A New Property of Noninvasive Control Methods Applied to Stabilize Unstable Periodic Orbits

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Saeed Montazeri ◽  
Ali Rahmani Hanzaki
Keyword(s):  
Energy Consumption ◽  
Periodic Orbits ◽  
Parameter Optimization ◽  
Control Methods ◽  
System State ◽  
Unstable Periodic Orbits ◽  
Optimal Energy

This paper is devoted to present a theorem on a new property of noninvasive control methods applied to stabilize unstable periodic orbits (UPOs). This property is related to the optimal energy consumption of the controller in the presence of noise. The approach of parameter optimization is applied to study optimal energy consumption of the controller. Throughout this paper, the problem of energy consumption of the controller is studied when the system state is close to the UPO, and fluctuates around it because of the presence of noise.

STABILIZING UNSTABLE PERIODIC ORBITS OF CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2000 ◽  
Vol 10 (03) ◽  
pp. 611-620 ◽  
Author(s):  
YU-PING TIAN ◽  
XINGHUO YU
Keyword(s):  
Periodic Orbits ◽  
Chaotic Systems ◽  
Control Method ◽  
Uncertain System ◽  
Parameter Estimates ◽  
System State ◽  
Unstable Periodic Orbits ◽  
Unknown Parameters ◽  
Model Following ◽  
Delayed System

A novel adaptive time-delayed control method is proposed for stabilizing inherent unstable periodic orbits (UPOs) in chaotic systems with unknown parameters. We first explore the inherent properties of chaotic systems and use the system state and time-delayed system state to form an asymptotically stable invariant manifold so that when the system state enters the manifold and stays in it thereafter, the resulting motion enables the stabilization of the desired UPOs. We then use the model following concept to construct an identifier for the estimation of the uncertain system parameters. We shall prove that under the developed scheme, the system parameter estimates will converge to their true values. The effectiveness of the method is confirmed by computer simulations.

scholarly journals Feedback control modulation for controlling chaotic maps

2021 ◽  
Vol 26 (3) ◽  
pp. 419-439
Author(s):  
Roberta Hansen ◽  
Graciela A. González
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Periodic Orbits ◽  
Waiting Time ◽  
Control Parameter ◽  
Chaotic Maps ◽  
Noise Sensitivity ◽  
Control Methods ◽  
Unstable Periodic Orbits ◽  
Discrete Maps

Based on existing feedback control methods such as OGY and Pyragas, alternative new schemes are proposed for stabilization of unstable periodic orbits of chaotic and hyperchaotic dynamical systems by suitable modulation of a control parameter. Their performances are improved with respect to: (i) robustness, (ii) rate of convergences, (iii) reduction of waiting time, (iv) reduction of noise sensitivity. These features are analytically investigated, the achievements are rigorously proved and supported by numerical simulations. The proposed methods result successful for stabilizing unstable periodic orbits in some classical discrete maps like 1-D logistic and standard 2-D Hénon, but also in the hyperchaotic generalized n-D Hénon-like maps.

scholarly journals Energy efficient cutting parameter optimization

2021 ◽  
Author(s):  
Xingzheng Chen ◽  
Congbo Li ◽  
Ying Tang ◽  
Li Li ◽  
Hongcheng Li
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Parameter Optimization ◽  
Energy Efficient ◽  
Cutting Parameters ◽  
Machining Process ◽  
Cutting Fluid ◽  
Current Status ◽  
Cutting Parameter ◽  
Cutting Parameter Optimization

AbstractMechanical manufacturing industry consumes substantial energy with low energy efficiency. Increasing pressures from energy price and environmental directive force mechanical manufacturing industries to implement energy efficient technologies for reducing energy consumption and improving energy efficiency of their machining processes. In a practical machining process, cutting parameters are vital variables set by manufacturers in accordance with machining requirements of workpiece and machining condition. Proper selection of cutting parameters with energy consideration can effectively reduce energy consumption and improve energy efficiency of the machining process. Over the past 10 years, many researchers have been engaged in energy efficient cutting parameter optimization, and a large amount of literature have been published. This paper conducts a comprehensive literature review of current studies on energy efficient cutting parameter optimization to fully understand the recent advances in this research area. The energy consumption characteristics of machining process are analyzed by decomposing total energy consumption into electrical energy consumption of machine tool and embodied energy of cutting tool and cutting fluid. Current studies on energy efficient cutting parameter optimization by using experimental design method and energy models are reviewed in a comprehensive manner. Combined with the current status, future research directions of energy efficient cutting parameter optimization are presented.

On the Potential for Entangled States Between Chaotic Systems

2014 ◽  
Vol 24 (06) ◽  
pp. 1450077 ◽  
Author(s):  
Matthew A. Morena ◽  
Kevin M. Short
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Entangled States ◽  
Future Research ◽  
Unstable Periodic Orbits ◽  
Qualitative Information ◽  
Chaotic Dynamical System ◽  
Naturally Occurring ◽  
External Intervention

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

scholarly journals Optimal energy consumption and throughput for workflow applications on distributed architectures

2014 ◽  
Vol 4 (1) ◽  
pp. 44-51
Author(s):  
Abdallah Ben Othman ◽  
Jean-Marc Nicod ◽  
Laurent Philippe ◽  
Veronika Rehn-Sonigo
Keyword(s):  
Energy Consumption ◽  
Distributed Architectures ◽  
Optimal Energy
Sign in / Sign up

Export Citation Format

Share Document