Steepest-Ascent Revisited: Unconstrained Missile Trajectory

Abstract

A Steepest-Ascent numerical procedure for offline trajectory optimization of a surface-to-surface missile attacking a stationary target is presented. A detailed numerical solution, starting from building the mathematical formulation till generating an offline angle of attack control history, is illustrated. A novel approach for guessing a nominal control program is conducted. The formulation entails nonlinear 2-DOF missile flight dynamics with mixed boundary conditions. The technique of changing of variables is adopted to convert the free-final-time optimization problem to a fixed-final-time one. The influences of the optimization algorithm controlling parameters are investigated. A new form of the weighting matrix is proposed. A novel technique of relaxation factors for eliminating the terminal states violation is described. Finally, a comparison between the obtained control history and the one obtained by a nonlinear optimal control package “GPOPS” is presented. The results indicate that the use of Steepest-Ascent method, to a great extent, is comparable in accuracy and iteration time to the pseudospectral optimization package “GPOPS.” This paper, to a great extent, is a detailed procedure for the method of Steepest-Ascent analyzed and verified by the authors from many undetailed sources to disclosure of the main problems faced by user of Steepest-Ascent.