Sliding Hopf bifurcation in interval systems
E. Hooton, Z. Balanov, W. Krawcewicz, D. Rachinskii
TL;DR
This paper uses equivariant degree theory and interval polynomial techniques to analyze Hopf bifurcations in interval systems, demonstrating the existence of periodic solutions relevant to robust control.
Contribution
It introduces a novel combination of equivariant degree theory with Kharitonov's theorem for analyzing Hopf bifurcations in interval systems.
Findings
Existence of periodic solutions in interval systems under mild conditions
Application of equivariant degree theory to bifurcation analysis
Illustrative examples demonstrating the theoretical results
Abstract
In this paper, the equivariant degree theory is used to analyze the occurrence of the Hopf bifurcation under effectively verifiable mild conditions. We combine the abstract result with standard interval polynomial techniques based on Kharitonov's theorem to show the existence of a branch of periodic solutions emanating from the equilibrium in the settings relevant to robust control. The results are illustrated with a number of examples.
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Taxonomy
TopicsAdvanced Control Systems Optimization · Model Reduction and Neural Networks · Adaptive Control of Nonlinear Systems