Related papers: Fast cycles detecting in non-linear discrete syste…
We explore the problem of stabilization of unstable periodic orbits in discrete nonlinear dynamical systems. This work proposes the generalization of predictive control method for resolving the stabilization problem. Our method embodies the…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
A method of stabilizing 2-cycles in discrete dynamic systems by Delayed Feedback Control is developed by using classic Harmonic Analysis.
We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f:…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode…
The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative…
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the "robust identification error" framework in…
In this paper we develop further a method for detecting unstable periodic orbits (UPOs) by stabilising transformations, where the strategy is to transform the system of interest in such a way that the orbits become stable. The main…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…