scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

scholarly journals Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
P. K. Santra ◽  
G. S. Mahapatra ◽  
G. R. Phaijoo
Keyword(s):  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Phase Portraits ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
And Control

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

Energy-based output feedback control of the underactuated 2DTORA system with saturated inputs

2020 ◽  
Vol 42 (14) ◽  
pp. 2822-2829
Author(s):  
Kexin Xu ◽  
Xianqing Wu ◽  
Miao Ma ◽  
Yibo Zhang
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Output Feedback ◽  
Control Method ◽  
Actuator Saturation ◽  
Output Feedback Control ◽  
Lyapunov Theory ◽  
Velocity Signal ◽  
Feedback Control Method ◽  
The Stability

In this paper, we consider the control issues of the two-dimensional translational oscillator with rotational actuator (2DTORA) system, which has two translational carts and one rotational rotor. An output feedback controller for the 2DTORA system is proposed, which can prevent the unwinding behaviour. In addition, the velocity signal unavailability and actuator saturation are taken into account, simultaneously. In particular, the dynamics of the 2DTORA system are given first. On the basis of the passivity and control objectives of the 2DTORA system, an elaborate Lyapunov function is constructed. Then, based on the introduced Lyapunov function, a novel output feedback control method is proposed straightforwardly for the 2DTORA system. Lyapunov theory and LaSalle’s invariance principle are utilized to analyse the stability of the closed-loop system and the convergence of the states. Finally, simulation results are provided to illustrate the excellent control performance of the proposed controller in comparison with the existing method.

scholarly journals Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jing Wang ◽  
Shaojuan Ma ◽  
Peng Hao ◽  
Hehui Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Magnetic Bearing ◽  
Uncertain Parameter ◽  
Equivalent Model ◽  
Linear Feedback ◽  
Feedback Control Method ◽  
And Control ◽  
Bearing System

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

ON SYNCHRONIZATION AND CONTROL OF COUPLED WILSON–COWAN NEURAL OSCILLATORS

2003 ◽  
Vol 13 (01) ◽  
pp. 163-175 ◽  
Author(s):  
TETSUSHI UETA ◽  
GUANRONG CHEN
Keyword(s):  
Control Method ◽  
Complex Dynamics ◽  
Mapping Method ◽  
Control Of Chaos ◽  
Neural Oscillators ◽  
Higher Dimensional ◽  
Strongly Connected ◽  
Feedback Control Method ◽  
And Control ◽  
Simple Feedback

This paper investigates the complex dynamics, synchronization and control of chaos in a system of strongly connected Wilson–Cowan neural oscillators. Some typical synchronized periodic solutions are analyzed by using the Poincaré mapping method, for which bifurcation diagrams are obtained. It is shown that topological change of the synchronization mode is mainly caused and carried out by the Neimark–Sacker bifurcation. Finally, a simple feedback control method is presented for stabilizing an in-phase synchronizing periodic solution embedded in the chaotic attractor of a higher-dimensional model of such coupled neural oscillators.

scholarly journals ORDERING CHAOS IN CHUA'S CIRCUIT: A SAMPLED-DATA FEEDBACK AND DIGITAL REDESIGN APPROACH

2000 ◽  
Vol 10 (09) ◽  
pp. 2221-2231 ◽  
Author(s):  
SHU-MEI GUO ◽  
LEANG S. SHIEH ◽  
GUANRONG CHEN ◽  
MARITZA ORTEGA
Keyword(s):  
Control Method ◽  
Digital Design ◽  
Chua’S Circuit ◽  
Sampled Data ◽  
Nonlinear Circuit ◽  
Chua's Circuit ◽  
Digital Redesign ◽  
Data Feedback ◽  
Feedback Control Method ◽  
Sampling Times

In this paper, we develop and apply some digital design and redesign techniques for ordering the chaotic Chua's circuit. The idea of using sampled-data feedback for controlling the circuit was previously suggested [Yang & Chua, 1998], which relies on small sampling periods. We show how this sampled-data feedback control method can be significantly improved, so that large sampling times are allowed, for the same purpose of ordering the nonlinear circuit, from anywhere within the chaotic attractor towards a predesired periodic cycle of the circuit.

GLOBAL ANALYSIS ON n-SCROLL CHAOTIC ATTRACTORS OF MODIFIED CHUA'S CIRCUIT

2009 ◽  
Vol 19 (01) ◽  
pp. 135-157 ◽  
Author(s):  
FEI XU ◽  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Feedback Control ◽  
Global Analysis ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Nonlinear Feedback ◽  
Control Laws ◽  
Chua's Circuit ◽  
Constructive Feedback ◽  
Globally Attractive

In this paper, we present a further mathematical study on the report of existence of n-scroll chaotic attractors in a modified Chua's circuit. A series of results based on mathematical theory are given. First, we show that the chaotic attractors of the modified Chua's circuit are globally attractive, with estimations given for the globally attractive set and positive invariant set. Then, we study the positions, number and local stability of the equilibrium points. We also design simple feedback control laws to globally exponentially stabilize any given equilibrium point. Finally, we use the theory and methodology of absolute stability of Luré nonlinear control systems and nonlinear feedback control to exponentially synchronize two modified Chua's circuits with the same structure. The design of constructive feedback control laws for synchronization is also discussed.

EXPERIMENTAL EVIDENCE FOR SPATIOTEMPORAL STABILITY AND CONTROL OF A ONE-WAY OPEN CML

2002 ◽  
Vol 12 (12) ◽  
pp. 2937-2944 ◽  
Author(s):  
TAKUYA IMAI ◽  
KEIJI KONISHI ◽  
HIDEKI KOKAME ◽  
KENTARO HIRATA
Keyword(s):  
Feedback Control ◽  
Experimental Evidence ◽  
Control Method ◽  
Spatiotemporal Chaos ◽  
Coupled Map Lattice ◽  
Delayed Feedback Control ◽  
Electronic Circuits ◽  
Stability And Control ◽  
Feedback Control Method ◽  
And Control

We present an experimental evidence for spatiotemporal stability of a real one-way open coupled map lattice implemented by electronic circuits. Furthermore, it is shown that the decentralized delayed feedback control method can suppress the spatial instability and the spatiotemporal chaos in the coupled map lattice circuits.

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