Modified SOMA for Optimal Control Problem

This paper is addressed to application of SOMA to the optimal control problem of a group of objects with static and dynamic phase constraints. The optimization problem is not convex and unimodal. In the practical part a synthesized optimal control problem is considered. Firstly, it is necessary to solve a control synthesis problem to stabilize each object relatively a point on the state space. To solve the synthesis problem a network operator method was used. For each control object the coordinates of some stabilization points were found. While moving from point to point in given time interval all objects reach their terminal states without violation of constraints and with optimal quality criterion. A modified SOMA is proposed for the search of stabilization points.