THE MAXIMUM PRINCIPLE AND COMBINATORICS: A SOLUTION METHOD FOR A CLASS OF OPTIMAL CONTROL PROBLEMS

摘要

This paper proposes a solution method for a class of one-dimensional optimal control problems by reducing them to a combinatorial search for the shortest path in a specially constructed graph. Since the nodes of the graph are weighted in a sequence-dependent manner, we extend the classical, shortest-path algorithm to our case. A train operation problem is optimally solved to illustrate the solution method.