Hybrid optimal control with mixed-integer Lagrangian methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918022426394624 |
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| author | Nikitina, Viktoriya De Marchi, Alberto Gerdts, Matthias |
| author_facet | Nikitina, Viktoriya De Marchi, Alberto Gerdts, Matthias |
| contents | Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to decomposition techniques, does not require relaxing the integrality constraints. Based on the discretize-then-optimize approach, our scheme addresses mixed-integer nonlinear problems under mild assumptions. The proposed numerical algorithm builds upon the augmented Lagrangian framework, whose subproblems are handled using successive mixed-integer linearizations with trust regions. We validate the performance of the numerical routine with extensive investigations using hybrid optimal control problems from different fields of application. Promising preliminary results are presented for a motion planning task with hysteresis and a Lotka-Volterra fishing problem with total variation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid optimal control with mixed-integer Lagrangian methods Nikitina, Viktoriya De Marchi, Alberto Gerdts, Matthias Optimization and Control 65K05, 90C06, 90C11, 90C30 Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to decomposition techniques, does not require relaxing the integrality constraints. Based on the discretize-then-optimize approach, our scheme addresses mixed-integer nonlinear problems under mild assumptions. The proposed numerical algorithm builds upon the augmented Lagrangian framework, whose subproblems are handled using successive mixed-integer linearizations with trust regions. We validate the performance of the numerical routine with extensive investigations using hybrid optimal control problems from different fields of application. Promising preliminary results are presented for a motion planning task with hysteresis and a Lotka-Volterra fishing problem with total variation. |
| title | Hybrid optimal control with mixed-integer Lagrangian methods |
| topic | Optimization and Control 65K05, 90C06, 90C11, 90C30 |
| url | https://arxiv.org/abs/2403.06842 |