ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 17, 35, 60, 93 Tang, Shanjian, Fudan University, China Brockett’s problem of classification of finite-dimensional estimation algebras for Nonlinear Filtering Systems In his talk at the International Congress of Mathematicians in 1982, Brockett proposed classifying all finite-dimensional estimation algebras arising in nonlinear filters. Recently, Chen, Yau and Leung (1997) classified all finitedimensional estimation algebras of maximal rank when the dimension of the state space is less than or equal to four. In this paper, without dimension assumption on the state space, we succeed in classifying all finite-dimensional estimation algebras of maximal rank with the state-space dimension being arbitrary. Reference: Chen, J., Yau, S. S. -T. and Leung, C. W. , Finite-dimensional filters with nonlinear drift VIII: classification of finite-dimensional estimation algebras of maximal rank with state-space dimension 4, SIAM J. Control & Optim., 35(4)(1997), 1132–1141