Continuous-time constrained linear quadratic regulator for switched linear systems
Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for s...
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| Vydané v: | Nonlinear analysis. Hybrid systems Ročník 58; s. 101625 |
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| Médium: | Journal Article |
| Jazyk: | English |
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01.11.2025
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| ISSN: | 1751-570X |
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| Abstract | Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications.
•The considered LQR optimizes control inputs and switching instants.•Time partitioning is crucial for the problem reformulation.•Parameterizing the switching sequence reduces the complexity against standard methods.•Offline pre-calculation of shared terms reduces numerical computational load. |
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| AbstractList | Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications.
•The considered LQR optimizes control inputs and switching instants.•Time partitioning is crucial for the problem reformulation.•Parameterizing the switching sequence reduces the complexity against standard methods.•Offline pre-calculation of shared terms reduces numerical computational load. |
| ArticleNumber | 101625 |
| Author | Gori, Pietro Pierallini, Michele Angelini, Franco Garabini, Manolo |
| Author_xml | – sequence: 1 givenname: Pietro orcidid: 0009-0002-4989-321X surname: Gori fullname: Gori, Pietro email: pietro.gori@phd.unipi.it – sequence: 2 givenname: Michele orcidid: 0000-0003-0547-2747 surname: Pierallini fullname: Pierallini, Michele email: michele.pierallini@phd.unipi.it – sequence: 3 givenname: Franco orcidid: 0000-0003-2559-9569 surname: Angelini fullname: Angelini, Franco email: frncangelini@gmail.com – sequence: 4 givenname: Manolo orcidid: 0000-0002-5873-3173 surname: Garabini fullname: Garabini, Manolo email: manolo.garabini@gmail.com |
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| Cites_doi | 10.1007/s10626-014-0187-5 10.1007/s10626-014-0198-2 10.1109/ACC.2012.6314919 10.1137/16M1070530 10.1109/TAI.2022.3225366 10.1109/9.704994 10.1186/s13660-024-03124-2 10.1016/j.automatica.2021.109548 10.1007/s10957-014-0533-7 10.1109/TAC.2005.861711 10.1109/TAC.2011.2174694 10.1016/j.automatica.2022.110565 10.1007/s40305-013-0021-z 10.1007/s12532-018-0139-4 10.1080/0020717021000023825 10.1109/CDC.2016.7799384 10.1080/01691864.2023.2168134 10.1109/TAC.2018.2872204 10.1016/j.nahs.2006.10.007 10.1016/j.jfranklin.2019.05.020 10.1016/j.automatica.2023.111456 10.1007/s10107-004-0559-y 10.1007/s10957-007-9305-y 10.1109/TAC.2017.2697681 10.1109/TAC.1978.1101743 |
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| Keywords | Switched systems Linear systems Nonlinear programming Optimal control |
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| Snippet | Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent... |
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| StartPage | 101625 |
| SubjectTerms | Linear systems Nonlinear programming Optimal control Switched systems |
| Title | Continuous-time constrained linear quadratic regulator for switched linear systems |
| URI | https://dx.doi.org/10.1016/j.nahs.2025.101625 |
| Volume | 58 |
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