Optimal planar interception with fixed end conditions: Closed-form solution

A planar constant-speed interception with prescribed end conditions is analyzed. The performance index is the time of capture penalized by the control energy. For this problem, the optimal control of the pursuer is obtained in closed form, based on solving a set of nonlinear algebraic equations involving elliptic integrals. The construction of the solution is inspired by the singularly perturbed structure of the nondimensional equations of motion.

[1]  Rufus Isaacs,et al.  Differential Games , 1965 .

[2]  J. Yong.  Differential pursuit games , 1987, 26th IEEE Conference on Decision and Control.

[3]  Josef Shinar,et al.  An explicit feedback approximation for medium-range interceptions in a vertical plane , 1983 .

[4]  M. Briggs,et al.  Near-optimal midcourse guidance for air-to-air missiles , 1990 .

[5]  A. Ioffe,et al.  Theory of extremal problems , 1979 .

[6]  A. J. Calise,et al.  Piloted simulation of an onboard trajectory optimization algorithm , 1984 .

[7]  A. Calise.  Singular perturbation methods for variational problems in aircraft flight , 1976 .

[8]  Hassan K. Khalil,et al.  Singular perturbations in systems and control , 1986 .

[9]  John C. Clements,et al.  Minimum-time turn trajectories to fly-to-points , 1990 .

[10]  Josef Shinar,et al.  On the structure of a class of time‐optimal trajectories , 1993 .

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

[12]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[13]  Josef Shinar,et al.  Game Optimal Guidance Law Synthesis for Short Range Missiles , 1992 .

[14]  R. M. Howe,et al.  Application of singular perturbation methods for three-dimensional minimum-time interception , 1991 .

[15]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[16]  J. Shinar,et al.  Optimal guidance law in the plane , 1984 .

[17]  D. Hull,et al.  Time-to-go prediction for homing missiles based on minimum-time intercepts , 1991 .

[18]  H. B. Dwight,et al.  Tables of Integrals and Other Mathematical Data , 1934 .

[19]  J. Shinar,et al.  Analysis of Optimal Evasive Maneuvers Based on a Linearized Two-Dimensional Kinematic Model , 1977 .

[20]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[21]  Jiongmin Yong.  Differential pursuit games , 1987 .

[22]  Josef Shinar,et al.  A Highly Accurate Feedback Approximation for Horizontal Variable-Speed Interceptions , 1986 .

[23]  E. Cockayne.  Plane Pursuit with Curvature Constraints , 1967 .