zbMATH — the first resource for mathematics

Control of the dynamics of a system with differential constraints. (English. Russian original) Zbl 1432.93137
J. Comput. Syst. Sci. Int. 58, No. 4, 515-527 (2019); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2019, No. 4, 16-28 (2019).
Summary: We propose a method for solving the control problem of a system with allowance for the dynamics of actuation mechanisms. The aim of the control and kinematic properties of the system are determined by the holonomic and nonholonomic constraints imposed on the phase coordinates of the control plant. Control actions are generated with allowance for conditions for stabilizing the constraints in the numerical solution of the equations of the dynamics of a closed system.

93C15 Control/observation systems governed by ordinary differential equations
93D20 Asymptotic stability in control theory
Full Text: DOI
[1] H. F. Olson, Dynamical Analogies (Van Nostrand, New York, 1943).
[2] R. A. Layton, Principles of Analytical System Dynamics (Springer, New York, 1998). · Zbl 0902.70001
[3] H. Béghin, Étude théorique des compas gyrostatiques Anschütz et Sperry (C. R. Acad. Sci., Paris, 1922) [in French]. · JFM 48.0902.04
[4] G. V. Korenev, Purpose and Adaptability of Movement (Nauka, Moscow, 1974) [in Russian].
[5] A. S. Galiullin, I. A. Mukhametzyanov, R. G. Mukharlyamov, and V. D. Furasov, Building Software Systems Movement (Nauka, Moscow, 1971) [in Russian]. · Zbl 0233.70002
[6] R. G. Mukharlyamov,“To inverse problems of the qualitative theory of differential equations” Differ. Uravn. 3, 1673-1681 (1967). · Zbl 0167.37502
[7] O. V. Matukhina,“On the problem of simulating kinematics and dynamics of controllable systems with software links” Inzhen. Zh.: Nauka Innov., No. 4 (2018). https://doi.org/10.18698/2308-6033-2018-4-1753
[8] J. Baumgarte,“Stabilization of constraints and integrals of motion in dynamical systems” Comput. Methods Appl. Mech. Eng., No. 1, 1-16 (1972). · Zbl 0262.70017
[9] J. Baumgarte,“Stabilized Kepler motion connected with analytic step adaptation” Celest. Mech. 13, 105-109 (1976). · Zbl 0338.70008
[10] V. A. Avdyushev, Numerical Orbit Modeling (NTL, Tomsk, 2010) [in Russian].
[11] A. A. Burov and I. I. Kosenko,“The Lagrange differential-algebraic equations” J. Appl. Math. Mech. 78, 587-598 (2014). · Zbl 1432.70039
[12] J. Wittenburg, Dynamics of Systems of Rigid Bodies (Vieweg Teubner, Berlin, 1977). · Zbl 0363.70004
[13] F. Amirouche, Fundamentals of Multibody Dynamics: Theory and Applications (Birkhäuser, Boston, 2006). · Zbl 1083.70001
[14] Shih-Tin Lin and Jiann-Nan Huang,“Numerical integration of multibody mechanical systems using Baumgarte’s constraint stabilization method” J. Chin. Inst. Eng. 25, 243-252 (2002).
[15] U. M. Ascher, Hongsheng Chin, L. R. Petzold, and S. Reich,“Stabilization of constrained mechanical systems with DAEs and invariant manifolds” J. Mech. Struct. Mach. 23, 135-158 (1995).
[16] U. M. Ascher,“Stabilization of invariant of discretized differential systems” Numer. Algorithms 14, 1-24 (1997). · Zbl 0911.65058
[17] U. M. Ascher, Hongsheng Chin, and S. Reich,“Stabilization of DAEs and invariant manifolds” Numer. Math. 67, 131-149 (1994). · Zbl 0791.65051
[18] Shih-Tin Lin and Ming-Chong Hong,“Stabilization method for the numerical integration of controlled multibody mechanical system: a hybrid integration approach” JSME Int. J., Ser. C 44, 79-88 (2001).
[19] G. K. Suslov, On the Force Function, Admitting Given Integrals (Kievsk. Univ., Kiev, 1890) [in Russian].
[20] N. E. Zhukovskii,“Determination of the force function for this family of trajectories” in Complete Collection of Works (ONTI NKTP SSSR, Moscow, Leningrad, 1937), Vol. 1, pp. 293-308 [in Russian].
[21] T. Levi Chivita and U. Amaldi, Lezioni di meccanica razionale (Compomat, Italy, 2013), Vol. 2, Part 2 [in Italian].
[22] A. S. Galiullin, Solving Methods for Inverse Dynamics Problems (Nauka, Moscow, 1986) [in Russian]. · Zbl 0658.70001
[23] G. Bozis and S. Ichtiaroglou,“Existence and construction of dynamical systems having a prescribed integral of motion – an inverse problem” Inverse Probl. 3, 213-227 (1987). · Zbl 0647.34044
[24] N. P. Erugin,“Construction of the entire set of systems of differential equations with a given integral curve” Prikl. Mat. Mekh. 21, 659-670 (1952).
[25] R. G. Mukharlyamov,“On the construction of differential equations of optimal motion for a given variety” Differ. Uravn. 7, 1825-1834 (1971).
[26] R. G. Mukharlyamov,“On the construction of the set of systems of differential equations of stable motion on an integral manifold” Differ. Uravn. 5, 688-699 (1969).
[27] R. G. Mukharlyamov,“On solving systems of nonlinear equations” Zh. Vychisl. Mat. Mat. Fiz. 11, 829-836 (1971).
[28] R. G. Mukharlyamov,“On equations of motion of mechanical systems” Differ. Uravn. 19, 2048-2056 (1983). · Zbl 0544.70029
[29] R. G. Mukharlyamov and Deressa Chernet Tuge,“Stabilization of redundantly constrained dynamic system” Vestn. RUDN, Ser.: Mat. Inform. Fiz., No. 1, 60-72 (2015).
[30] R. G. Mukharlyamov,“Control of dynamics of systems with positional relations” in Analytical Mechanics, Stability and Control, Proceedings of the 11th International Chetaev Conference, Sect. 3: Control (KNITU-KAI, Kazan’, 2017), Vol. 3, Part 2, pp. 140-146.
[31] V. V. Kozlov,“The dynamics of systems with servoconstraints. I” Regular Chaot. Dyn. 20, 205-224 (2015). · Zbl 1353.70036
[32] V. V. Kozlov,“The dynamics of systems with servoconstraints. II” Regular Chaot. Dyn. 20, 401-427 (2015). · Zbl 1353.70012
[33] A. W. Beshaw,“Dynamic equation of constrained mechanical system” Vestn. RUDN. Ser.: Mat. Inform. Fiz., No. 3, 115-124 (2014).
[34] Adaptive Optics: Collection of Articles, Ed. by E. A. Vitrichenko (Mir, Moscow, 1980) [in Russian].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.