Control of system dynamics and constraints stabilization. (English) Zbl 1465.70078
Vishnevskiy, Vladimir M. (ed.) et al., Distributed computer and communication networks. 20th international conference, DCCN 2017, Moscow, Russia, September 25–29, 2017. Proceedings. Cham: Springer. Commun. Comput. Inf. Sci. 700, 431-442 (2017).
Summary: The equations of classical mechanics used for describing a dynamical process of controlled systems containing different elements. The method of constructing differential equations of known partial integrals is used to stabilize the constraints imposed on the mechanical system dynamics which is described by Lagrange equations and Hamilton equations. The problem of constructing the dynamics equations with known properties of motion in the class of Ito stochastic differential equations was investigated by M. I. Tleubergenov and D. T. Azhymbaev. Assuming that some of the properties of the motion are known and the random perturbing forces belong to the class of processes with independent increments, Lagrange functions, Hamilton functions and Birkhoff functions can be constructed. Stability conditions for solutions of equations of dynamics with respect to the constraint equations are obtained, and an algorithm for constructing equations of constraint perturbations that guarantees the stabilization of constraints in the course of numerical solution is proposed. The problem of controlling the rectilinear motion of a cart with inverted pendulum is solved.
For the entire collection see [Zbl 1393.68018].
For the entire collection see [Zbl 1393.68018].
MSC:
| 70Q05 | Control of mechanical systems |
| 93D15 | Stabilization of systems by feedback |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34F05 | Ordinary differential equations and systems with randomness |
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