Evaluation of Penalty Functions for Optimal Control

Abstract

To handle final state equality constraints, two types of penalty functions are evaluated and compared in solving three optimal control problems. Both the absolute value penalty function and the quadratic penalty function with shifting terms yielded the optimal control policy in each case. The quadratic penalty function with shifting terms gave the optimum more accurately, and the approach to the optimum is less oscillatory than with the use of absolute value penalty function. In solving for the optimal control in the third example, the use of the absolute value penalty function required a series of runs to get the performance index to within 0.035% of the optimum. A further advantage in using the quadratic penalty function is obtaining sensitivity information with respect to the final state constraints from the shifting terms.KeywordsPenalty functionsiterative dynamic programmingoptimal controlstate constraints