Tertychnyi-Dauri, Vladimir Yurievich

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Total publications: 24
Scientific articles: 24

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Doctor of physico-mathematical sciences (1994)
Speciality: 01.02.01 (Theoretical mechanics)
Birth date: 12.02.1954
Keywords: adaptive systems; stochastic dynamics; optimal control theory; hyperreactive mechanics; synthesis of nonlinear dynamical systems; stability theory; canonical transformations of controlled systems
UDC: 519.95, 519.71, 517.2, 62-50, 621.391.1, 517.97, 519.21, 62-506.1:62-501.52, 62-50:714.3
MSC: 70H03, 70H14, 70H15, 70P05, 70Q05, 93C40, 93D21, 93E03, 93E15, 60J60, 93E35, 93C15, 93D15


The problem of the synthesis of adaptive nonlinear dynamical systems providing unknown parametrical drift was solved. The problem of the optimal stabilization of nonlinear holonomic and nonholonomic systems into adaptive statement was formulated and solved. The solution of the problem of optimal synthesis of adaptive nonlinear dynamical systems with the general form connections was obtained. The synthesis of adaptive controlled systems on the basis of the Hamilton-Jacobi canonical transformations was realized. The solution was achieved for the optimization problem of adaptive controlled systems with distributive parameters. The problem of optimal stabilization of nonlinear stochastic systems was solved. Some problems of the solid body stochastic motion were formulated and solved. The investigation was conducted for the question about motion of nonlinear dynamical systems with stochastic connections and concerning of stochastic nonstability presence. Optimal parametrical synthesis of nonlinear stochastic systems with the random stoppage moment was realized. The solution of the problem for the optimal nonlinear adaptive filtering about Kalman-Bucy method was obtained. The differential principle of motion completness for the variable-mass point into space was proposed. Using this principle as the base the equations describing the hyperreactive motion was derived and properties of this motion was studied.


Graduated from Faculty of Mathematics and Mechanics of Leningrad State University (LSU) in 1977 (department of theoretical mechanics) and post-graduate course of LSU in 1980 (department of theoretical cybernetics). Ph.D. thesis was defended in 1980. D.Sci thesis was defended in 1994. A list of my works contains about 100 titles and 5 monographs.

