A numerical scheme for solving optimal control problems

Abstract

METHODS based on variations in the space of states have been applied with success in recent years to solving optimal control problems with contraints on the phase coordinates and on the control functions. The methods were developed in [1–3], where the concept of an elementary operation (EO) was introduced and the walking tube method was used to find the local extremum. A method of local variations was later proposed in [4], in which the variation of the trajectory is performed at each node in succession, by an amount equal to one step. These methods proved especially effective when the number of phase-space dimensions n is not greater than the number of control space dimensions m. In this case no difficulties arise in constructing the EO [3, 4]. The present paper describes a numerical scheme for solving optimal control problems in cases when m⩽ n. When m = n the scheme is the same as the method of local variations.