Cyclic coordinate descent in a class of bang-singular-bang problems. (English) Zbl 1321.49010
Summary: In this paper, we study a class of optimal control problems inspired by the hydroelectric context. These problems model a continuous production process with several interrelated pre-set availability inputs in a finite time interval with production functions which are linear with respect to the consumption rate over time. It constitutes a bang-singular-bang control problem, which we solve using a cyclic coordinate descent strategy combined with a suitable adaptation of the shooting method. Finally, the proposed algorithm is implemented using the Mathematica package and applied to a hydraulic optimization problem in which the potential of the algorithm is evidenced.
MSC:
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| 49M25 | Discrete approximations in optimal control |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 49N90 | Applications of optimal control and differential games |
Keywords:
optimal control; bang-singular-bang problems; hydrothermal coordination; cyclic coordinate descent strategy; shooting methodSoftware:
MathematicaReferences:
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