Ellipsoidal filtering of the state of an infinite-dimensional system. II. Filtering by discrete-continuous observations with a vector measure
type: Item
instance of: scholarly article
title: Ellipsoidal filtering of the state of an infinite-dimensional system. II. Filtering by discrete-continuous observations with a vector measure
zbMATH Open document ID: 0922.93007
author: Michael Basin
published in: Automation and Remote Control
publication date: 1999-09-13T00:00:00Z
review text: [For Part I see Autom. Remote Control 58, No. 7, Pt. 1, 1110-1118 (1997); translation from Avtom. Telemekh. 1997, No. 7, 54-65 (1997; Zbl 0921.34061).] The paper deals with the problem of guaranteed state estimation for an infinite-dimensional system defined in a Hilbert space by the equation \[ dx(t)=(Ax(t)+ b(t))dt, \;x(t_0) =x_0 \] and by the discrete-continuous observations \[ dy_i(t)=C_ix(t)du_i(t)+ \xi _i(t)du_i(t) \;(i=1, \dots , m), \;y(t_0 -) =y_0. \] Here the functions \(u_i(t)\) are of bounded variation and may be treated as observation impulse controls. The uncertainties \(x_0, \xi (t)\) belong to ellipsoids in the corresponding spaces. The ellipsoidal filtering differential equations are derived by limit procedures from finite-dimensional discretizations of the system and it is shown that these differential equations have state discontinuities at their right-hand sides. The author studies both cases for the solution to the filtering equations to be unique (when the Frobenius condition is satisfied) or not. In the latter case as in impulse control systems theory, the set of generalized solutions is introduced with an additional optimization problem for choosing the unique optimal element to be used in state estimation.
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 49N10
zbMATH DE Number: 1263099
zbMATH Keywords: infinite-dimensional system
zbMATH Keywords: uncertainty
zbMATH Keywords: ellipsoidal guaranteed estimation
zbMATH Keywords: discrete-continuous observations
zbMATH Keywords: state discontinuities
reviewed by: T. F. Filippova
MaRDI profile type: Publication
Recommended article: Ellipsoidal filtering over discrete-continuous observations with a vector measure
Recommended article: Q4892215
Recommended article: Q3655156
Recommended article: Guaranteed estimation of linear dynamic systems based on discrete- continuous observations
Recommended article: Q4385123
Recommended article: State estimation in continuous dynamic systems by the ellipsoid method
Recommended article: Constructing an analogue of the Kalman filter for a guaranteed state estimation of a dynamic system
Recommended article: Filtering under nonrandom disturbances: the method of invariant ellipsoids
Recommended article: Robust filtering under nonrandom disturbances: the invariant ellipsoid approach
Recommended article: Comparison of stochastic and guaranteed approaches to the estimation of the state of dynamic systems
description: scientific article; zbMATH DE number 1263099