Systems and Means of Informatics
2021, Volume 31, Issue 1, pp 37-56ANALYTICAL MODELING AND FILTERING FOR INTEGRODIFFERENTIAL SYSTEMS WITH UNSOLVED DERIVATIVES
- I. N. Sinitsyn
Abstract
For nonlinear integrodifferential stochastic systems (IDStS) with unsolved derivatives reducible to differential stochastic systems (StS) by means of singular kernels, the following methods and algorithms are proposed: analytical modeling of normal (Gaussian) stochastic processes and analytical synthesis of normal suboptimal filters for information processing in IDStS. Both Gaussian and non-Gaussian StS white noises are considered. Quality estimation methods based on the sensitivity theory are suggested. An example with discontinuous nonlinearity is considered in details. Directions for future investigations are given.[+] References (20)
- Pugachev, V.S., and I.N. Sinitsyn. 1987. Stochastic differential systems. Analysis and filtering. Chichester, NY: J. Wiley & Sons. 549 p.
- Pugachev, V.S., and I. N. Sinitsyn. 2001. Stochastic systems. Theory and applications. Singapore: World Scientific. 908 p.
- Sinitsyn, I.N. 2014. Analiz i modelirovanie raspredeleniy v ereditarnykh stokhasticheskikh sistemakh [Analysis and modeling of distributions in hereditary stochastic systems]. Informatika i ee Primeneniya - Inform. Appl. 8(1):2- 11.
- Sinitsyn, I.N., I.V. Sergeev, V. I. Sinitsyn, E.R. Korepanov, and V.V. Belousov. 2014. Matematicheskoe obespechenie parametricheskogo modelirovaniya raspredeleniy v integrodifferentsial'nykh stokhasticheskikh sistemakh [Mathematical software for parametric modeling of distributions in integrodifferential stochastic systems]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 24(1): 4-4 5.
- Sinitsyn, I.N. 2014. Analiticheskoe modelirovanie raspredeleniy s invariantnoy meroy v negaussovskikh differentsial ' nykh i privodimykh k nim ereditarnykh stokhasticheskikh sistemakh [Analytical modeling of distributions with invariant measure in non-Gaussian differential and reducible to differential hereditary stochastic systems]. Informatika i ee Primeneniya - Inform. Appl. 8(2): 2-14.
- Sinitsyn, I.N., and V.I. Sinitsyn. 2014. Normal'nye i ellipsoidal'nye raspredeleniya v integrodifferentsial'nykh sistemakh [Normal and ellipsoidal distributions in integrodifferential systems]. Sistemy komp'yuternoy matematiki i ikh prilozheniya: Matly XV Mezhdunar. konf. [15th Conference (International) "Systems of Computer Mathematics and Their Applications" Proceedings]. Smolensk: SmolGU. 15:196-197.
- Sinitsyn, I.N., V.I. Sinitsyn, and E.R. Korepanov. 2014. Analiticheskoe modelirovanie ereditarnykh stokhasticheskikh sistem so slozhnymi nelineynostyami [Analytical modeling of hereditary stochastic systems with complex nonlinearities]. Sovremennye problemy prikladnoy matematiki, informatiki, avtomatizatsii, upravleniya: Mat-ly 4-go Mezhdunar. nauchn.-tekhnich. seminara [4th Science and Technology Seminar (International) "Recent Developments in Applied Mathematics, Computer Science, Automation, and Control" Proceedings]. Moscow: IPI RAN. CD-R. 29-34.
- Sinitsyn, I.N., I.V. Sergeev, V.I. Sinitsyn, E.R. Korepanov, and V.V. Belousov. 2014. Analiticheskoe komp'yuternoe modelirovanie v ereditarnykh stokhasticheskikh sistemakh s avtokorrelirovannymi shumami [Analytical computer modeling in hereditary stochastic systems with autocorrelated noise]. Kibernetika i vysokie tekhnologii XXI veka: Sb. dokl. XV Mezhdunar. nauchn.-tekhnich. konf. [15th Science and Technology Conference (International) "Cybernetics and High Technology of the XXI Century" Proceedings]. Voronezh: SAKVOEE. CD-R. 543-551.
- Sinitsyn, I.N., E.R. Korepanov, and V.V. Belousov. 2015. Razvitie matematicheskogo obespecheniya analiticheskogo i statisticheskogo modelirovaniya ereditarnykh stokhasticheskikh sistem [Development of analytical and statistical modeling for gered- itary stochastic systems]. Identifikatsiya sistem i zadachi upravleniya: Tr. X Mezhdunar. konf. [10th Conference (International) on System Identification and Control Problems Proceedings]. Moscow: IPU RAN. 1275-1297.
