Finite-dimensional Filters with Nonlinear Drift Xiii: Classification of Finite-dimensional Estimation Algebras of Maximal Rank with State Space Dimension Five∗
نویسنده
چکیده
Abstract. The idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by Brockett and Mitter independently. For this approach, one needs to know explicitly the structure of these estimation algebras in order to construct finite dimensional nonlinear filters. Therefore Brockett proposed to classify all finite dimensional estimation algebras. Chiou and Yau [ChYa1] classify all finite dimensional estimation algebras of maximal rank with dimension of the state space less than or equal to two. The purpose of this paper is to give a new result on classification of all finite dimensional estimation algebras of maximal rank with state space dimension less than or equal to five.
منابع مشابه
On normalizers of maximal subfields of division algebras
Here, we investigate a conjecture posed by Amiri and Ariannejad claiming that if every maximal subfield of a division ring $D$ has trivial normalizer, then $D$ is commutative. Using Amitsur classification of finite subgroups of division rings, it is essentially shown that if $D$ is finite dimensional over its center then it contains a maximal subfield with non-trivial normalize...
متن کاملOn Nonlinear Filters for Mixed H 2 / H " Estimation *
We study the problem of mixed least-meansquares/H"-optimal (or mixed H2/Hm-optimal) estimation of signals generated by discrete-time, finitedimensional, linear state-space models. The major result is that, for finite-horizon problems, and when the stochastic disturbances have Gaussian distributions, the optimal solutions have finite-dimensional (i.e. , bounded-order) nonlinear state-space struc...
متن کاملOn dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کاملFinite dimensional rank 2 Nichols algebras of diagonal type I : Examples
Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are listed. Each of them is described in terms of generators and relations. A Poincaré–Birkhoff–Witt basis of all of these Nichols algebras is given and their dimensi...
متن کاملA classification of finite rank dimension groups by their representations in ordered real vector spaces
This paper systematically studies finite rank dimension groups, as well as finite dimensional ordered real vector spaces with Riesz interpolation. We provide an explicit description and classification of finite rank dimension groups, in the following sense. We show that for each n, there are (up to isomorphism) finitely many ordered real vector spaces of dimension n that have Riesz interpolatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006