Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Three Mathematical Problems from Synergetic Control Theory

Author(s):

Alexander V. Bratishchev

Don State Technical University
Professor of Applied Mathematics Department
Rostov-on-Don, Gagarin sq.,1
Professor, doctor fiz.-mat. nauk

avbratishchev@spark-mail.ru

Abstract:

In the synergetic control theory for a given dynamic system and a manifold in the phase space there is the method of constructing the regulator for which this manifold will be invariant and attracting as a whole. In the article the criterion of the asymptotic stability of the equilibrium states of this regulator is obtained. We compare methods of parallel and sequential introduction of the attracting manifolds on the example of a third order autonomous system. The task about permissible equilibrium states of the synthesized regulator is discussed.

Keywords

• additive control
• aggregated variable
• autonomous system
• dynamical system
• equilibrium
• synergetic controller

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