm is used to provide an approximate solution, an initial guess, for the nonlinear programming problem solver. The method is applied to the challenging problem of optimal fighter aircraft pursuit-evasion in three dimensions. The obtained optimal trajectories are identified as having two phases: first a rapid change, primarily in direction, followed by a period of primarily vertical maneuvering. Solutions for various initial positions and velocities of the evader aircraft with respect to the pursuer are determined.

[1]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[2]  A. L. Herman,et al.  Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules , 1996 .

[3]  P. Enright.  Optimal finite-thrust space craft trajectories using direct transcription and nonlinear programming , 1991 .

[4]  J. Shinar,et al.  Qualitative study of a planar pursuit evasion game in the atmosphere , 1990 .

[5]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[6]  Bruce A. Conway,et al.  Genetic Algorithm Preprocessing for Numerical Solution of Differential Games Problems , 2004 .

[7]  B. Jarmark,et al.  Pursuit-evasion between two realistic aircraft , 1984 .

[8]  A. W. Merz,et al.  Minimum Required Capture Radius in a Coplanar Model of the Aerial Combat Problem , 1977 .

[9]  H. J. Pesch,et al.  Complex differential games of pursuit-evasion type with state constraints, part 2: Numerical computation of optimal open-loop strategies , 1993 .

[10]  H. J. Pesch,et al.  Three-Dimensional Air Combat: Numerical Solution of Complex Differential Games , 1995 .

[11]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[12]  Albert Lee Herman.  Improved collocation methods with application to direct trajectory optimization , 1995 .

[13]  Bruce A. Conway,et al.  Optimal, Low-Thrust, Earth-Moon Orbit Transfer , 1998 .

[14]  Bruce A. Conway,et al.  Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming , 1991 .

[15]  H. J. Pesch,et al.  Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies , 1993 .

[16]  Kazuhiro Horie.  Collocation With Nonlinear Programming for Two-Sided Flight Path Optimization , 2002 .

[17]  A. W. Merz,et al.  The variable-speed tail-chase aerial combat problem , 1981 .

[18]  Bruce A. Conway,et al.  Discrete approximations to optimal trajectories using direct transcription and nonlinear programming , 1992 .

[19]  J. B. Cruz,et al.  Nonclassical control problems and Stackelberg games , 1979 .

[20]  Anil V. Rao,et al.  Practical Methods for Optimal Control Using Nonlinear Programming , 1987 .

[21]  L. T. Nguyen,et al.  Simulator study of the effectiveness of an automatic control system designed to improve the high-angle-of-attack characteristics of a fighter airplane , 1976 .

[22]  Harri Ehtamo,et al.  Visual Aircraft Identification as a Pursuit-Evasion Game , 2000 .