Lossless convexification of non-convex optimal control problems with disjoint semi-continuous inputs
| Autor: | Malyuta, Danylo, Szmuk, Michael, Acikmese, Behcet |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a semi-continuous variable that can be zero or lower- and upper-bounded. Using lossless convexification, the non-convex problem is relaxed to a convex problem whose optimal solution is proved to be optimal almost everywhere for the original problem. The relaxed problem can be solved using second-order cone programming, which is a subclass of convex optimization for which there exist numerically reliable solvers with convergence guarantees and polynomial time complexity. This is the first lossless convexification result for mixed-integer optimization problems. An example of spacecraft docking with a rotating space station corroborates the effectiveness of the approach and features a computation time almost three orders of magnitude shorter than a mixed-integer programming formulation. Comment: 9 pages, 7 figures |
| Databáze: | arXiv |
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