Abstract
Optimal Control Problems (OCP) consist in optimising an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation is discretised in time. In particular, we analyse a OCP with a quadratic functional and linear ODE, discretised with Mid-point and implicit Euler. We show that the numerical stability and the presence of numerical oscillations depends not only on the time-step size, but also on the parameters of the objective functional, which measures the amount of control input. Finally, we also show with an illustrative example that these results also carry over non-linear optimal control problems.
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Acknowledgements
This work is financially supported by the Spanish Ministry of Science and Innovation, under Severo Ochoa program CEX2018-000797-S, and the research project DynAd2, with reference PID2020-116141GB-I00.
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Bijalwan, A., Muñoz, J.J. (2024). On the Numerical Stability of Discretised Optimal Control Problems. In: Nachbagauer, K., Held, A. (eds) Optimal Design and Control of Multibody Systems. IUTAM 2022. IUTAM Bookseries, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-031-50000-8_13
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DOI: https://doi.org/10.1007/978-3-031-50000-8_13
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