Related papers: Anticontrol Techniques for Systems of Lorenz Type
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…
It is demonstrated that improved entrainment control of chaotic systems can maintain periodic goal dynamics near unstable periodic orbits without feedback. The method is based on the optimization of goal trajectories and leads to small…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
In this work we study the periodic orbits which bifurcate from a zero-Hopf bifurcations that a Lorenz-Haken system in R 4 can exhibit. The main tool used is the averaging theory.
This paper studies the dynamical properties of closed-loop systems obtained from control barrier function-based safety filters. We provide a sufficient and necessary condition for the existence of undesirable equilibria and show that the…
Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
The ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…
We will show that there is a universal connection between the achievable closed-loop dynamics and the corresponding feedback controller that produces it. This connection shows promise to lead to new methods for robust nonlinear control in…
In this work we study the existence of mechanisms of transition to global chaos in a closed Friedmann-Robertson-Walker universe with a massive conformally coupled scalar field. We propose a complexification of the radius of the universe so…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an…
This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic…
We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional…