Learning to Boost the Performance of Stable Nonlinear Systems
The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Open Journal of Control Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/10633771/ |
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| author | Luca Furieri Clara Lucia Galimberti Giancarlo Ferrari-Trecate |
| author_facet | Luca Furieri Clara Lucia Galimberti Giancarlo Ferrari-Trecate |
| author_sort | Luca Furieri |
| collection | DOAJ |
| description | The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over specific classes of deep neural network performance-boosting controllers for stable nonlinear systems; crucially, we guarantee <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> closed-loop stability even if optimization is halted prematurely. When the ground-truth dynamics are uncertain, we learn over robustly stabilizing control policies. Our robustness result is tight, in the sense that all stabilizing policies are recovered as the <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> -gain of the model mismatch operator is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments. |
| format | Article |
| id | doaj-art-71bd8993ce954cd19a7aa25a2ed76f9d |
| institution | Kabale University |
| issn | 2694-085X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj-art-71bd8993ce954cd19a7aa25a2ed76f9d2025-02-08T00:00:22ZengIEEEIEEE Open Journal of Control Systems2694-085X2024-01-01334235710.1109/OJCSYS.2024.344176810633771Learning to Boost the Performance of Stable Nonlinear SystemsLuca Furieri0https://orcid.org/0000-0001-6103-4480Clara Lucia Galimberti1https://orcid.org/0000-0003-0700-6811Giancarlo Ferrari-Trecate2https://orcid.org/0000-0002-9492-9624École Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandÉcole Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandÉcole Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandThe growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over specific classes of deep neural network performance-boosting controllers for stable nonlinear systems; crucially, we guarantee <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> closed-loop stability even if optimization is halted prematurely. When the ground-truth dynamics are uncertain, we learn over robustly stabilizing control policies. Our robustness result is tight, in the sense that all stabilizing policies are recovered as the <inline-formula><tex-math notation="LaTeX">$\mathcal {L}_{p}$</tex-math></inline-formula> -gain of the model mismatch operator is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments.https://ieeexplore.ieee.org/document/10633771/Closed-loop stabilitydistributed controlinternal model controllearning for controloptimal controluncertain systems |
| spellingShingle | Luca Furieri Clara Lucia Galimberti Giancarlo Ferrari-Trecate Learning to Boost the Performance of Stable Nonlinear Systems IEEE Open Journal of Control Systems Closed-loop stability distributed control internal model control learning for control optimal control uncertain systems |
| title | Learning to Boost the Performance of Stable Nonlinear Systems |
| title_full | Learning to Boost the Performance of Stable Nonlinear Systems |
| title_fullStr | Learning to Boost the Performance of Stable Nonlinear Systems |
| title_full_unstemmed | Learning to Boost the Performance of Stable Nonlinear Systems |
| title_short | Learning to Boost the Performance of Stable Nonlinear Systems |
| title_sort | learning to boost the performance of stable nonlinear systems |
| topic | Closed-loop stability distributed control internal model control learning for control optimal control uncertain systems |
| url | https://ieeexplore.ieee.org/document/10633771/ |
| work_keys_str_mv | AT lucafurieri learningtoboosttheperformanceofstablenonlinearsystems AT claraluciagalimberti learningtoboosttheperformanceofstablenonlinearsystems AT giancarloferraritrecate learningtoboosttheperformanceofstablenonlinearsystems |