Direct, precise method for optimizing linear systems having multiple inputs (Q1093157)

A method for solving a linear problem in optimal control is presented for a class of piecewise continuous control functions. The continuous system is optimized without quantization. There are terminal constraints on the phase trajectories and polyhedral restrictions are placed on the multidimensionality. The problem is solved by a finite number of integrations of the primal and conjugated systems. The technique does not use the principle of a maximum. The algorithm is direct, precise and relaxational. The method is illustrated by the solution of the optimal control of the motion of two mechanical objects.