Synthesizing Control Lyapunov-Value Functions for High-Dimensional Systems Using System Decomposition and Admissible Control Sets
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910395961180160 |
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| author | Gong, Zheng Jeong, Hyun Joe Herbert, Sylvia |
| author_facet | Gong, Zheng Jeong, Hyun Joe Herbert, Sylvia |
| contents | Control Lyapunov functions (CLFs) play a vital role in modern control applications, but finding them remains a problem. Recently, the control Lyapunov-value function (CLVF) and robust CLVF have been proposed as solutions for nonlinear time-invariant systems with bounded control and disturbance. However, the CLVF suffers from the ''curse of dimensionality,'' which hinders its application to practical high-dimensional systems. In this paper, we propose a method to decompose systems of a particular coupled nonlinear structure, in order to solve for the CLVF in each low-dimensional subsystem. We then reconstruct the full-dimensional CLVF and provide sufficient conditions for when this reconstruction is exact. Moreover, a point-wise optimal controller can be obtained using a quadratic program. We also show that when the exact reconstruction is impossible, the subsystems' CLVFs and their ``admissible control sets'' can be used to generate a Lipschitz continuous CLF. We provide several numerical examples to validate the theory and show computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synthesizing Control Lyapunov-Value Functions for High-Dimensional Systems Using System Decomposition and Admissible Control Sets Gong, Zheng Jeong, Hyun Joe Herbert, Sylvia Optimization and Control Systems and Control Control Lyapunov functions (CLFs) play a vital role in modern control applications, but finding them remains a problem. Recently, the control Lyapunov-value function (CLVF) and robust CLVF have been proposed as solutions for nonlinear time-invariant systems with bounded control and disturbance. However, the CLVF suffers from the ''curse of dimensionality,'' which hinders its application to practical high-dimensional systems. In this paper, we propose a method to decompose systems of a particular coupled nonlinear structure, in order to solve for the CLVF in each low-dimensional subsystem. We then reconstruct the full-dimensional CLVF and provide sufficient conditions for when this reconstruction is exact. Moreover, a point-wise optimal controller can be obtained using a quadratic program. We also show that when the exact reconstruction is impossible, the subsystems' CLVFs and their ``admissible control sets'' can be used to generate a Lipschitz continuous CLF. We provide several numerical examples to validate the theory and show computational efficiency. |
| title | Synthesizing Control Lyapunov-Value Functions for High-Dimensional Systems Using System Decomposition and Admissible Control Sets |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2404.01829 |