Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises
The problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the s...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/3/370 |
| _version_ | 1827660002551136256 |
|---|---|
| author | Mikhail Kamenshchikov |
| author_facet | Mikhail Kamenshchikov |
| author_sort | Mikhail Kamenshchikov |
| collection | DOAJ |
| description | The problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the second and third order are obtained in the canonical basis. Analytical expressions of the transfer function matrix from the input noise to the estimation error are presented. A numerical example is given to compare the performance of filters by the quadratic criterion in the steady state. |
| first_indexed | 2024-03-09T23:33:07Z |
| format | Article |
| id | doaj.art-60bc485f0a7f437fb48391f3eebf469c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:33:07Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-60bc485f0a7f437fb48391f3eebf469c2023-11-23T17:06:24ZengMDPI AGMathematics2227-73902022-01-0110337010.3390/math10030370Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive NoisesMikhail Kamenshchikov0Department of Nonlinear Dynamical Systems and Control Processes, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, RussiaThe problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the second and third order are obtained in the canonical basis. Analytical expressions of the transfer function matrix from the input noise to the estimation error are presented. A numerical example is given to compare the performance of filters by the quadratic criterion in the steady state.https://www.mdpi.com/2227-7390/10/3/370discrete time functional filteroptimal unbiased estimationsteady state |
| spellingShingle | Mikhail Kamenshchikov Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises Mathematics discrete time functional filter optimal unbiased estimation steady state |
| title | Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises |
| title_full | Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises |
| title_fullStr | Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises |
| title_full_unstemmed | Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises |
| title_short | Conditions for Existence of Second-Order and Third-Order Filters for Discrete Systems with Additive Noises |
| title_sort | conditions for existence of second order and third order filters for discrete systems with additive noises |
| topic | discrete time functional filter optimal unbiased estimation steady state |
| url | https://www.mdpi.com/2227-7390/10/3/370 |
| work_keys_str_mv | AT mikhailkamenshchikov conditionsforexistenceofsecondorderandthirdorderfiltersfordiscretesystemswithadditivenoises |