MI4Hybrid is a model invalidation toolbox for hybrid systems.
####Installation Instructions:
This toolbox can be used in MATLAB with the following necessary packages/softwares installed:
For Polynomial State-Space Model Invalidation and T-Detectability:
- [SparsePOP] (http://www.is.titech.ac.jp/~kojima/SparsePOP/)
For Switched Affine and Reggressive Model Invalidation and T-Detectability:
####Contents:
#####In the folder "lib":
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StateSpace.m is a class for state-space models with input, state, and noise specifications.
- UnStateSpace.m is a class for state-space models with parameter uncertainty in addition.
- UnStateSpace.m is a subclass of StateSpace.m
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ARXmodel.m is a class for ARX models with input and noise specifications.
- UnARXmodel.m is a class for ARX models with parameter uncertainty in addition.
- UnARXmodel.m is a subclass of ARXmodel.m
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PolyModel.m is a class for (non-switched) polynomial models with noise specifications.
- UnPolyModel.m is a class for (non-switched) polynomial models parameter uncertainty in addition.
- UnPolyModel.m is a subclass of PolyModel.m
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PWAModel.m is a class for (non-switched) piece-wise affine models without noise
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bounded_noise.m is a function generating l_p norm bounded noise (a matrix) whose number of rows is the noise dimension and number of columns is the time horizon.
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swarx_sim.m is a function that generates simulated I/O data for ARX models defined on ARXmodel.m or UnARXmodel.m
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swss_sim.m is a function that generates simulated I/O data for state-space models defined on StateSpace.m or UnStateSpace.m
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poly_sim.m is a function that generates simulated I/O data for polynomial models defined on PolyModel.m or UnPolyModel.m
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pwa_sim.m is a function that generates simulated I/O data for piece-wise affine models defined on PWAModel.m
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invalidation_arx.m is a function that applies an invalidation algorithm to non-switched ARX models.
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invalidation_ss.m is a function that applies an invalidation algorithm to non-switched state-space models.
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invalidation_sarx_milp.m is a function that applies an invalidation algorithm to any switched or non-switched ARX models.
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invalidation_swa_milp_old.m is a function that applies an invalidation algorithm to any switched or non-switched state-space models.
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invalidation_swa_milp.m is a function that applies an invalidation algorithm to any switched or non-switched state-space models.
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invalidation_uswa_milp_old.m is a function that applies an invalidation algorithm to any switched or non-switched state-space models subject to parameter uncertainty. (old version, which works with the old examples)
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invalidation_poly.m is a function that applies an invalidation algorithm to any certain or uncertain polynomial state-space models.
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invalidation_pwa.m is a function that applies an invalidation algorithm to any certain piece-wise affine models.
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Tdetect_swa_milp.m is a function that checks whether an SWA fault model sysf is T-detectable for an SWA system model sys for a given T.
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Tdetect_uswa_milp.m is a function that checks whether an uncertain SWA fault model sysf is T-detectable for an uncertain SWA system model sys for a given T.
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tdet_poly.m is a function that checks whether a polynomial fault model sysf is T-detectable for a polynomial system model sys for a given T.
#####In the folder "examples":
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Examples for switched, non-switched ARX/state-space, polynomial and PWA model invalidation using different functions.
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Examples for fault detection in SWA, uncertain SWA models as well as weak detectability are included.
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Examples of the publications cited below are also provided.
#####In the folder "extras":
Extra files are inside this folder.
- SMT-based T-Detectability functions are located here.
####Related publications:
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F. Harirchi and N. Ozay, "Model Invalidation for Switched Affine Systems with Applications to Fault and Anomaly Detection", IFAC ADHS, 2015.
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F. Harirchi, Z. Luo and N. Ozay, "Model (In)validation and Fault Detection for Systems with Polynomial State-Space Models", ACC, 2016.
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F. Harirchi and N. Ozay, "Guaranteed Model-Based Fault Detection in Cyber-Physical Systems: A Model Invalidation Approach", arXiv:1609.05921, 2016.
####Acknowledgments: This research is supported in part by DARPA grant N66001-14-1-4045.