ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
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Connections in control strategy; pp. 26–32

Full article in PDF format | doi: 10.3176/proc.2014.1.05

Authors
Maido Rahula, Petr Vašík

Abstract

We present an infinitesimal interpretation of the control theory, particularly of the part concerning dynamic systems. We use the original concept of a bundle connection, which lies in the idea of fibre transportation along a path on the base manifold. The control of a process leads also to the transportation of fibres, and the control strategy, i.e. the choice of a suitable system control in order to optimize the process corresponds to the choice of a path on the base manifold. The triple of crucial terms of control, aim–control–strategy, translates in the terms of connections as fibre–connection–curve. Such a scheme is quite convincing, but it also works well in dynamic systems analysis.


References

1. Atanasiu, Gh., Balan, V., Brînzei, N., and Rahula, M. 2009. Differential-Geometric Structures. Tangent Bundles, Connections in Fiber Bundles, Exponential Law and Jet Spaces. Librokom, Moscow (in Russian).

2. Perko, L. Differential Equations and Dynamic Systems. Springer, 1991.
http://dx.doi.org/10.1007/978-1-4684-0392-3

3. Rahula, M. New Problems in Differential Geometry. World Scientific Publishing Co. Pte. Ltd., 1993.

4. Rahula, M. and Vašík, P. A note on jet and geometric approach to higher order connections. Springer Proc. Math. Statistics (to appear).


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