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A new approach to state estimation for uncertain linear systems in a moving horizon estimation setting

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Abstract

This paper addresses the state estimation problem for linear systems with additive uncertainties in both the state and output equations using a moving horizon approach. Based on the full information estimation setting and the game-theoretic approach to the H ∞ filtering, a new optimization-based estimation scheme for uncertain linear systems is proposed, namely the H ∞-full information estimator, H ∞-FIE in short. In this formulation, the set of processed data grows with time as more measurements are received preventing recursive formulations as in Kalman filtering. To overcome the latter problem, a moving horizon approximation to the H ∞-FIE is also presented, the H ∞-MHE in short. This moving horizon approximation is achieved since the arrival cost is suitably defined for the proposed scheme. Sufficient conditions for the stability of the H ∞-MHE are derived. Simulation results show the benefits of the proposed scheme when compared with two H ∞ filters and the well-known Kalman filter.

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Authors and Affiliations

  1. Faculty of Economic and Administrative Sciences, Quality, Metrology and Production Research Group, Metropolitan Institute of Technology of Medellin (ITM), Calle 73 # 76A-354, Medellin, 050034, Colombia

    J. Garcia-Tirado

  2. KALMAN Research Group, Faculty of Mines, Electric Energy and Automatics Department, National University of Colombia (Medellin Campus), Cra. 80 # 65-23, Medellin, 050041, Colombia

    H. Botero

  3. Perception and Intelligent Control Research Group, Department of Electrical, Electronics, and Computational Engineering, Faculty of Engineering and Architecture, National University of Colombia (Manizales), Q building, La Nubia campus, Manizales, 170003, Colombia

    F. Angulo

Authors
  1. J. Garcia-Tirado
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  2. H. Botero
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  3. F. Angulo
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Corresponding author

Correspondence to J. Garcia-Tirado.

Additional information

This work was supported by the European Community’ s Seventh Framework Programme FP7/2007-2013 (No. 223854) and COLCIENCIAS-Departamento Administrativo de Ciencia, Tecnologíae Innovación de Colombia.

Recommended by Associate Editor James Whidborne

J. Garcia-Tirado received the B. Sc. degree in control engineering from the National University of Colombia in 2006, and the M. Sc. degree from CINVESTAV at Guadalajara, Mexico in 2009. He got the Ph.D. degree with honors in the School of Processes and Energy at the National University of Colombia in the early 2014. He is currently associate professor in the Department of Quality and Production at the Metropolitan Institute of Technology, Medellin, Colombia.

His research interests include robust estimation theory, receding-horizon control and estimation, model-based control, and control of biological processes.

ORCID iD: 0000-0002-9970-2162

H. Botero received the B. Sc. degree in electrical engineering, his specialist degree in industrial automation from University of Antioquia, Colombia, and the M. Sc. degree in engineering from University of Valle, Colombia. Finally, he received the Ph.D. degree from National University of Colombia at Medellin Campus. He is currently with the Department of Electrical Energy and Automatics, National University of Colombia, Medellín-Colombia.

His research interests include state estimation, identification of generation control systems, and education in engineering.

F. Angulo received the B. Sc. degree in electrical engineering with honors, the M. Sc. degree in automatics, and the Ph.D. degree in automatics and robotics from the National University of Colombia, Colombia in 1989, National University of Colombia, Colombia in 2000, and Polytechnic University of Catalonia, Spain in 2004, respectively. She is currently an associate professor in the Department of Electrical Engineering, Electronics, and Computer Science, National University of Colombia, Colombia. She is a member of the Research Group Perception and Intelligent Control-PCI.

Her research interests include nonlinear control, nonlinear dynamics of nonsmooth systems, and applications to DC/DC converters.

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Garcia-Tirado, J., Botero, H. & Angulo, F. A new approach to state estimation for uncertain linear systems in a moving horizon estimation setting. Int. J. Autom. Comput. 13, 653–664 (2016). https://doi.org/10.1007/s11633-016-1015-1

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  • DOI: https://doi.org/10.1007/s11633-016-1015-1

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