- Sinitsyn, I.N. 2021 (in press.) Analytical modeling of "linear" and circular control stochastic systems. Advances in robotics and automatic control: Reviews. Book ser. IFSA Publishing. 2.
- Sinitsyn, I.N., V.I. Sinitsyn, I.V. Sergeev, E.R. Korepanov, and V.V. Belousov. 2015. Uslovno optimal ' naya fil 'tratsiya normal ' nykh protsessov v ereditarnykh stokhasticheskikh sistemakh [Conditionally optimal filtering of normal processes in hereditary stochastic systems]. Sovremennye problemy prikladnoy matematiki, informatiki, avtom- atizatsii i upravleniya: Tr. 5-go yubileynogo seminara ["Modern Problems of Applied Mathematics, Informatics, Automation and Control": 5th Anniversary Seminar Proceedings]. Sevastopol: SevSU. 23-33.
- Sinitsyn, I.N., I.V. Sergeev, V.I. Sinitsyn, E.R. Korepanov, V.V. Belousov, and V. S. Shorgin. 2015. Matematicheskoe obespechenie sinteza diskretnykh fil'trov Pugacheva dlya obrabotki normal'nykh protsessov v ereditarnykh stokhasticheskikh sistemakh [Software for synthesis of discrete Pugachev filters for normal processes in hereditary stochastic systems]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 25(2):62-101.
- Sinitsyn, I.N. 2017. Analiticheskoe modelirovanie shirokopolosnykh protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh [Analytical modeling of wide band processes in stochastic systems with unsolved derivatives]. Informatika i ee Primeneniya - Inform. Appl. 11(1): 3- 10.
- Sinitsyn, I.N. 2017. Parametricheskoe analiticheskoe modelirovanie protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh [Parametric analytical modeling of processes in stochastic systems that are not allowed with respect to derivatives]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 27(1):21-45.
- Sinitsyn, I.N. 2021. Normal'nye suboptimal'nyefil'try dlya differentsial'nykhstokhasticheskikh sistem, ne razreshennykh otnositel'no proizvodnykh [Normal suboptimal filtering for differential stochastic systems with unsolved derivatives]. Informatika i ee Primeneniya - Inform. Appl. 15 (1): 3- 10.
- Sinitsyn, I.N. 2007. Fil'try Kalmana i Pugacheva [Kalman and Pugachev filters]. 2nd ed. Moscow: Logos. 776 p.
- GOST 23743-88. 1993. Izdeliya aviatsionnoy tekhniki. Nomenklatura pokazateley bezopasnosti poleta, nadezhnosti, kontroleprigodnosti, ekspluatatsionnoy i remont- noy tekhnologichnosti [Aircraft products. Nomenclature of flight safety, reliability, testability, and operational and repair manufacturability]. Moscow: Standards Publs. 84 p.
- Aleksandrovskaya, L.N., I.Z. Aronov, V.I. Kruglov, et al. 2008. Bezopasnost' i nadezhnost' tekhnicheskikh system [Security and reliability of technical systems]. Moscow: Universitetskaya kniga, Logos. 376 p.
- Sinitsyn, I.N. 2009. Kanonicheskie predstavleniya sluchaynykh funktsiy i ikh prime- nenie v zadachakh komp'yuternoy podderzhki nauchnykh issledovaniy [Canonical expansions of random functions and their applications in computer-aided support]. Moscow: TORUS PRESS. 768 p.
- Sinitsyn, I.N. 2019. Lektsii po teorii sistem integrirovannoy logisticheskoy podderzhki [Lectures on theory of integrated logistic support systems]. Moscow: TORUS PRESS. 1072 p.
[+] About this article
Title
ANALYTICAL MODELING AND FILTERING FOR INTEGRODIFFERENTIAL SYSTEMS WITH UNSOLVED DERIVATIVESJournal
Systems and Means of InformaticsVolume 31, Issue 1, pp 37-56
Cover Date
2021-04-20DOI
10.14357/08696527210104Print ISSN
0869-6527Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
integrodifferential stochastic system (IDStS); method of analytical modeling (MAM); method of normal approximation (MNA); method of statistical linearization (MSL); normal suboptimal filter (NSOF); stochastic system (StS); stochastic systems with unsolved derivativesAuthors
I. N. Sinitsyn
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation