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2005 | 15 | 3 | 351-357
Tytuł artykułu

Stochastic multivariable self-tuning tracker for non-gaussian systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker's product is used, which allows us to represent unknown parameters in the form of vectors. For parameter estimation a stochastic approximation algorithm is employed. Using the concept of the stochastic Lyapunov function, global stability and optimality of the feedback system are established.
Rocznik
Tom
15
Numer
3
Strony
351-357
Opis fizyczny
Daty
wydano
2005
otrzymano
2005-03-25
poprawiono
2005-06-28
Twórcy
  • Regionalni Centar za Talente (RCT), PO Box 126, 15 300 Loznica, Serbia and Montenegro
Bibliografia
  • Åström K.J. and Wittenmark B. (1973): On self-tuning regulators.- Automatica, Vol. 9, No. 2, pp. 185-199.
  • Åström K.J. and Wittenmark B. (1989): Adaptive Control. - New York: Addison Wesley.
  • Åström K.J. and Wittenmark B. (1995): Adaptive Control. - New York: Addison Wesley.
  • Becker J.A.H, Kumar P.R. and Wei C.Z. (1985): Adaptive control with the stochastic approximation algorithm. - IEEE Trans. Automat. Contr., Vol. 30, pp. 330-338.
  • Bercu B. (1995): Weighted estimation and tracking for ARMAX models. - SIAM J. Contr. Optim., Vol. 33, No. 1, pp. 89-106.
  • Caines P. (1988): Linear Stochastic Systems. - New York: Wiley.
  • Chen H.F. and Guo L. (1991): Identification and Stochastic Adaptive Control. - Basel: Birkhauser.
  • Desoer C.A. and Vidyasagar M. (1975): Feedback Systems: Input-Output Properties. - New York: Academic Press.
  • Duflo M. (1997): Random Iterative Models. - New York: Springer.
  • Filipovic V. and Kovacevic B. (1994): On robust AML identification algorithms. - Automatica, Vol. 30, No. 12, pp. 1775-1778.
  • Filipovic V. (1996): Robustness of adaptive tracking for stochastic multivariable minimum variance controller. - Proc. 13th IFAC World Congress, San Francisco, USA, Vol. K, pp. 391-396.
  • Filipovic V. (1999): Convergence and optimality of stochastic adaptive control scheme when the disturbance is non-Gaussian. - Proc. 14th IFAC World Congress, Beijing, China, pp. 875-880.
  • Filipovic V. (2001): Robust adaptive one-step ahead predictor. - IMA J. Math. Contr. Inf., Vol. 18, pp. 491-500.
  • Goodwin G.C. and Sin K.S. (1984): Adaptive Filtering, Prediction and Control. - New Jersey: Prentice-Hall.
  • Goodwin G.C., Ramadge P. and Caines P. (1981): Discrete time stochastic adaptive control. - SIAM J. Contr. Optim., Vol. 19, No. 6, pp. 829-853.
  • Hall P. and Heyde C.C. (1980): Martingale Limit Theory and Its Applications. - New York: Academic Press.
  • Huber P. (2003): Robust Statistics. - New York: Wiley.
  • Hubert M., Pison G., Strouf A. and Van Aelst S. (Eds.) (2004): Theory and Applications of Recent Robust Methods. - Basel: Birkhauser.
  • Ioannou P.A. and Sun J. (1996): Robust Adaptive Control. - New Jersey: Prentice Hall.
  • Kumar P.R. and Varaija P. (1986): Stochastic Systems: Estimation, Identification, and Adaptive Control. - New Jersey: Prentice Hall.
  • Kumar P.R. and Praly L. (1987): Self-tuning tracker. - SIAM J. Contr. Optim., Vol. 25, No. 4, pp. 1053-1071.
  • Kushner J.H. and Yin G.G. (2003): Stochastic Approximation. Algorithms and Applications. - New York: Springer.
  • Landau I.D., Lozano R. and M'Saad M. (1998): Adaptive Control. -New York: Springer.
  • Lai T.L. and Wei C.Z. (1986): Extended least squares and their applications to adaptive control and prediction in linear systems. - IEEE Trans.Automat. Contr., Vol. 31, No. 6, pp. 898-906.
  • Lin W., Kumar P.R. and Seidman T. (1985): Will the self-tuning approach work for general cost criteria? - Syst. Contr. Lett., Vol. 6, No. 1, pp. 77-85.
  • Lucas A., Frances P.H. and Van Dijk D. (2005): Outlier Robust Analysis of Economic Time Series. - Oxford: Oxford University Press.
  • Praly L., Lin S.F. and Kumar P.R. (1989): A robust adaptive minimum variance controller. - SIAM J. Contr. Optim., Vol. 27, No. 2, pp. 235-266.
  • Radenkovic M.S. and Michel A.N. (1992): Robust adaptive systems and self-stabilization. - IEEE Trans. Automat. Contr., Vol. 37, No. 9,pp. 1355-1369.
  • Robins H. and Siegmund D. (1971): A convergence theory for nonnegative almost supermartingale and same applications, In: Optimization Methods in Statistics (J.S. Rustagi, Ed.). - New York: Academic Press, p. 233-257.
  • Rudin V. (1964): Principles of Mathematical Analysis. - New York: Mc Graw Hill.
  • Sastry S. and Bodson M. (1989): Adaptive Control: Stability, Convergence and Robustness. - New Jersey: Prentice Hall.
  • Shiryayev A.N. (2004): Probability, Vols. 1 and 2. - Moscow: MCNMO, (in Russian).
Typ dokumentu
Bibliografia
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