Solving a class of linear optimal control problems with several control variables by the method of orienting curves

Abstract

In this paper, we prove that the Method of Orienting Curves described in [14] can be applied to solve a class of linear optimal control problems with one state and several control variables,and with state constraints. By this method, optimal trajectories of problems in this class can be constructed as a path whichconsists of parts of orienting curves, boundary arcs, and a final curve.

Orienting Method for Obstacle Problems

“…The idea originated from the so-called Method of Orienting Curves which w as developed in [3], [4], [9], [12], and [14] for solving optimal control problems with state constraints. Its application area consists of problems with ordinary dierential equations (i.e.…”