Abstract

We prove that the method of orienting curves described by \textit{H. X. Phu} [Numer. Funct. Anal. Optimization 12, No. 1/2, 173-211 (1991; Zbl 0766.49016)] 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 which consists of parts of orienting curves, boundary arcs, and a final curve.