On the minimax robust Kalman Filter: A bounded estimation resources approach

This paper is devoted to a generalization of the non-standard Kalman Filter (KF) introduced in [4]. We deal with some restrictions of the technical resources in the context of a state estimation problem and study a constrained convex program. Moreover, we replace two main concepts of the conventiona...

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Fecha de publicación:
2018
Institución:
Universidad de Medellín
Repositorio:
Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/4884
Acceso en línea:
http://hdl.handle.net/11407/4884
Palabra clave:
Automation
Bandpass filters
Convex optimization
Process control
Estimation problem
Explicit solutions
Formal analysis
Non-linear filters
Robust Kalman filters
Standard Kalman filters
Technical resources
Unconstrained optimization
Kalman filters
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http://purl.org/coar/access_right/c_16ec
id REPOUDEM2_9766242c8e85dc490ada154384e37f7b
oai_identifier_str oai:repository.udem.edu.co:11407/4884
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.spa.fl_str_mv On the minimax robust Kalman Filter: A bounded estimation resources approach
title On the minimax robust Kalman Filter: A bounded estimation resources approach
spellingShingle On the minimax robust Kalman Filter: A bounded estimation resources approach
Automation
Bandpass filters
Convex optimization
Process control
Estimation problem
Explicit solutions
Formal analysis
Non-linear filters
Robust Kalman filters
Standard Kalman filters
Technical resources
Unconstrained optimization
Kalman filters
title_short On the minimax robust Kalman Filter: A bounded estimation resources approach
title_full On the minimax robust Kalman Filter: A bounded estimation resources approach
title_fullStr On the minimax robust Kalman Filter: A bounded estimation resources approach
title_full_unstemmed On the minimax robust Kalman Filter: A bounded estimation resources approach
title_sort On the minimax robust Kalman Filter: A bounded estimation resources approach
dc.contributor.affiliation.spa.fl_str_mv Azhmyakov, V., Universidad de Medellin;Castano, N., Tecnologico de Antioquia;Arango, J.P., Public Companies of Medellin E.S.P.;Graczyk, P., LAREMA, University of Angers;Murillo, F.H.S., Universidad de Medellin
dc.subject.spa.fl_str_mv Automation
Bandpass filters
Convex optimization
Process control
Estimation problem
Explicit solutions
Formal analysis
Non-linear filters
Robust Kalman filters
Standard Kalman filters
Technical resources
Unconstrained optimization
Kalman filters
topic Automation
Bandpass filters
Convex optimization
Process control
Estimation problem
Explicit solutions
Formal analysis
Non-linear filters
Robust Kalman filters
Standard Kalman filters
Technical resources
Unconstrained optimization
Kalman filters
description This paper is devoted to a generalization of the non-standard Kalman Filter (KF) introduced in [4]. We deal with some restrictions of the technical resources in the context of a state estimation problem and study a constrained convex program. Moreover, we replace two main concepts of the conventional KF, namely, the fundamental Normality Hypothesis (NH) and the unconstrained optimization approach. The minimax methodology we propose make it possible to develop an effective quasi-explicit solution method for the practically motivated generalization of the Kalman-type filter. We present a rigorous formal analysis of the obtained algorithm. The resulting non-linear filter possesses a strong optimality properties. © 2017 IEEE.
publishDate 2018
dc.date.accessioned.none.fl_str_mv 2018-10-31T13:44:21Z
dc.date.available.none.fl_str_mv 2018-10-31T13:44:21Z
dc.date.created.none.fl_str_mv 2018
dc.type.eng.fl_str_mv Conference Paper
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_c94f
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/conferenceObject
dc.identifier.isbn.none.fl_str_mv 9781538603987
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/4884
dc.identifier.doi.none.fl_str_mv 10.1109/CCAC.2017.8276395
identifier_str_mv 9781538603987
10.1109/CCAC.2017.8276395
url http://hdl.handle.net/11407/4884
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.spa.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-85047341894&doi=10.1109%2fCCAC.2017.8276395&partnerID=40&md5=592632a50fdd73be2edfb6f7672def3b
dc.relation.citationvolume.spa.fl_str_mv 2018-January
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationendpage.spa.fl_str_mv 6
dc.relation.ispartofes.spa.fl_str_mv 2017 IEEE 3rd Colombian Conference on Automatic Control, CCAC 2017 - Conference Proceedings
