
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 132–145
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MATHEMATICS
Turnpike processes of control systems on smooth manifolds
E. L. Tonkov^{ab} ^{a} Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
^{b} Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
Abstract:
We consider the socalled standard control systems. These are systems of differential equations defined on smooth manifolds of finite dimension that are uniformly continuous and timebound on the real axis and locally Lipschitz in the phase variables. In addition, we assume that the compact set is given, which defines geometric constraints on the admissible controls and moreover, the nondegeneracy condition holds. This condition means that for each point of the phase manifold and for all times there exists a control such that the value of vector field is contained in the Euclidean space that is tangent to the phase manifold at a given point.
Using the modified method of the Lyapunov function and constructing omegalimit set of the corresponding dynamical system of shifts, we give propositions about the existence of admissible control processes that are bounded on the positive semiaxis, and the assertion of uniform local controllability of the corresponding turnpike process.
Keywords:
turnpike processes, manifolds of finite dimension, uniform local controllability, omegalimit sets, Lyapunov functions.
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UDC:
515.163.1+517.977.1
MSC: 34A26, 34H05, 34A60 Received: 30.11.2013
Citation:
E. L. Tonkov, “Turnpike processes of control systems on smooth manifolds”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 132–145
Citation in format AMSBIB
\Bibitem{Ton13}
\by E.~L.~Tonkov
\paper Turnpike processes of control systems on smooth manifolds
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 4
\pages 132145
\mathnet{http://mi.mathnet.ru/vuu408}
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This publication is cited in the following articles:

E. L. Tonkov, “Barbashin and Krasovskii's asymptotic stability theorem in application to control systems on smooth manifolds”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 208–221

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