Jones, M. orcid.org/0000-0003-1803-4447, Nie, Y. and Peet, M.M. (2024) Model predictive bang-bang controller synthesis via approximate value functions. In: Sepulchre, R. and Smith, M.C., (eds.) IFAC-PapersOnLine. 26th International Symposium on Mathematical Theory of Networks and Systems MTNS 2024, 19-23 Aug 2024, Cambridge, United Kingdom. Elsevier BV , pp. 127-132.
Abstract
In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-Bellman (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Except as otherwise noted, this author-accepted version of a paper published in IFAC-PapersOnLine is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ © 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Non-smooth and discontinuous optimal control problems; Nonlinear predictive control; Generalized solutions of Hamilton-Jacobi equations; Systems with saturation; Discontinuous control |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > School of Electrical and Electronic Engineering |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Jan 2025 08:37 |
Last Modified: | 16 Jan 2025 08:37 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.ifacol.2024.10.125 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221905 |
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