Pub Date : 2018-12-22DOI: 10.1109/ICC47138.2019.9123213
A. Kundu
This paper deals with destabilizing switching signals for continuous-time switched linear systems. Our contributions are twofold: Firstly, we propose a class of switching signals under which a switched system is unstable. Our characterization of instability depends solely on the asymptotic behaviour of frequency of switching, frequency of transition between subsystems, and fraction of activation of subsystems. Secondly, we show that our class of destabilizing switching signals is a strict subset of the class of switching signals that does not satisfy asymptotic characterization of stability recently proposed in the literature. This observation identifies a gap between asymptotic characterizations of stabilizing and destabilizing switching signals for switched linear systems.
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Pub Date : 2017-12-06DOI: 10.1109/ICC47138.2019.9123219
Abhishek Dey, Kushal Chakrabarti, K. Gola, Shaunak Sen
An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this purpose, the choice of the process noise covariance is generally unclear. Here, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise covariance on the states and parameters, as given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering technique by updating the process noise covariance at each time step based on estimates. We compare the performance of this framework with different fixed values of process noise covariance in biomolecular system models, including an oscillator model, as well as in experimentally measured data for a negative transcriptional feedback circuit. We find that the parameter estimation with such process noise covariance can achieve balance between the mean square estimation error and parameter convergence time and we discuss the optimality of the filter. These results may help in the use of Extended Kalman Filters for systems where process noise covariance depends on states and/or parameters.
{"title":"A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating","authors":"Abhishek Dey, Kushal Chakrabarti, K. Gola, Shaunak Sen","doi":"10.1109/ICC47138.2019.9123219","DOIUrl":"https://doi.org/10.1109/ICC47138.2019.9123219","url":null,"abstract":"An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this purpose, the choice of the process noise covariance is generally unclear. Here, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise covariance on the states and parameters, as given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering technique by updating the process noise covariance at each time step based on estimates. We compare the performance of this framework with different fixed values of process noise covariance in biomolecular system models, including an oscillator model, as well as in experimentally measured data for a negative transcriptional feedback circuit. We find that the parameter estimation with such process noise covariance can achieve balance between the mean square estimation error and parameter convergence time and we discuss the optimality of the filter. These results may help in the use of Extended Kalman Filters for systems where process noise covariance depends on states and/or parameters.","PeriodicalId":231050,"journal":{"name":"2019 Sixth Indian Control Conference (ICC)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126594678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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