A nonlinear set-membership filter for on-line applications

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 15, 2003, Pages 1337-1358

  Scholte, Eelco ^a   Campbell, Mark E ^a  

^a Cornell University   (United States)

Author keywords

Nonlinear systems; Set membership estimation; Stability analysis; Uncertainty modelling

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; GAUSSIAN NOISE (ELECTRONIC); KALMAN FILTERING; LINEARIZATION; ONLINE SYSTEMS; SET THEORY; SYSTEM STABILITY;

FAULT DETECTION; LINEARIZATION ERRORS; SET-MEMBERSHIP FILTERS (SMF);

NONLINEAR SYSTEMS;

EID: 0347409101     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.856     Document Type: Article

References (33)

1. Kwakernaak H, Sivan R. Linear Optimal Control Systems, Wiley-Interscience: New York, 1972.
2. Jazwinski A. Stochastic Processes and Filtering Theory, vol. 64. Academic Press: New York, 1970.
3. Ljung L. Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems. IEEE Transactions on Automatic Control 1979; AC-24(1):36-50.
4. Ward D, Monaco J, Bodson M. Development and flight testing of a parameter identification algorithm for reconfigurable control. Journal of Guidance Navigation and Control 1998; 21:948-956.
5. Reif K, Unbehauen R. The extended Kalman filter as an exponential observer for nonlinear systems. IEEE Transactions on Signal Processing 1999; 47(8):2324-2328.
6. Julier S, Uhlmann J, Durrant-Whyte HF. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control 2000; 45(3):477-482.
7. Brunke S, Campbell, ME. Estimation architecture for future autonomous vehicles. In Proceedings of the American Control Conference, Anchorage, AK, May 2002; 1108-1114.
8. Jeremy Kasdin N, Haupt GT. Second-order correction and numerical considerations for the two-step optimal estimator. Journal of Guidance, Control, and Dynamics 1997; 20(2):362-369.
9. Bodson M, Groszkiewicz JE. Multivariable adaptive algorithms for reconfigurable flight control. IEEE Transactions on Control Systems Technology 1997; 5(2):217-229.
10. Murray RM, Hauser J, Jadbabaie A, Milam MB, Petit N, Dunbar WB, Franz R. Online Control Customization via Optimization Based Control in: Software Enabled Control: Information Technology for Dynamical Systems, Samad T, Balas G (eds). John Wiley, Hoboken, NJ, 2003.
11. Richards A, How JP. Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In Proceedings of the American Control Conference, Anchorage, AK, May 2002; 1936-1941.
12. Schweppe FC. Recursive state estimation: Unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control 1968; AC-13(1):22-28.
13. Bertsekas DP, Rhodes IB. Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control 1971; AC-16(2):117-128.
14. Schweppe FC. Uncertain Dynamic Systems (1st edn). Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1973.
15. Fogel E, Huang YF. On the value of information in system identification - bounded noise case. Automatica 1982; 18(2):229-238.
16. Bai E-W, Ye Y, Tempo R. Bounded error parameter estimation: a sequential analytic center approach. In Proceedings of the 36th Conference on Decision and Control, San Diego, CA, December 1997; 732-737.
17. Shamma JS, Tu K-Y. Approximate set-valued observers for nonlinear systems. IEEE Transactions on Automatic Control 1997; 42(5):648-658.
18. Garulli A, Vicino A. Set membership localization of mobile robots via angle measurements. IEEE Transactions on Robotics and Automation 2001; 17(4):450-463.
19. Chisci L, Garulli A, Zappa G. Recursive state bounding by parallelotopes. Automatica 1996; 32(7):1049-1055.
20. Tsakalis KS, Song L. Set-membership estimation for weakly nonlinear models: an application to the adaptive control of semiconductor manufacturing processes. In Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, December 1994; 1066-1071.
21. Jaulin L, Walter E. Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica 1993; 29(4):1053-1064.
22. Moore RE. Interval Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1966.
23. Hansen E. Global Optimization Using Interval Analysis. Monographs and Textbooks in Pure and Applied Mathematics (1st edn). Marcel Dekker, Inc.: New York, 1992.
24. Zemke J. b4m: A Free Interval Arithmetic Toolbox for Matlab. http://www.ti3.tu-harburg.de/̃zemke/b4m/index.html. version 1.0.2.004.
25. Chernousko FL. State Estimation for Dynamic Systems (1st edn). CRC Press, Inc.: Boca Raton, FL, 1994.
26. Reif K, Guenther S, Yaz E, Unbehauen R. Stochastic stability of the discrete-time extended Kalman filter. IEEE Transactions on Automatic Control 1999; 44(4):714-728.
27. Schlaepfer FM. Set theoretic estimation of distributed parameter systems. Technical Report ESL-R-413, M.I.T., January 1970.
28. Song Y, Grizzle JW. The extended Kalman filter as a local asymptotic observer for discrete-time nonlinear systems. Journal of Mathematical Systems, Estimation and Control 1995; 5(1):59-78.
29. Anderson BDO, Moore JB. Detectability and stabilizability of time-varying discrete-time linear systems. SIAM Journal on Control and Optimization 1981; 19(1):20-32.
30. Moraal PE, Grizzle JW. Observer design for nonlinear systems with discrete-time measurements. IEEE Transactions on Automatic Control 1995; 40(3):395-404.
31. Scholte E, Campbell ME. On-line nonlinear guaranteed estimation with application to a high performance aircraft. In Proceedings of the American Control Conference, Anchorage, AK, May 2002; 184-190.
32. Campbell ME, Ousingsawat J. On-line estimation and path planning for multiple vehicles in an uncertain environment. In Proceedings of the AIAA Guidance, Navigation and Control Conference, 2002.
33. Campbell ME. Collision monitoring and avoidance in satellite clusters. 2002, submitted for publication.