New suboptimal approach to the filtering problem for bilinear stochastic differential systems

SIAM Journal on Control and Optimization

Volumn 38, Issue 4, 2000, Pages 1171-1203

  Carravetta, Francesco ^a   Germani, Alfredo ^a,b   Shuakayev, Marat K ^c  

^a CNR   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

^c SATBAYEV UNIVERSITY   (Kazakhstan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONTROL SYSTEM ANALYSIS; LINEAR SYSTEMS; MULTIVARIABLE CONTROL SYSTEMS; OPTIMAL SYSTEMS; SIGNAL FILTERING AND PREDICTION; STATE ESTIMATION; STATISTICAL METHODS;

FINITE DIMENSIONAL FILTERS; POLYNOMIAL FILTERING; STOCHASTIC BILINEAR SYSTEMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 0033683643     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997320912     Document Type: Article

References (15)

1. R. E. KALMAN, A new approach to linear filtering and prediction problems, J. Basic. Engrg., 1 (1960), pp. 35-45.
2. R. E. KALMAN AND R. S. BUCY, New results in linear filtering and prediction theory, Trans. ASME Ser. D. J. Basic Engrg., 83 (1961), pp. 95-108.
3. R. S. LIPTSER AND A. N. SHIRYAYEV, Statistics of Random Processes, Vol. 2, Springer-Verlag, New York, 1978.
4. R. R. MOHLER, Bilinear Control Processes, Academic Press, New York, 1970.
5. C. BRUNI, G. DI PILLO, AND G. KOCH, Bilinear systems: An appealing class of "nearly linear" systems in theory and applications, IEEE Trans. Automat. Control, 19 (1974), pp. 334-348.
6. C. BRUNI AND G. KOCH, Suboptimal filtering for linear-in-control systems with small observation noise, in IV International Federation of Automatic Control Symposium on Identification and System Parameter Estimation, Tblisi, SSSR, Sept. 1976.
7. X. YANG, R. R. MOHLER, AND R. M. BURTON, Adaptive suboptimal filtering of bilinear systems, Internat. J. Control, 52 (1990), pp. 135-158.
8. E. YAZ, Full and reduced order observer design for discrete stochastic bilinear systems, IEEE Trans. Automat. Control, 37 (1992), pp. 503-505.
9. F. CARRAVETTA, A. GERMANI, AND M. RAIMONDI, Polynomial filtering for linear discrete-time non-Gaussian systems, SIAM J. Control Optim., 34 (1996), pp. 1666-1690.
10. F. CARRAVETTA, A. GERMANI, AND M. RAIMONDI, Polynomial filtering of discrete-time stochastic linear systems with multiplicative state noise, IEEE Trans. Automat. Control, 42 (1997), pp. 1106-1126.
11. G. KALLIANPUR, Stochastic Filtering Theory, Springer-Verlag, New York, 1980.
12. V. KRISHNAN, Nonlinear Filtering and Smoothing, John Wiley, New York, 1984.
13. d by a finite-element technique, Stochastics, 23 (1988), pp. 131-148.
14. R. BELLMAN, Introduction to Matrix Analysis, McGraw-Hill, New York, 1970.
15. G. S. RODGERS, Matrix Derivatives, Lecture Notes in Statist. 2, Marcel Dekker, New York, 1980.