The isopone method in optimal control (Q1200598)

The minimum-time problem is a well-known problem in optimal control and several methods are available to solve this problem. In this article an extension of the wave propagation method to solve minimum time problems is discussed. The generalization deals with minimum energy rather than minimum time of trajectories of ships. This optimal control problem will be treated and the so-called isopone method (which is the generalization of the wave propagation method) to determine the optimal control is discussed. In this isopone method, multidimensional reachable sets are computed repeatedly. This method is similar to dynamic programming in that it is a recursive algorithm, but it is designed to reduce the amount of calculation time. The current algorithm yields, as a degenerate case, also the time-optimal route of these ships.