Forward Invariance in Neural Network Controlled Systems
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929217075150848 |
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| author | Harapanahalli, Akash Jafarpour, Saber Coogan, Samuel |
| author_facet | Harapanahalli, Akash Jafarpour, Saber Coogan, Samuel |
| contents | We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers. The framework (i) constructs localized first-order inclusion functions for the closed-loop system using Jacobian bounds and existing neural network verification tools; (ii) builds a dynamical embedding system where its evaluation along a single trajectory directly corresponds with a nested family of hyper-rectangles provably converging to an attractive set of the original system; (iii) utilizes linear transformations to build families of nested paralleletopes with the same properties. The framework is automated in Python using our interval analysis toolbox $\texttt{npinterval}$, in conjunction with the symbolic arithmetic toolbox $\texttt{sympy}$, demonstrated on an $8$-dimensional leader-follower system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Forward Invariance in Neural Network Controlled Systems Harapanahalli, Akash Jafarpour, Saber Coogan, Samuel Systems and Control Machine Learning Optimization and Control We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers. The framework (i) constructs localized first-order inclusion functions for the closed-loop system using Jacobian bounds and existing neural network verification tools; (ii) builds a dynamical embedding system where its evaluation along a single trajectory directly corresponds with a nested family of hyper-rectangles provably converging to an attractive set of the original system; (iii) utilizes linear transformations to build families of nested paralleletopes with the same properties. The framework is automated in Python using our interval analysis toolbox $\texttt{npinterval}$, in conjunction with the symbolic arithmetic toolbox $\texttt{sympy}$, demonstrated on an $8$-dimensional leader-follower system. |
| title | Forward Invariance in Neural Network Controlled Systems |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2309.09043 |