Augmented Neural Lyapunov Control
Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws a...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10171339/ |
| _version_ | 1797782829970489344 |
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| author | Davide Grande Andrea Peruffo Enrico Anderlini Georgios Salavasidis |
| author_facet | Davide Grande Andrea Peruffo Enrico Anderlini Georgios Salavasidis |
| author_sort | Davide Grande |
| collection | DOAJ |
| description | Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an <italic>Augmented</italic> NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: <uri>https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control</uri>. |
| first_indexed | 2024-03-13T00:17:28Z |
| format | Article |
| id | doaj.art-8329f8a68f75446aa736bf6228b0cf3e |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T00:17:28Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-8329f8a68f75446aa736bf6228b0cf3e2023-07-11T23:00:38ZengIEEEIEEE Access2169-35362023-01-0111679796798610.1109/ACCESS.2023.329134910171339Augmented Neural Lyapunov ControlDavide Grande0https://orcid.org/0000-0002-4936-6797Andrea Peruffo1https://orcid.org/0000-0002-7767-2935Enrico Anderlini2https://orcid.org/0000-0002-8860-8330Georgios Salavasidis3https://orcid.org/0000-0002-0716-6682Department of Mechanical Engineering, University College London, London, U.KMechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The NetherlandsDepartment of Mechanical Engineering, University College London, London, U.KNational Oceanography Centre, Southampton, U.KMachine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approach combines Artificial Neural Networks (ANNs) with Satisfiability Modulo Theories (SMT) solvers to synthesise stabilising control laws and to prove their formal correctness. The ANNs are trained over a dataset of state-space samples to generate candidate control and Lyapunov functions, while the SMT solvers are tasked with certifying the correctness of the Lyapunov function over a continuous domain or by returning a counterexample. Despite the approach’s attractiveness, issues can occur due to subsequent calls of the SMT module at times returning similar counterexamples, which can turn out to be uninformative and may lead to dataset overfitting. Additionally, the control network weights are usually initialised with pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. To properly perform the initialisation requires user time and control expertise. In this work, we present an <italic>Augmented</italic> NLC method that mitigates these drawbacks, removes the need for the control initialisation and further improves counterexample generation. As a result, the proposed method allows the synthesis of nonlinear (as well as linear) control laws with the sole requirement being the knowledge of the system dynamics. The ANLC is tested over challenging benchmarks such as the Lorenz attractor and outperformed existing methods in terms of successful synthesis rate. The developed framework is released open-source at: <uri>https://github.com/grande-dev/Augmented-Neural-Lyapunov-Control</uri>.https://ieeexplore.ieee.org/document/10171339/Computer-aided control designLyapunov methodsneural networks |
| spellingShingle | Davide Grande Andrea Peruffo Enrico Anderlini Georgios Salavasidis Augmented Neural Lyapunov Control IEEE Access Computer-aided control design Lyapunov methods neural networks |
| title | Augmented Neural Lyapunov Control |
| title_full | Augmented Neural Lyapunov Control |
| title_fullStr | Augmented Neural Lyapunov Control |
| title_full_unstemmed | Augmented Neural Lyapunov Control |
| title_short | Augmented Neural Lyapunov Control |
| title_sort | augmented neural lyapunov control |
| topic | Computer-aided control design Lyapunov methods neural networks |
| url | https://ieeexplore.ieee.org/document/10171339/ |
| work_keys_str_mv | AT davidegrande augmentedneurallyapunovcontrol AT andreaperuffo augmentedneurallyapunovcontrol AT enricoanderlini augmentedneurallyapunovcontrol AT georgiossalavasidis augmentedneurallyapunovcontrol |