scholarly journals A SIMPLE APPROACH TO CALCULATION AND CONTROL OF UNSTABLE PERIODIC ORBITS IN CHAOTIC PIECEWISE-LINEAR SYSTEMS

2001 ◽  
Vol 11 (01) ◽  
pp. 215-224 ◽  
Author(s):  
TETSUSHI UETA ◽  
GUANRONG CHEN ◽  
TOHRU KAWABE
Keyword(s):  
Periodic Orbits ◽  
State Feedback ◽  
Piecewise Linear ◽  
Autonomous Systems ◽  
Simple Approach ◽  
State Feedback Control ◽  
Unstable Periodic Orbits ◽  
Simple Method ◽  
Controlled System ◽  
And Control

This paper describes a simple method for calculating unstable periodic orbits (UPOs) and their control in piecewise-linear autonomous systems. The algorithm can be used to obtain any desired UPO embedded in a chaotic attractor, and the UPO can be stabilized by a simple state feedback control. A brief stability analysis of the controlled system is also given.

Advanced Model-Based Disturbance Compensation Control Using Proportional-Integral-Observer

2005 ◽  
Author(s):  
Idriz Krajcin ◽  
Dirk So¨ffker
Keyword(s):  
State Feedback ◽  
Dynamical Behavior ◽  
State Feedback Control ◽  
Disturbance Compensation ◽  
Proportional Integral ◽  
Compensation Control ◽  
Model Based ◽  
Simulation Results ◽  
And Control ◽  
Advanced Model

This contribution presents a state feedback control and a new disturbance compensation method using the Proportional-Integral-Observer (PI-Observer). For a suitable class of systems the observer estimates the unmeasured states as well as unknown inputs acting on a structure using a small number of measurements. Here, the observer is applied to elastic structures where the PI-Observer can be used for model-based diagnosis and control. An extended disturbance compensation is proposed to improve the dynamical behavior, to decouple the effect of disturbances on defined outputs using the PI-Observer. The observer and the control are applied to an all side clamped elastic plate. The performance of the control is illustrated by simulation results.

GENERATION AND IMPLEMENTATION OF HYPERCHAOTIC CHUA SYSTEM VIA STATE FEEDBACK CONTROL

2012 ◽  
Vol 22 (05) ◽  
pp. 1250119 ◽  
Author(s):  
HUILING XI ◽  
SIMIN YU ◽  
CHAOXIA ZHANG ◽  
YOULIN SUN
Keyword(s):  
Feedback Control ◽  
Theoretical Analysis ◽  
State Feedback ◽  
Piecewise Linear ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Cubic Nonlinearity ◽  
State Equations ◽  
Dynamical Behaviors ◽  
Simulation Based

In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

scholarly journals Optimisation of dynamic quantisation and control for quantised state feedback control system

2020 ◽  
Vol 2020 (7) ◽  
pp. 251-258
Author(s):  
Than Zaw Soe ◽  
Tadanao Zanma ◽  
Atsuki Tokunaga ◽  
Kenta Koiwa ◽  
Kang Zhi Liu
Keyword(s):  
Control System ◽  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Feedback Control System ◽  
And Control

scholarly journals Computing and Controlling Basins of Attraction in Multistability Scenarios

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
John Alexander Taborda ◽  
Fabiola Angulo
Keyword(s):  
Fixed Point ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Control Effort ◽  
Coexistence Of Attractors ◽  
And Control

The aim of this paper is to describe and prove a new method to compute and control the basins of attraction in multistability scenarios and guarantee monostability condition. In particular, the basins of attraction are computed only using a submap, and the coexistence of periodic solutions is controlled through fixed-point inducting control technique, which has been successfully used until now to stabilize unstable periodic orbits. In this paper, however, fixed-point inducting control is used to modify the domains of attraction when there is coexistence of attractors. In order to apply the technique, the periodic orbit whose basin of attraction will be controlled must be computed. Therefore, the fixed-point inducting control is used to stabilize one of the periodic orbits and enhance its basin of attraction. Then, using information provided by the unstable periodic orbits and basins of attractions, the minimum control effort to stabilize the target periodic orbit in all desired ranges is computed. The applicability of the proposed tools is illustrated through two different coupled logistic maps.

BORDER-COLLISION CRISES IN A TWO-DIMENSIONAL MAP

1995 ◽  
Vol 05 (01) ◽  
pp. 275-279
Author(s):  
José Alvarez-Ramírez
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Piecewise Linear ◽  
Two Dimensional ◽  
Unstable Periodic Orbits ◽  
Straight Lines

We examine crisis phenomena for a map that is piecewise linear and depend continuously of a parameter λ0. There are two straight lines Γ+ and Γ− along which the map is continuous but has two one-sided derivatives. As the parameter λ0 is varied, a periodic orbit Ƶp may collide with the borders Γ+ and Γ− to disappear. While in most reported crisis structures, a chaotic attractor is destroyed by the presence of (homoclinic or heteroclinic) tangencies between unstable periodic orbits, in this case the chaotic attractor is destroyed by the birth of an attracting periodic orbit Ƶp into that of attraction of the chaotic set. The birth of Ƶp is due to a border-collision phenomenon taking place at Γ+ ∪Γ−.

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