Solution techniques for periodic control problems: a case study in production planning
✍ Scribed by H. Maurer; Ch. Büskens; G. Feichtinger
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 161 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0143-2087
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✦ Synopsis
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 -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.