Main publications:
  • Tertychny-Dauri V. Yu. Adaptive Mechanics. Dordrecht, Boston, London: Kluwer Academic Publishers, 2002. 507 p.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. V. Yu. Tertychnyi-Dauri, “Designing adaptive control in the problem of optimal damping of perturbations”, Avtomat. i Telemekh., 2012, 9,  88–110  mathnet  zmath; Autom. Remote Control, 73:9 (2012), 1511–1528  isi  scopus
2. V. Yu. Tertychny-Dauri, “Integral and integro-differential control plants: Optimality conditions”, Avtomat. i Telemekh., 2009, 10,  45–74  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 70:10 (2009), 1635–1661  isi  elib  scopus
3. V. Yu. Tertychny-Dauri, “Conditional variational problems of control for distributed-parameter systems”, Avtomat. i Telemekh., 2008, 11,  62–81  mathnet  mathscinet  zmath; Autom. Remote Control, 69:11 (2008), 1873–1891  isi  scopus
4. V. Yu. Tertychny-Dauri, “A conditional optimal control problem and its adaptive solution method”, Avtomat. i Telemekh., 2006, 3,  54–67  mathnet  mathscinet  zmath; Autom. Remote Control, 67:3 (2006), 393–404  scopus
5. V. Yu. Tertychnyi-Dauri, “Optimal stabilization in problems of adaptive nuclear kinetics”, Differ. Uravn., 42:3 (2006),  374–384  mathnet  mathscinet; Differ. Equ., 42:3 (2006), 400–411
6. V. Yu. Tertychny-Dauri, “Variational dynamic problems with parameters and their adaptive interpretation”, Avtomat. i Telemekh., 2005, 9,  114–128  mathnet  mathscinet; Autom. Remote Control, 66:9 (2005), 1465–1477  scopus
7. V. Yu. Tertychny-Dauri, “Solution of Variational Dynamic Problems under Parametric Uncertainty”, Probl. Peredachi Inf., 41:1 (2005),  53–67  mathnet  mathscinet  zmath; Problems Inform. Transmission, 41:1 (2005), 45–58
8. V. Yu. Tertychny-Dauri, “Adaptive Optimal Nonlinear Filtration and Certain Related Topics. II”, Avtomat. i Telemekh., 2002, 1,  86–101  mathnet  mathscinet  zmath; Autom. Remote Control, 63:1 (2002), 76–89  isi  scopus
9. V. Yu. Tertychnyi-Dauri, “Adaptive Design of Nonlinear Dynamic Systems under Noise-Corrupted Control”, Avtomat. i Telemekh., 2001, 12,  122–128  mathnet  mathscinet  zmath; Autom. Remote Control, 62:12 (2001), 2042–2047  isi  scopus
10. V. Yu. Tertychnyi-Dauri, “Optimal Adaptive Nonlinear Filtering and Related Topics. I”, Avtomat. i Telemekh., 2001, 9,  125–137  mathnet  mathscinet  zmath; Autom. Remote Control, 62:9 (2001), 1511–1522  isi  scopus
11. V. Yu. Tertychnyi-Dauri, “Optimal Stabilization of Adaptive Dynamical Systems with Distributed Parameters: II”, Differ. Uravn., 37:11 (2001),  1542–1550  mathnet  mathscinet; Differ. Equ., 37:11 (2001), 1618–1626
12. V. Yu. Tertychnyi-Dauri, “Optimal Stabilization of Adaptive Dynamical Systems with Distributed Parameters: I”, Differ. Uravn., 37:8 (2001),  1096–1107  mathnet  mathscinet; Differ. Equ., 37:8 (2001), 1148–1159
13. V. Yu. Tertychny-Dauri, “Parametric Filtering: Optimal Synthesis on a Nonlinear Dynamic Variety”, Probl. Peredachi Inf., 37:4 (2001),  97–111  mathnet  mathscinet  zmath; Problems Inform. Transmission, 37:4 (2001), 365–379
14. V. Yu. Tertychnyi, “On the Equivalence of Optimization Criteria in the General Adaptive Synthesis Problem for Controllable Lagrangian Systems”, Avtomat. i Telemekh., 1996, 3,  116–127  mathnet  mathscinet  zmath; Autom. Remote Control, 57:3 (1996), 396–405
15. V. Yu. Tertychnyi, “Optimal parametric correction of stochastic Lagrangian systems. The asymptotic approach. III”, Avtomat. i Telemekh., 1995, 2,  81–91  mathnet  mathscinet  zmath; Autom. Remote Control, 56:2 (1995), 219–227
16. V. Yu. Tertychnyi, “Optimal parametric correction of stochastic Lagrangian systems. The asymptotic approach. II”, Avtomat. i Telemekh., 1995, 1,  129–144  mathnet  mathscinet  zmath; Autom. Remote Control, 56:1 (1995), 106–118
17. V. Yu. Tertychnyĭ, “Optimal parametric correction of stochastic Lagrangian systems. An asymptotic approach. I”, Avtomat. i Telemekh., 1994, 12,  104–116  mathnet  mathscinet  zmath; Autom. Remote Control, 55:12 (1994), 1791–1801
18. V. Yu. Tertychnyĭ, “Optimal stochastic stabilization of adaptive mechanical systems”, Avtomat. i Telemekh., 1993, 1,  111–118  mathnet  mathscinet  zmath; Autom. Remote Control, 54:1 (1993), 104–111
19. V. Yu. Tertychnyi, “Adaptive integro-differential algorithms for the stochastic optimization of dynamical systems”, Differ. Uravn., 29:4 (1993),  610–616  mathnet  mathscinet; Differ. Equ., 29:4 (1993), 518–523
20. V. Yu. Tertychny-Dauri, “A model problem of the adaptive stabilization for the non-linear dynamic object under conditions of the strong parameter indenermination”, Matem. Mod., 5:9 (1993),  98–110  mathnet  mathscinet
21. V. Yu. Tertychnyĭ, “Design of an adaptive system for the stabilization of nonlinear dynamical objects using integral transformations”, Avtomat. i Telemekh., 1992, 3,  112–123  mathnet  mathscinet; Autom. Remote Control, 53:3 (1992), 420–429
22. V. Yu. Tertychnyi, “On asymptotic properties of a stochastic algorithm for adaptive control”, Avtomat. i Telemekh., 1988, 8,  105–115  mathnet  mathscinet  zmath; Autom. Remote Control, 49:8 (1988), 1042–1051
23. V. Yu. Tertychnyĭ, “Stochastic stabilizability of controlled diffusion processes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1986, 5,  84–87  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 30:5 (1986), 113–116
24. V. Yu. Tertychnyĭ, “Finite convergence of a self-tuning adaptation algorithm”, Avtomat. i Telemekh., 1985, 12,  156–160  mathnet  mathscinet

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