Recursive triangulation description of the feasible parameter set for bounded-noise models

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Recursive triangulation description of the feasible parameter set for bounded-noise models

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The problem of estimating feasible parameter sets for linear discrete-time systems with unknown-but-bounded noise is investigated. Considering that the feasible parameter set of a linear discrete-time system with bounded noise is a convex polytope and that a convex polytope can be triangulated into a limited number of simplexes with good properties, the authors propose an exact triangulation description method for the feasible parameter set. A convex polytope triangulation algorithm is introduced and a recursive algorithm of estimating the feasible parameter set in correspondence with the system description is developed. Simulation examples show the effectiveness of the proposed method.

Inspec keywords: geometry; discrete time systems; linear systems; parameter estimation

Other keywords: parameter estimation; unknown-but-bounded noise; bounded-noise models; recursive triangulation description; recursive algorithm; feasible parameter set; convex polytope triangulation algorithm; linear discrete-time systems

Subjects: Combinatorial mathematics; Simulation, modelling and identification; Discrete control systems

References

    1. 1)
      • M. Kieffer , E. Walter . Interval analysis for guaranteed non-linear parameter and state estimation. Math. Comput. Model. Dyn. Syst. , 2 , 171 - 181
    2. 2)
      • Sun, X.F., Fan, Y.Z.: `Guaranteed sensor fault detection and isolation via recursive rectangular parallelepiped bounding in state-set estimation', Proc. Third ASCC, July 2000, Shanghai, China, p. 3041–3046.
    3. 3)
      • Ashokaraj, I., Tsourdos, A., Silson, P., White, B.: `Sensor based robot localisation and navigation: using interval analysis and extended Kalman filter', Proc. Fifth Asian Control Conf., July 2004, Melbourne, Australia, 2, p. 1086–1093.
    4. 4)
      • Piet-lahanier, H., Walter, E.: `Further results on recursive polyhedral description of parameter uncertainty in the bounded-error context', Proc. 28th IEEE Conf. on Decision and Control, December 1989, Tampa, Florida, USA, 3, p. 1964–1966.
    5. 5)
      • E. Walter , H. Piet-lahanier . Exact recursive polyhedral description of the feasible parameter set for bounded-error models. IEEE Trans. Autom. Control , 8 , 911 - 915
    6. 6)
      • Mo, S.H., Norton, J.P.: `Recursive parameter-bounding algorithms which compute polytope bounds', Proc. 12th IMACS World Conf. Scientific Computation, July 1988, Paris, France, 2, p. 477–480.
    7. 7)
      • F.L. Chernousko . Optimal guaranteed estimates of indeterminacies with the aid of ellipsoids, I, II, III. Engng. Cybern. , 3
    8. 8)
      • T. Alamo , J.M. Bravo , E.F. Camacho . Guaranteed state estimation by zonotopes. Automatica , 6 , 1035 - 1043
    9. 9)
      • E. Fogel , Y.F. Huang . On the value of information in system identification-bounded noise case. Automatica , 2 , 229 - 238
    10. 10)
      • J. Cohen , T. Hickey . Two algorithms for determining volumes of convex polyhedra. J. Assoc. Comput. Mach. , 3 , 401 - 414
    11. 11)
      • Kieffer, M., Jaulin, L., Walter, E., Meizel, D.: `Guaranteed mobile robot tracking using interval analysis', Proc. Workshop on Applications of Interval Analysis to Systems and Control, MISC'99, 1999, Girona, Spain, p. 347–359.
    12. 12)
      • J.R. Jr. Deller , S. Gollamudi , S. Nagaraj , D. Joachim , Y.F. Huang . Convergence analysis of the quasi-OBE algorithm and related performance issues. Int. J. Adapt. Control Signal Process. , 6 , 499 - 527
    13. 13)
      • Y.F. Huang . A recursive estimation algorithm using selective updating for spectral analysis and adaptive signal processing. IEEE Trans. Acoust. Speech Signal Process. , 5 , 1331 - 1334
    14. 14)
      • Belforte, G., Bona, B.: `An improved parameter identification algorithm for signals with unknown-but-bounded errors', Seventh IFAC/IFORS Symp. on Identification and System Parameter Estimation, 1985, York, p. 1507–1512.
    15. 15)
      • L. Jaulin , E. Walter . Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica , 4 , 1053 - 1064
    16. 16)
      • Piet-lahanier, H., Walter, E.: `Practical implementation of an exact and recursive algorithm for characterizing likelihood sets', Proc. 12th IMACS World Conf. on Scientific Computation, July 1988, Paris, France, 2, p. 481–483.
    17. 17)
      • F.C. Schweppe . Recursive state estimation: unknown but bounded errors and system inputs. IEEE Trans. Autom. Control , 1 , 22 - 28
    18. 18)
      • L. Chisci , A. Garulli , G. Zappa . Recursive state bounding by parallelotopes. Automatica , 7 , 1049 - 1055
    19. 19)
      • Piet-lahanier, H., Walter, E.: `Polyhedric approximation and tracking for bounded-error models', IEEE Int. Symp. on Circuits and Systems, May 1993, Chicago, Illinois, USA, 1, p. 782–785.
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