Comparative Study of Pontryagin Maximum Principle and Direct Method in Aircraft Optimal Control Design

Abstract

Abstract This paper deals with the problem of open-loop control design for a dynamic object which is described by a nonlinear system of differential equations. To solve this problem a direct method is used, in which the target functional is minimized by population-based algorithm. The method is applied to a test problem which consists of finding optimal control for spacial motion of maneuverable aircraft. Proposed technique is compared with two classical solutions to considered problem. One of them is based on equating to zero the partial control derivatives of the Hamilton function, wherease the other on the Hamilton function maximum over controls (Pontryagin maximum principle). The paper confirms high degree of similarity between solutions obtained by all considered methods of selecting target functional. However, classical algotithms show slightly worse accuracy and higher sensitivity to the quality of initial approximation. In addition, proposed direct method permits to evade the necessity to solve a two–point boundary value problem required in classical algorithms.