dc.relation.references.spa.fl_str_mv Aliprantis, C.D., Border, K.C., (2006) Infinite Dimensional Analysis, , Springer, Berlin;Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, pp. 1-3;Auger, F., Hilairet, M., Guerrero, J., Monmasson, E., Orlowska-Kowalska, T., Katsura, S., Industrial applications of the Kalman Filter: A review (2013) IEEE Transactions on Industrial Electronics, 60, pp. 1-16;Azhmyakov, V., Optimal control of a well-stired bioreactor in the presence of stochastic perturbations (2002) Informatica, 13, pp. 133-148;Azhmyakov, V., A gradient type algorithm for a class of optimal control processes governed by hybrid dynamical systems (2011) IMA Journal of Mathematical Control and Information, 28, pp. 291-307;Azhmyakov, V., Basin, M.V., Garcia, A.E.G., Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics (2014) Kybernetika, 50, p. 518;Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014) Proceedings of the 19th IFAC World Congress, pp. 6976-6981. , Cape Town, South Africa;Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th IEEE Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Azhmyakov, V., Cabrera, J., Poznyak, A., Optimal fixed-levels control for non-linear systems with quadratic costs functional (2016) Optimal Control: Applications and Methods, 37, pp. 1035-1055;Azhmyakov, V., Juarez, R., A first-order numerical approach to switchedmode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, 25, pp. 126-137;Bahmani, O., Ford, B., Kalman Filter approach to estimate the demand for international reserves (2004) Applied Economics, 36, pp. 1655-1668;Barut, M., Demir, R., Zerdali, E., Inan, R., Real-time implementation of bi input-extended Kalman filter-based estimator for speed-sensorless control of induction motors (2012) IEEE Transactions on Industrial Electronics, 59, pp. 4197-4206;Bertsekas, D., (1995) Nonlinear Programming, , Athena Scientific, Belmont, USA;Bucy, R., Joseph, P., (1968) Filtering for Stochastic Processes with Applications to Guidance, , Wiley, New Jersey;Chow, M., Sun, Z., Li, H., Optimal stabilizing gain selection for networked control systems with time delays and packet losses (2009) IEEE Transactions on Control Systems Technology, 17, pp. 1154-1162;Gill, P.E., Murray, W., Wright, M.H., (1981) Practical Optimization, , Academic Press, New York, USA;Goldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710;Haykin, S., (1996) Adaptive Filter Theory, , Prentice-Hall, New York;Huber, P.J., Ronchetti, E.M., (2005) Robust Statistics, , Wiley, New York;Kailath, T., (1981) Lectures Notes on Wiener and Kalman Filtering, , Springer, New York;Kalman, R., A new approach to linear filtering and prediction problems (1960) Transactions of the ASME-Journal of Basic Engineering, 82, pp. 35-45;Lewis, F.L., (1986) Optimal Estimation, , Wiley, New York;Polak, E., (1997) Optimization, , Springer-Verlag, New York, USA;Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhauser, Basel, Switzerland;Prakash, J., Srinivasan, K., Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor (2009) ISA Transactions, 48, pp. 273-282;Raab, F.H., Blood, E.B., Steiner, T.O., Jones, H.R., Magnetic position and orientation tracking system (1979) IEEE Transactions on Aerospace and Electronic Systems, AES15, pp. 709-718;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Taylor, S., (1986) Modeling Financial Time Series, , Wiley, Chichester;Teo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley, New York;Vogelsbergera, M., Grubic, S., Habetler, T., Wolbank, T., Using PWM-induced transient excitation and advanced signal processing for zero-speed sensorless control of AC machines (2010) IEEE Transactions on Industrial Electronics, 57, pp. 365-374;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara, Mexico;Welch, G., Bishop, G., (2006) An Introduction to the Kalman Filter, , University of North Carolina Press, Chapel Hill;Zaltni, D., Ghanes, M., Barbot, J., Abdelkrim, M., Synchronous motor observability study and an improved zero-speed position estimation design (2010) Proceedings of the 49th IEEE Conference on Decision and Control, pp. 5074-5079. , Atlanta, USA
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.publisher.program.spa.fl_str_mv Ciencias Básicas
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 2018-10-31T13:44:21Z2018-10-31T13:44:21Z20189781538603987http://hdl.handle.net/11407/488410.1109/CCAC.2017.8276395This paper is devoted to a generalization of the non-standard Kalman Filter (KF) introduced in [4]. We deal with some restrictions of the technical resources in the context of a state estimation problem and study a constrained convex program. Moreover, we replace two main concepts of the conventional KF, namely, the fundamental Normality Hypothesis (NH) and the unconstrained optimization approach. The minimax methodology we propose make it possible to develop an effective quasi-explicit solution method for the practically motivated generalization of the Kalman-type filter. We present a rigorous formal analysis of the obtained algorithm. The resulting non-linear filter possesses a strong optimality properties. © 2017 IEEE.engInstitute of Electrical and Electronics Engineers Inc.Ciencias BásicasFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85047341894&doi=10.1109%2fCCAC.2017.8276395&partnerID=40&md5=592632a50fdd73be2edfb6f7672def3b2018-January162017 IEEE 3rd Colombian Conference on Automatic Control, CCAC 