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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.03879 |
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| _version_ | 1866912395794841600 |
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| author | Kazi, Saif R. Wang, Kexin Biegler, Lorenz T. |
| author_facet | Kazi, Saif R. Wang, Kexin Biegler, Lorenz T. |
| contents | Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas-liquid tank model and an optimal control problem with a sliding mode solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Optimal Control of Hybrid Dynamical Systems using Complementarity Constraints Kazi, Saif R. Wang, Kexin Biegler, Lorenz T. Optimization and Control 34A36, 93C30, 90C33, 49M37 Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas-liquid tank model and an optimal control problem with a sliding mode solution. |
| title | On Optimal Control of Hybrid Dynamical Systems using Complementarity Constraints |
| topic | Optimization and Control 34A36, 93C30, 90C33, 49M37 |
| url | https://arxiv.org/abs/2503.03879 |