title: A new approach to finding the control transporting a system from one phase state to another
metadata.name: dc.contributor.author
metadata.value: Zegzhda, Sergey A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shatrov, Egor A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Yushkov, Mikhail P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-01T11:57:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-01T11:57:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2465
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In their previous papers the authors have considered a possibility of application of the theory of motion
  for nonholonomic systems with high-order constraints to solving one of the main problems of the control
  theory. This is a problem of transporting a mechanical system with the finite number of degrees of freedom
  from a given phase state to another given phase state during a fixed time. It was shown that when solving
  such a problem using the Pontryagin maximum principle with minimization of the integral of the control
  force squared, a nonholonomic high-order constraint is realized continuously during the motion of the
  system. But in this case, one can also apply a generalized Gauss principle, which is commonly used in the
  motion of nonholonomic systems with high-order constraints. It is essential that the latter principle makes
  it possible to find the control as a polynomial, while the use of the Pontryagin maximum principle yields the
  control containing harmonics with natural frequencies of the system. The latter fact determines increasing
  the amplitude of oscillation of the system if the time of motion is long. Besides this, a generalized Gauss
  principle allows us to formulate and solve extended boundary problems in which along with the conditions
  for generalized coordinates and velocities at the beginning and at the end of motion, the values of anyorder
  derivatives of the coordinates are introduced at the same time instants. This makes it possible to
  find the control without jumps at the beginning and at the end of motion. The theory presented has been
  demonstrated when solving the problem of the control of horizontal motion of a trolley with pendulums.
  A similar problem can be considered as a model, since when the parameters are chosen correspondingly it
  becomes equivalent to the problem of suppression of oscillations of a given elastic body some cross-section
  of which should move by a given distance in a fixed time. Equivalence of these problems widens essentially
  a range of possible applications of the problem of a trolley with pendulums.
  Earlier solving the problem has been reduced to the choice of a horizontal force that is a solution of
  the problem formulated. In the present paper it is offered to seek an acceleration of a trolley, with which
  it moves by a given distance in a fixed time, as a time function but not a force applied to the trolley, the
  velocities and accelerations being equal to zero at the beginning and at the end of motion. In this new
  problem the rotation angles of pendulums are the principal coordinates. This makes it possible to find a
  sought acceleration of a trolley on the basis of a generalized Gauss principle according to the technique
  developed before. Knowing the motion of a trolley and pendulums it is easy to determine the required
  control force. The results of numerical calculation are presented. Refs 11. Figs 7.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: control of motion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: control force
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Pontryagin maximum principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized Gauss principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: extended boundary problem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A new approach to finding the control transporting a system from one phase state to another
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
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