Comparative Analysis of Optimal Filters of the Second and Third Order for Continuous-Time Systems

We consider the problem of constructing functional filters (optimal functional observers, i.e., observers for linear functionals of the state vector) for linear time-invariant control systems in which the inhomogeneity contains additive white noise as a term in addition to control. The output of the...

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Bibliographic Details
Published in:Differential equations 2021-11, Vol.57 (11), p.1527-1535
Main Authors: Fomichev, V. V., Kamenshchikov, M. A.
Format: Article
Language:English
Subjects:
Comparative analysis
Continuous time systems
Control Theory
Difference and Functional Equations
Differential equations
Inhomogeneity
Mathematics
Mathematics and Statistics
Observers
Optimization
Ordinary Differential Equations
Partial Differential Equations
State vectors
White noise
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Summary:We consider the problem of constructing functional filters (optimal functional observers, i.e., observers for linear functionals of the state vector) for linear time-invariant control systems in which the inhomogeneity contains additive white noise as a term in addition to control. The output of the system is linear in the state vector and also contains additive white noise as a term. With the help of canonical representations, a comparative analysis of the second- and third-order filters by the mean square observation error in the steady state is carried out. An example of a fourth-order system is given, showing that with an increase in the dynamic order of the filter, the optimality by a quadratic criterion increases.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266121110112