TOWARD GLOBAL OPTIMIZATION OF A DIFFICULT OPTIMAL CONTROL PROBLEM

Abstract

The optimal control problem introduced in 1980 by Yeo exhibits numerous local optima which have not been reported in the literature. When 50 time stages of equal length are used, there are only two local optima. When 80 time stages are taken, there are over 50 local optima. It was found that there are at least 15 local optima which are better than the one reported in the literature as the global optimum. With the use of 100 time stages of equal length, the number of local optima is increased substantially to over 150. With 100 time stages of equal length, the global optimum solution found with iterative dynamic programming (IDP) gives I=0.119044. This value of the performance index is 0.2% better than the value that had been accepted in the literature as the global optimum. IDP provides a good means of getting the global optimum solution for this problem, but numerous runs are necessary due to the presence of a large number of local optima.