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Special issue on the set membership modelling of uncertainties in dynamical systems

Special issue on the set membership modelling of uncertainties in dynamical systems Mathematical and Computer Modelling of Dynamical Systems Vol. 11, No. 2, June 2005, 123 – 124 Editorial Special issue on the set membership modelling of uncertainties in dynamical systems Modelling of systems in the presence of unknown-but-bounded errors attracts the permanent attention of researchers in the fields of parameter estimation, identification, control and optimization. It is a natural counterpart to the stochastic approach (with such traditional tools as the least-squares method, Kalman filtering and maximum- likelihood estimates), where all perturbations are assumed to be random with known distributions. However, often the statistics of these perturbations are not available and it is more natural to consider them as belonging to some bounded sets with no other hypothesis on their distributions. This approach originates in the pioneering works by Schweppe [1], Withenhausen [2] and Bertsekas and Rhodes [3] at the end of the 1960s. Later this technique has been developed by many researchers including those providing papers for the present issue (see the monographs [4 – 9], the survey papers [10, 11] and special issues of journals [12 – 14]). The unknown-but-bounded model of perturbations becomes very useful for experts in modelling dynamical systems. There were special sessions on this subject at the 3rd and 4th IMACS Symposia on Mathematical Modelling held in Vienna in 2000 and 2003 respectively. The talks at the sessions were the basis for the present special issue. We are proud to report that top experts in the field have contributed to it. The contents of the issue provide an extensive presentation of modern developments and techniques in the set-membership approach to modelling. Numerous applications to industry, space and economic models are also provided. Felix Chernousko Boris Polyak Guest Editors References [1] Schweppe, F.C., 1968, Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control, 13, 22 – 28. [2] Witsenhausen, H.S., 1968, Sets of possible states of linear systems given perturbed observations. IEEE Transctions on Automatic Control, 13, 556 – 558. [3] Bertsekas, D.P. and Rhodes, I.B., 1971, Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control, 16, 117 – 128. [4] Schweppe, F.C., 1973, Uncertain Dynamic Systems (Englewood Cliffs, New Jersey: Prentice Hall). [5] Kurzhanski, A.B., 1977, Control and Observation under Uncertainty (Moscow: Nauka) (in Russian). Mathematical and Computer Modelling of Dynamical Systems ISSN 1387-3954 print/ISSN 1744-5051 online ª 2005 Taylor & Francis Group Ltd http://www.tandf.co.uk/journals DOI: 10.1080/13873950500067296 124 Editorial [6] Chernousko, F.L., 1988, Estimation of Phase State for Dynamical Systems (Moscow: Nauka) (in Russian). [7] Chernousko, F.L., 1994, State Estimation for Dynamic Systems (Boca Raton, Florida: CRC Press). [8] Kurzhanski, A.B. and Valyi, I., 1996, Ellipsoidal Calculus for Estimation and Control (Boston, Massachusetts: Birkha¨ user). [9] Milanese, M., Norton, J., Pet-Lahanier, H. and Walter, E. (Eds), 1996, Bounding Approaches to System Identification (New York: Plenum Press). [10] Combettes, P.L., 1993, The foundations of set-theoretic estimation. Proceedings of the IEEE, 81, 182 – [11] Durieu, C., Walter E. and Polyak, B., 2001, Multi-input multi-output ellipsoidal state bounding. Journal of Optimization Theory and Applications, 111, 273 – 303. [12] Walter, E. (Ed.), 1990, Special issue on parameter identifications with error bound. Mathematics and Computers in Simulation, 32, 447 – 607. [13] Norton, J. (Ed.), 1994, Special issue on bounded-error estimation, 1. International Journal of Adaptive Control and Signal Processing, 8, 1 – 118. [14] Norton, J. (Ed.), 1995, Special issue on bounded-error estimation, 2. International Journal of Adaptive Control and Signal Processing, 9, 1 – 132. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical and Computer Modelling of Dynamical Systems Taylor & Francis

Special issue on the set membership modelling of uncertainties in dynamical systems

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Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1744-5051
eISSN
1387-3954
DOI
10.1080/13873950500067296
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Abstract

