document: A combinatorial , graph-based solution method for a class of continuous-time optimal control problems The paper addresses a class of continuous-time , optimal control problems whose solutions are typically characterized by both bang-bang and `` singular '' control regimes . Analytical study and numerical computation of such solutions are very difficult and far from complete when only techniques from control theory are used . This paper solves optimal control problems by reducing them to the 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 . The proposed solution method is currently limited to single-state problems with multiple control functions . A production planning problem and a train operation problem are optimally solved to illustrate the method
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extractive_keyphrases: numerical computation combinatorial search multiple control functions production planning problem train operation problem
abstractive_keyphrases: continuous-time optimal control problems combinatorial graph-based solution bang-bang control regimes singular control regimes shortest path algorithm single-state problems weighted graph nodes sequence-dependent manner