Multipoint Numerical Criterion for Manifolds to Guarantee Attractor Properties in the Problem of Synergetic Control Design

• Published in: ITM Web of Conferences Vol. 18; p. 1001
• Main Authors: Diveev, Askhat, Shmalko, Elizaveta, Sofronova, Elena
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Les Ulis EDP Sciences 2018
• Subjects: Control methods; Criteria; Manifolds (mathematics); Numerical methods; Properties (attributes); Synthesis
• ISSN: 2271-2097; 2431-7578; 2271-2097
• DOI: 10.1051/itmconf/20181801001

The paper presents the results of our research on the application of symbolic regression methods for the numerical solution of the problem of synthesis of synergetic control. Synergetic control is characterized by the presence of manifolds in the state space that must have the properties of an attractor, in particular terminal manifolds, as well as the existence of regions of state space through which system solutions do not pass, for example, phase constraints, that must have the properties of repellers. In the present paper we formulate a numerical criterion for ensuring the property of an attractor for a terminal manifold of arbitrary dimension, taking into account the dynamic behavior of the system in a neighborhood of a given manifold. The results of computational experiments on the effective application of the proposed criterion are presented. It is shown that the proposed approach makes it possible to automate the synthesis of synergistic control using the methods of symbolic regression.