OPTIMAL CONTROL PROBLEMS WITH CONSTRAINTED CONDITIONS AT BOTH ENDS OF THE TRAJECTORY
轨綫两端均受限制时的最优控制问題

In this paper the problems of minimal time control are studied by using the method in 4] for the case when both ends of the trajectory are constrained by some giving manifolds. The necessary and sufficient conditions for optimality are obtained. The boundary conditions of the related systems of differential equations are determined and their geometrical senses, i.e. the transversality conditions, are explained. In addition, the characteristics of the Lagrange multipliers used in this paper are discussed.The method may also be applied to the optimal control problems with constrained conditions at both ends in general sense.