Julia Package for computing [controlled] invariant sets of Hybrid Systems using Sum Of Squares Programming
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Documentation | Build Status | Zenodo |
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This packages implements methods for computing invariant sets using Sum Of Squares Programming. It supports:
It also includes utilities for approximation the Joint Spectral Radius.
The package currently requires Julia v1.0, you can download it here. Once Julia is installed, simply launch the REPL an type
] add SwitchOnSafety
Example notebooks are available in the examples
folder.
We link them below with the literature.
The linked notebooks reproduce the results of the following papers:
The linked notebooks explores the examples of the following papers using this package:
For the soslyapb
and sosbuildsequence
functions, cite:
@Article{legat2020certifying,
author = {Legat, Beno\^it and Parrilo, Pablo A. and Jungers, Rapha\"el M.},
journal = {{SIAM} Journal on Control and Optimization},
title = {Certifying Unstability of Switched Systems Using Sum of Squares Programming},
year = {2020},
month = jan,
number = {4},
pages = {2616--2638},
volume = {58},
doi = {10.1137/18M1173460},
publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
}
and for the lower bound obtained by soslyapb
, see:
@Article{legat2019entropy,
author = {Beno\^it Legat and Pablo A. Parrilo and Rapha\"el M. Jungers},
title = {An entropy-based bound for the computational complexity of a switched system},
journal = {IEEE Transactions on Automatic Control},
year = {2019},
doi = {10.1109/TAC.2019.2902625},
publisher = {IEEE},
}
For the getis
and fillis!
functions with ellipsoids or polysets, cite:
@InProceedings{legat2018computing,
author = {Beno\^it Legat and Paulo Tabuada and Rapha\"el M. Jungers},
title = {Computing controlled invariant sets for hybrid systems with applications to model-predictive control},
year = {2018},
volume = {51},
number = {16},
pages = {193--198},
note = {6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018},
doi = {https://doi.org/10.1016/j.ifacol.2018.08.033},
issn = {2405-8963},
journal = {IFAC-PapersOnLine},
keywords = {Controller Synthesis, Set Invariance, LMIs, Scalable Methods},
url = {http://www.sciencedirect.com/science/article/pii/S2405896318311480},
}
or with piecewise semi-ellipsoids, cite:
@Article{legat2020piecewise,
author = {Beno{\^\i}t Legat and Sa{\v{s}}a V. Rakovi{\'c} and Rapha{\"e}l M. Jungers},
journal = {{IEEE} Control Systems Letters},
title = {Piecewise Semi-Ellipsoidal Control Invariant Sets},
year = {2021},
month = jul,
number = {3},
pages = {755--760},
volume = {5},
doi = {10.1109/LCSYS.2020.3005326},
publisher = {Institute of Electrical and Electronics Engineers ({IEEE})},
}