Fast and accurate method for computing non-smooth solutions to constrained control problems
| Autor: | Lucian Nita, Eduardo M. G. Vila, Marta A. Zagorowska, Eric C. Kerrigan, Yuanbo Nie, Ian McInerney, Paola Falugi |
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| Přispěvatelé: | Engineering & Physical Science Research Council (E |
| Rok vydání: | 2022 |
| Předmět: |
Computer Science::Graphics
Optimization and Control (math.OC) FOS: Mathematics FOS: Electrical engineering electronic engineering information engineering Systems and Control (eess.SY) Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control ComputingMethodologies_COMPUTERGRAPHICS Mathematics::Numerical Analysis |
| Zdroj: | European Control Conference |
| DOI: | 10.23919/ecc55457.2022.9838569 |
| Popis: | Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh. Comment: 6 pages, 4 figures, Accepted to 20th European Control Conference (ECC 2022) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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