Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910917776637952 |
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| author | Ramesh, Nikilesh Drummond, Ross Monasterios, Pablo Rodolfo Baldivieso Nie, Yuanbo |
| author_facet | Ramesh, Nikilesh Drummond, Ross Monasterios, Pablo Rodolfo Baldivieso Nie, Yuanbo |
| contents | Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires tailored treatments, suitable for offline trajectory optimization. This approach can become increasingly impractical for online closed-loop implementations, especially for large-scale engineering problems. Recent development of Integrated Residual Methods (IRM) have indicated their suitability for handling singular arcs; the convergence of error measures in IRM automatically suppresses singular arc-induced fluctuations and leads to non-fluctuating solutions more suitable for practical problems. Through several examples, we demonstrate the advantages of solving OCPs with singular arcs using {IRM} under an economic model predictive control framework. In particular, the following observations are made: (i) IRM does not require special treatment for singular arcs, (ii) it solves the OCPs reliably with singular arc fluctuation suppressed, and (iii) the closed-loop results closely match the analytic optimal solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds Ramesh, Nikilesh Drummond, Ross Monasterios, Pablo Rodolfo Baldivieso Nie, Yuanbo Optimization and Control Systems and Control Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires tailored treatments, suitable for offline trajectory optimization. This approach can become increasingly impractical for online closed-loop implementations, especially for large-scale engineering problems. Recent development of Integrated Residual Methods (IRM) have indicated their suitability for handling singular arcs; the convergence of error measures in IRM automatically suppresses singular arc-induced fluctuations and leads to non-fluctuating solutions more suitable for practical problems. Through several examples, we demonstrate the advantages of solving OCPs with singular arcs using {IRM} under an economic model predictive control framework. In particular, the following observations are made: (i) IRM does not require special treatment for singular arcs, (ii) it solves the OCPs reliably with singular arc fluctuation suppressed, and (iii) the closed-loop results closely match the analytic optimal solutions. |
| title | Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2504.17093 |