Mathematical and Computer Modelling of Dynamical Systems Vol. 11, No. 2, June 2005, 123 – 124 Editorial Special issue on the set membership modelling of uncertainties in dynamical systems Modelling of systems in the presence of unknown-but-bounded errors attracts the permanent attention of researchers in the fields of parameter estimation, identification, control and optimization. It is a natural counterpart to the stochastic approach (with such traditional tools as the least-squares method, Kalman filtering and maximum- likelihood estimates), where all perturbations are assumed to be random with known distributions. However, often the statistics of these perturbations are not available and it is more natural to consider them as belonging to some bounded sets with no other hypothesis on their distributions. This approach originates in the pioneering works by Schweppe [1], Withenhausen [2] and Bertsekas and Rhodes [3] at the end of the 1960s. Later this technique has been developed by many researchers including those providing papers for the present issue (see the monographs [4 – 9], the survey papers [10, 11] and special issues of journals [12 – 14]). The unknown-but-bounded model of perturbations becomes very useful for experts in modelling dynamical systems. There were special sessions on this subject at the 3rd and 4th IMACS Symposia on Mathematical Modelling held in Vienna in 2000 and 2003 respectively. The talks at the sessions were the basis for the present special issue. We are proud to report that top experts in the field have contributed to it. The contents of the issue provide an extensive presentation of modern developments and techniques in the set-membership approach to modelling. Numerous applications to industry, space and economic models are also provided. Felix Chernousko Boris Polyak Guest Editors References [1] Schweppe, F.C., 1968, Recursive state estimation: unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control, 13, 22 – 28. [2] Witsenhausen, H.S., 1968, Sets of possible states of linear systems given perturbed observations. IEEE Transctions on Automatic Control, 13, 556 – 558. [3] Bertsekas, D.P. and Rhodes, I.B., 1971, Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control, 16, 117 – 128. [4] Schweppe, F.C., 1973, Uncertain Dynamic Systems (Englewood Cliffs, New Jersey: Prentice Hall). [5] Kurzhanski, A.B., 1977, Control and Observation under Uncertainty (Moscow: Nauka) (in Russian). Mathematical and Computer Modelling of Dynamical Systems ISSN 1387-3954 print/ISSN 1744-5051 online ª 2005 Taylor & Francis Group Ltd http://www.tandf.co.uk/journals DOI: 10.1080/13873950500067296 124 Editorial [6] Chernousko, F.L., 1988, Estimation of Phase State for Dynamical Systems (Moscow: Nauka) (in Russian). [7] Chernousko, F.L., 1994, State Estimation for Dynamic Systems (Boca Raton, Florida: CRC Press). [8] Kurzhanski, A.B. and Valyi, I., 1996, Ellipsoidal Calculus for Estimation and Control (Boston, Massachusetts: Birkha¨ user). [9] Milanese, M., Norton, J., Pet-Lahanier, H. and Walter, E. (Eds), 1996, Bounding Approaches to System Identification (New York: Plenum Press). [10] Combettes, P.L., 1993, The foundations of set-theoretic estimation. Proceedings of the IEEE, 81, 182 – [11] Durieu, C., Walter E. and Polyak, B., 2001, Multi-input multi-output ellipsoidal state bounding. Journal of Optimization Theory and Applications, 111, 273 – 303. [12] Walter, E. (Ed.), 1990, Special issue on parameter identifications with error bound. Mathematics and Computers in Simulation, 32, 447 – 607. [13] Norton, J. (Ed.), 1994, Special issue on bounded-error estimation, 1. International Journal of Adaptive Control and Signal Processing, 8, 1 – 118. [14] Norton, J. (Ed.), 1995, Special issue on bounded-error estimation, 2. International Journal of Adaptive Control and Signal Processing, 9, 1 – 132.

Journal

Mathematical and Computer Modelling of Dynamical Systems – Taylor & Francis

Published: Jun 1, 2005

References

  • Special issue on parameter identifications with error bound
  • Special issue on bounded-error estimation, 1
  • Special issue on bounded-error estimation, 2