Random spherical uncertainty in estimation and robustness

IEEE Transactions on Automatic Control

Volumn 45, Issue 11, 2000, Pages 2145-2150

  Polyak, B T ^a   Shcherbakov, P S ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; GEOMETRY; LINEAR SYSTEMS; MONTE CARLO METHODS; PARAMETER ESTIMATION; POLYNOMIALS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); SET THEORY; UNCERTAIN SYSTEMS; VECTORS;

LINEAR FUNCTION; RANDOM SPHERICAL UNCERTAINTY; RANDOM VECTOR;

CONTROL THEORY;

EID: 0034316629     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.887645     Document Type: Article

References (16)

1. J. Ackermann, Robust Control: Systems with Uncertain Physical Parameters. New York: Springer-Verlag, 1993.
2. B. R. Barmish, New Tools for Robustness of Linear Systems. New York: Macmillan, 1994.
3. B. R. Barmish, C. M. Lagoa, and R. Tempo, "Radially truncated uniform distribution for probabilistic robustness of control systems," in Proc. Amer. Control Conf., Albuquerque, NM, 1997.
4. B. R. Barmish and B. T. Polyak, "A new approach to open robustness problems based on probabilistic prediction formulae," in Proc. 13th IFAC World Congress, vol. H, San Francisco, CA, July 1996, pp. 1-6.
5. S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control: The Parametric Approach. Upper Saddle River, NJ: Prentice-Hall, 1995.
6. p balls for probabilistic robustness analysis," in Proc. 37th CDC, Tampa, FL, 1998.
7. X. Chen and K. Zhou, "'On the probabilistic characterization of model uncertainty and robustness," in Proc. 36th CDC, vol. 4, San Diego, CA, 1997, pp. 3816-3825.
8. F. L. Chernous'ko, State Estimation for Dynamic Systems. Boca Raton, FL: CRC Press, 1994.
9. X. Zhu, Y. Huang, and J. Doyle, "Soft vs. hard bounds in probabilistic robustness analysis," in Proc. 35th CDC, Kobe, Japan, 1996.
10. A. B. Kurzhanskii and I. Valyi, Ellipsoidal Calculus for Estimation and Control. Basel: Birkhäuser, 1997.
11. M. E. Muller, "A note on a method for generating random points uniformly on n-dimensional spheres," Commun. ACM, vol. 2, pp. 19-20, 1959.
12. K. Pearson, Tables of the Incomplete Beta Function. Cambridge, U.K.: Cambridge Univ. Press, 1934.
13. L. R. Ray and R. F. Stengel, "A Monte Carlo approach to the analysis of control systems robustness," Automatica, vol. 29, no. 1, pp. 229-236, 1993.
14. F. C. Schweppe, Uncertain Dynamic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1973.
15. C. B. Soh, C. S. Berger, and K. P. Dabke, "On the stability properties of polynomials with perturbed coefficients," IEEE Trans. Automat. Contr., vol. AC-30, pp. 1033-1036, Oct. 1985.
16. S. Wilks, Mathematical Statistics. New York: Wiley, 1963.