Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets
This paper presents an efficient and scalable reachability analysis algorithm for nonlinear analog/mixed-signal circuits. In particular, it addresses the challenges in computing the time evolution of the reachable set of the circuit’s continuous states and its intersection with the guard...
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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/10184416/ |
| _version_ | 1797772605077323776 |
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| author | Seyoung Kim Jaeha Kim |
| author_facet | Seyoung Kim Jaeha Kim |
| author_sort | Seyoung Kim |
| collection | DOAJ |
| description | This paper presents an efficient and scalable reachability analysis algorithm for nonlinear analog/mixed-signal circuits. In particular, it addresses the challenges in computing the time evolution of the reachable set of the circuit’s continuous states and its intersection with the guard planes, i.e., the partitioning planes of the equivalent piecewise-linear system modeling the circuit’s dynamics. The proposed algorithm utilizes a trajectory form of the reachable set, which can describe its exact evolution over time using analytical expressions until the set crosses one of the guard planes of the system. When it does, a naive computation of the reachable set may require splitting the set into multiple sub-sets, each using its own trajectory form. This is problematic since the number of reachable sets may grow indefinitely over time. To mitigate this, this work proposes a way of processing a group of reachable sets together that cross a common guard plane during a finite time interval. This method can keep the number of sets and the associated computational cost constant over time. The experimental results with a DC–DC converter example demonstrate that the proposed algorithm can achieve the average speed-ups of 79–<inline-formula> <tex-math notation="LaTeX">$107\times $ </tex-math></inline-formula> compared to the existing algorithms with errors of less than 2%. |
| first_indexed | 2024-03-12T21:54:20Z |
| format | Article |
| id | doaj.art-a16e391cc9f44e318b240bf5c0274b94 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-12T21:54:20Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a16e391cc9f44e318b240bf5c0274b942023-07-25T23:00:30ZengIEEEIEEE Access2169-35362023-01-0111746027461310.1109/ACCESS.2023.329582510184416Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable SetsSeyoung Kim0https://orcid.org/0000-0001-8674-8383Jaeha Kim1https://orcid.org/0000-0003-2237-3134Department of Electrical and Computer Engineering, Inter-University Semiconductor Research Center, Seoul National University, Seoul, South KoreaDepartment of Electrical and Computer Engineering, Inter-University Semiconductor Research Center, Seoul National University, Seoul, South KoreaThis paper presents an efficient and scalable reachability analysis algorithm for nonlinear analog/mixed-signal circuits. In particular, it addresses the challenges in computing the time evolution of the reachable set of the circuit’s continuous states and its intersection with the guard planes, i.e., the partitioning planes of the equivalent piecewise-linear system modeling the circuit’s dynamics. The proposed algorithm utilizes a trajectory form of the reachable set, which can describe its exact evolution over time using analytical expressions until the set crosses one of the guard planes of the system. When it does, a naive computation of the reachable set may require splitting the set into multiple sub-sets, each using its own trajectory form. This is problematic since the number of reachable sets may grow indefinitely over time. To mitigate this, this work proposes a way of processing a group of reachable sets together that cross a common guard plane during a finite time interval. This method can keep the number of sets and the associated computational cost constant over time. The experimental results with a DC–DC converter example demonstrate that the proposed algorithm can achieve the average speed-ups of 79–<inline-formula> <tex-math notation="LaTeX">$107\times $ </tex-math></inline-formula> compared to the existing algorithms with errors of less than 2%.https://ieeexplore.ieee.org/document/10184416/Analog/mixed-signal circuitsguard intersectionhybrid systemspiecewise-linear systemreachability analysissafe operating area |
| spellingShingle | Seyoung Kim Jaeha Kim Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets IEEE Access Analog/mixed-signal circuits guard intersection hybrid systems piecewise-linear system reachability analysis safe operating area |
| title | Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets |
| title_full | Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets |
| title_fullStr | Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets |
| title_full_unstemmed | Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets |
| title_short | Reachability Analysis for Nonlinear Analog/Mixed-Signal Circuits With Trajectory-Based Reachable Sets |
| title_sort | reachability analysis for nonlinear analog mixed signal circuits with trajectory based reachable sets |
| topic | Analog/mixed-signal circuits guard intersection hybrid systems piecewise-linear system reachability analysis safe operating area |
| url | https://ieeexplore.ieee.org/document/10184416/ |
| work_keys_str_mv | AT seyoungkim reachabilityanalysisfornonlinearanalogmixedsignalcircuitswithtrajectorybasedreachablesets AT jaehakim reachabilityanalysisfornonlinearanalogmixedsignalcircuitswithtrajectorybasedreachablesets |