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Performance Improvement of Discrete-time Linear Control Systems Subject to Varying Sampling Rates Using the Tikhonov Regularization Method

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Abstract

Methods to stabilize discrete-time linear control systems subject to variable sampling rates, i.e., using state feedback controllers, are well known in the literature. Several recent works address the use of the Tikhonov regularization method, originally designed to attenuate the noise effects on ill-posed problems, with the aim of improving performance and stabilizing approximately controllable dynamical systems. Inspired by these works, we propose the use of a feedback controller designed using the Tikhonov method to regularize discrete-time linear systems subject to varying sampling rates. The goal is to minimize an error function, thus improving the performance of the closed loop system and reducing the possibility of instability. Illustrative examples show the effectiveness of the proposed method.

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Acknowledgments

The authors would like to thank the editor and the anonymous reviewers for their valuable comments and helpful suggestions that have contributed to the improvement of the paper.

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Authors and Affiliations

  1. Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro, Rua São Fransciso Xavier 524, Rio de Janeiro, 20550-900, Brazil

    Fernando Agustín Pazos

  2. Universidad de Buenos Aires - ITHES-UBA- CONICET, Departamento de Ingeniería Química, Pabellón de Industrias, Ciudad Universitaria, Buenos Aires, C1428EGA, Argentina

    Anibal Zanini

  3. Department of Electrical Engineering, Federal University of Rio de Janeiro, PEE/COPPE/UFRJ, Rio de Janeiro, 21945-970, Brazil

    Amit Bhaya

Authors
  1. Fernando Agustín Pazos
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Corresponding author

Correspondence to Fernando Agustín Pazos.

Additional information

Fernando Agustín Pazos received the B. Sc. degree in electronic engineering from the University of Buenos Aires, Argentina in 1990, the M.Sc. and D.Sc. degrees in electrical engineering from the Federal University of Rio de Janeiro, Brazil in 2000 and 2007, respectively. He is a professor in the Electronic and Telecommunications Engineering Department, the State University of Rio de Janeiro, Brazil. He is an author of “Automação de Sistemas & Robótica” (Axcel Books, Rio de Janeiro, Brazil 2002).

His research interest is development of algorithms to solve several optimization problems interpreting them as closed loop control systems.

Anibal Zanini received the B.Eng. degree in electrical engineering from Universidad Nacional de Rosario, Argentina in 1977, and recived the Ph. D. degree in electrical engineering at the Escuela Técnica Superior de Ingenieros Industriales of the Universidad Politécnica de Madri, Spain in 1983. He has worked for 20 years as project leader and senior researcher in the automation area at metallurgical industry. Since 1998, his main activity is at Universidad de Buenos Aires. He is a professor at the Engineering School of “Universidad de Buenos Aires”.

His research interests include industrial control, identification and adaptive control.

Amit Bhaya received the B.Eng. degree in eletrical engineering from the Indian Institute of Technology, India in 1981, and received the Ph.D. degree in eletrical engineering from the University of California at Berkeley, USA in 1986. He is a professor in the Electrical Engineering Department, Graduate School of Engineering, the Federal University of Rio de Janeiro (COPPE/UFRJ), Brazil. He coauthored the books “Matrix Diagonal Stability in Systems and Computation” (Birkhäuser, 2000), and “Control Perspectives on Numerical Algorithms and Matrix Problems” (SIAM, 2006). He was an associate editor of the IEEE Transactions on Neural Networks and Learning Systems from 2010 to 2012.

His research interests include systems and control theory, parallel computation, neural networks, matrix stability theory, mathematical ecology and optimization of economic dynamic systems.

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Pazos, F.A., Zanini, A. & Bhaya, A. Performance Improvement of Discrete-time Linear Control Systems Subject to Varying Sampling Rates Using the Tikhonov Regularization Method. Int. J. Autom. Comput. 17, 453–463 (2020). https://doi.org/10.1007/s11633-019-1205-8

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