Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds

Fuente: arXiv
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Main Authors: Ramesh, Nikilesh, Drummond, Ross, Monasterios, Pablo Rodolfo Baldivieso, Nie, Yuanbo
Format: Preprint
Published: 2025
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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
id 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