Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises
The paper states a problem and considers two possible methods to estimate the anisotropic norm upper bound for discrete multiplicative noise systems. Shows that standard algorithms of anisotropic norm counting are disabled for multiplicative noise systems. It is impossible to design “the worst” form...
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| Format: | Article |
| Language: | Russian |
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MGTU im. N.È. Baumana
2017-09-01
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| Series: | Matematika i Matematičeskoe Modelirovanie |
| Subjects: | |
| Online Access: | https://www.mathmelpub.ru/jour/article/view/75 |
| _version_ | 1818058361662341120 |
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| author | A. V. Yurchenkov |
| author_facet | A. V. Yurchenkov |
| author_sort | A. V. Yurchenkov |
| collection | DOAJ |
| description | The paper states a problem and considers two possible methods to estimate the anisotropic norm upper bound for discrete multiplicative noise systems. Shows that standard algorithms of anisotropic norm counting are disabled for multiplicative noise systems. It is impossible to design “the worst” former filter with bounded mean anisotropy because of the noise components in the mathematical description of the system. Such a filter generates a sequence producing the gain maximum as an induced norm. Since there is no algorithm to calculate an anisotropic norm for multiplicative systems a problem of upper bound evaluation is considered. The main result includes two methods. Both of them use an idea of synthesis of some systems without noises. The first algorithm uses a parametric uncertain model with majorant anisotropic norm for original multiplicative noise system. The second one uses decomposition of original systems into two separate subsystems with outputs equivalent to multiplicative noise system output.The article describes advantage and disadvantage of each method. Both algorithms are based on the bounded real lemma widely used in anisotropic theory. Thanks to this lemma a problem of the upper bound anisotropic norm computation is formulated in terms of solvability of specialized matrix systems of inequalities and equalities. The specialized matrix system is convex. That’s why it is possible to find a solution by means of standard semidefinite programming procedure. The MATLAB contains many optimization methods, for example, yalmip with SeDuMi solver is feasible for the problem under consideration. The article presents different values of anisotropic norm of mechanical oscillator system for different values of mean anisotropy input level. Results are given in tabular form. |
| first_indexed | 2024-12-10T12:59:25Z |
| format | Article |
| id | doaj.art-8231313c4a0b4c5ea77bde8cb6c2e1cb |
| institution | Directory Open Access Journal |
| issn | 2412-5911 |
| language | Russian |
| last_indexed | 2024-12-10T12:59:25Z |
| publishDate | 2017-09-01 |
| publisher | MGTU im. N.È. Baumana |
| record_format | Article |
| series | Matematika i Matematičeskoe Modelirovanie |
| spelling | doaj.art-8231313c4a0b4c5ea77bde8cb6c2e1cb2022-12-22T01:48:00ZrusMGTU im. N.È. BaumanaMatematika i Matematičeskoe Modelirovanie2412-59112017-09-0104284171Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative NoisesA. V. Yurchenkov0Bauman Moscow State Technical University, Moscow; V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, MoscowThe paper states a problem and considers two possible methods to estimate the anisotropic norm upper bound for discrete multiplicative noise systems. Shows that standard algorithms of anisotropic norm counting are disabled for multiplicative noise systems. It is impossible to design “the worst” former filter with bounded mean anisotropy because of the noise components in the mathematical description of the system. Such a filter generates a sequence producing the gain maximum as an induced norm. Since there is no algorithm to calculate an anisotropic norm for multiplicative systems a problem of upper bound evaluation is considered. The main result includes two methods. Both of them use an idea of synthesis of some systems without noises. The first algorithm uses a parametric uncertain model with majorant anisotropic norm for original multiplicative noise system. The second one uses decomposition of original systems into two separate subsystems with outputs equivalent to multiplicative noise system output.The article describes advantage and disadvantage of each method. Both algorithms are based on the bounded real lemma widely used in anisotropic theory. Thanks to this lemma a problem of the upper bound anisotropic norm computation is formulated in terms of solvability of specialized matrix systems of inequalities and equalities. The specialized matrix system is convex. That’s why it is possible to find a solution by means of standard semidefinite programming procedure. The MATLAB contains many optimization methods, for example, yalmip with SeDuMi solver is feasible for the problem under consideration. The article presents different values of anisotropic norm of mechanical oscillator system for different values of mean anisotropy input level. Results are given in tabular form.https://www.mathmelpub.ru/jour/article/view/75multiplicative noisesanisotropic theoryrobustness |
| spellingShingle | A. V. Yurchenkov Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises Matematika i Matematičeskoe Modelirovanie multiplicative noises anisotropic theory robustness |
| title | Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises |
| title_full | Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises |
| title_fullStr | Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises |
| title_full_unstemmed | Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises |
| title_short | Anisotropic Norm Estimation for Discrete Time-Invariant System with Multiplicative Noises |
| title_sort | anisotropic norm estimation for discrete time invariant system with multiplicative noises |
| topic | multiplicative noises anisotropic theory robustness |
| url | https://www.mathmelpub.ru/jour/article/view/75 |
| work_keys_str_mv | AT avyurchenkov anisotropicnormestimationfordiscretetimeinvariantsystemwithmultiplicativenoises |