Multilevel Selective Harmonic Modulation via optimal control
| dc.contributor.author | Biccari, Umberto | |
| dc.contributor.author | Esteve Yagüe, Carlos | |
| dc.contributor.author | Oroya-Villalta, Deyviss Jesús | |
| dc.date.accessioned | 2024-12-12T10:40:25Z | |
| dc.date.available | 2024-12-12T10:40:25Z | |
| dc.date.issued | 2022 | |
| dc.date.updated | 2024-12-12T10:40:24Z | |
| dc.description.abstract | We consider the Selective Harmonic Modulation (SHM) problem, consisting in the design of a staircase control signal with some prescribed frequency components. In this work, we propose a novel methodology to address SHM as an optimal control problem in which the admissible controls are piecewise constant functions, taking values only in a given finite set. In order to fulfill this constraint, we introduce a cost functional with piecewise affine penalization for the control, which, by means of Pontryagin’s maximum principle, makes the optimal control have the desired staircase form. Moreover, the addition of the penalization term for the control provides uniqueness and continuity of the solution with respect to the target frequencies. Another advantage of our approach is that the number of switching angles and the waveform need not be determined a priori. Indeed, the solution to the optimal control problem is the entire control signal, and therefore, it determines the waveform and the location of the switches. We also provide numerical examples in which the SHM problem is solved by means of our approach. | en |
| dc.description.sponsorship | This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement NO: 694126-DyCon). The work of U.B. is partially supported by the Elkartek grant KK-2020/00091 CONVADP of the Basque government, by the Air Force Office of Scientific Research (AFOSR) under Award NO: FA9550-18-1-0242 and by the Grant PID2020-112617GB-C22 KILEARN of MINECO (Spain) | en |
| dc.identifier.citation | Biccari, U., Esteve-Yagüe, C., & Oroya-Villalta, D. J. (2022). Multilevel Selective Harmonic Modulation via Optimal Control. Applied Mathematics and Optimization, 86(3). https://doi.org/10.1007/S00245-022-09917-5 | |
| dc.identifier.doi | 10.1007/S00245-022-09917-5 | |
| dc.identifier.eissn | 1432-0606 | |
| dc.identifier.issn | 0095-4616 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.14454/2160 | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.rights | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 | |
| dc.subject.other | Optimal control theory | |
| dc.subject.other | Piecewise affine penalization | |
| dc.subject.other | Selective harmonic modulation | |
| dc.subject.other | Switching controllers | |
| dc.title | Multilevel Selective Harmonic Modulation via optimal control | en |
| dc.type | journal article | |
| dcterms.accessRights | metadata only access | |
| oaire.citation.issue | 3 | |
| oaire.citation.title | Applied Mathematics and Optimization | |
| oaire.citation.volume | 86 |