Fast and accurate method for computing non-smooth solutions to constrained control problems
- Conference Paper
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. Show more
Book title2022 European Control Conference (ECC)
Pages / Article No.
Organisational unit02650 - Institut für Automatik / Automatic Control Laboratory
NotesConference lecture held on July 13, 2022
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