2017 - Conference ProceedingsAliprantis, C.D., Border, K.C., (2006) Infinite Dimensional Analysis, , Springer, Berlin;Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, pp. 1-3;Auger, F., Hilairet, M., Guerrero, J., Monmasson, E., Orlowska-Kowalska, T., Katsura, S., Industrial applications of the Kalman Filter: A review (2013) IEEE Transactions on Industrial Electronics, 60, pp. 1-16;Azhmyakov, V., Optimal control of a well-stired bioreactor in the presence of stochastic perturbations (2002) Informatica, 13, pp. 133-148;Azhmyakov, V., A gradient type algorithm for a class of optimal control processes governed by hybrid dynamical systems (2011) IMA Journal of Mathematical Control and Information, 28, pp. 291-307;Azhmyakov, V., Basin, M.V., Garcia, A.E.G., Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics (2014) Kybernetika, 50, p. 518;Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014) Proceedings of the 19th IFAC World Congress, pp. 6976-6981. , Cape Town, South Africa;Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th IEEE Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Azhmyakov, V., Cabrera, J., Poznyak, A., Optimal fixed-levels control for non-linear systems with quadratic costs functional (2016) Optimal Control: Applications and Methods, 37, pp. 1035-1055;Azhmyakov, V., Juarez, R., A first-order numerical approach to switchedmode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, 25, pp. 126-137;Bahmani, O., Ford, B., Kalman Filter approach to estimate the demand for international reserves (2004) Applied Economics, 36, pp. 1655-1668;Barut, M., Demir, R., Zerdali, E., Inan, R., Real-time implementation of bi input-extended Kalman filter-based estimator for speed-sensorless control of induction motors (2012) IEEE Transactions on Industrial Electronics, 59, pp. 4197-4206;Bertsekas, D., (1995) Nonlinear Programming, , Athena Scientific, Belmont, USA;Bucy, R., Joseph, P., (1968) Filtering for Stochastic Processes with Applications to Guidance, , Wiley, New Jersey;Chow, M., Sun, Z., Li, H., Optimal stabilizing gain selection for networked control systems with time delays and packet losses (2009) IEEE Transactions on Control Systems Technology, 17, pp. 1154-1162;Gill, P.E., Murray, W., Wright, M.H., (1981) Practical Optimization, , Academic Press, New York, USA;Goldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710;Haykin, S., (1996) Adaptive Filter Theory, , Prentice-Hall, New York;Huber, P.J., Ronchetti, E.M., (2005) Robust Statistics, , Wiley, New York;Kailath, T., (1981) Lectures Notes on Wiener and Kalman Filtering, , Springer, New York;Kalman, R., A new approach to linear filtering and prediction problems (1960) Transactions of the ASME-Journal of Basic Engineering, 82, pp. 35-45;Lewis, F.L., (1986) Optimal Estimation, , Wiley, New York;Polak, E., (1997) Optimization, , Springer-Verlag, New York, USA;Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhauser, Basel, Switzerland;Prakash, J., Srinivasan, K., Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor (2009) ISA Transactions, 48, pp. 273-282;Raab, F.H., Blood, E.B., Steiner, T.O., Jones, H.R., Magnetic position and orientation tracking system (1979) IEEE Transactions on Aerospace and Electronic Systems, AES15, pp. 709-718;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Taylor, S., (1986) Modeling Financial Time Series, , Wiley, Chichester;Teo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley, New York;Vogelsbergera, M., Grubic, S., Habetler, T., Wolbank, T., Using PWM-induced transient excitation and advanced signal processing for zero-speed sensorless control of AC machines (2010) IEEE Transactions on Industrial Electronics, 57, pp. 365-374;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara, Mexico;Welch, G., Bishop, G., (2006) An Introduction to the Kalman Filter, , University of North Carolina Press, Chapel Hill;Zaltni, D., Ghanes, M., Barbot, J., Abdelkrim, M., Synchronous motor observability study and an improved zero-speed position estimation design (2010) Proceedings of the 49th IEEE Conference on Decision and Control, pp. 5074-5079. , Atlanta, USAScopusAutomationBandpass filtersConvex optimizationProcess controlEstimation problemExplicit solutionsFormal analysisNon-linear filtersRobust Kalman filtersStandard Kalman filtersTechnical resourcesUnconstrained optimizationKalman filtersOn the minimax robust Kalman Filter: A bounded estimation resources approachConference Paperinfo:eu-repo/semantics/conferenceObjecthttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_c94fAzhmyakov, V., Universidad de Medellin;Castano, N., Tecnologico de Antioquia;Arango, J.P., Public Companies of Medellin E.S.P.;Graczyk, P., LAREMA, University of Angers;Murillo, F.H.S., Universidad de MedellinAzhmyakov V.Castano N.Arango J.P.Graczyk P.Murillo F.H.S.http://purl.org/coar/access_right/c_16ec11407/4884oai:repository.udem.edu.co:11407/48842020-05-27 15:40:30.133Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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