Article ID: | iaor2000993 |
Country: | United Kingdom |
Volume: | 19 |
Issue: | 3 |
Start Page Number: | 185 |
End Page Number: | 203 |
Publication Date: | May 1998 |
Journal: | Optimal Control Applications & Methods |
Authors: | Feichtinger Gustav, Maurer H., Bskens C.H. |
Keywords: | production |
Two numerical techniques for solving optimal periodic control problems with a free period are developed. The first method uses shooting techniques for solving an appropriate boundary value problem associated with the necessary conditions of the minimum principle. A convenient form of the transversality condition for the free period is incorporated. The second method is a direct optimization method that applies non-linear programming techniques to a discretized version of the control problem. Both numerical methods are illustrated in detail by a non-convex economic production planning problem. In this model, the π-test reveals that the steady-state operation is not optimal. The optimal periodic control is computed such that a complete set of necessary conditions is verified. The solution techniques are extended to obtain the optimal periodic control under various state constraints. A sensitivity analysis of the optimal solution is performed with respect to a specific parameter in the model.