scholarly journals Rate Estimation of Identical Synchronization by Designing Controllers

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mitul Islam ◽  
Bipul Islam ◽  
Nurul Islam
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Chaotic System ◽  
Tracking Control ◽  
Sufficient Conditions ◽  
Graphical Analysis ◽  
Control Technique ◽  
Chaotic Dynamical Systems ◽  
Necessary And Sufficient ◽  
Maximum Minimum

This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system.

scholarly journals Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft

1996 ◽  
Vol 2 (4) ◽  
pp. 277-299 ◽  
Author(s):  
Xinzhi Liu ◽  
Allan R. Willms
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Necessary And Sufficient

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete-time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

scholarly journals Constrained control and rate or increment for linear systems with additive disturbances

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Fouad Mesquine ◽  
Fernando Tadeo ◽  
Abdellah Benzaouia
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Ball Screw ◽  
Control Law ◽  
Constrained Control ◽  
Stabilizing Feedback Control ◽  
Bounded Disturbances ◽  
Control Of Linear Systems ◽  
Necessary And Sufficient

This paper is devoted to the control of linear systems with constrained control and rate or increment with additive bounded disturbances. Necessary and sufficient conditions such that the system evolution respects rate or increment constraints are used to derive stabilizing feedback control. The control law respects both constraints on control and its rate or increment and is robust against additive bounded disturbances. An application to a surface mount robot, where theY-axis of the machine uses a typical ball screw transmission driven by a DC motor to position circuits boards, is achieved.

Switchability in Discontinuous, Discrete Dynamical Systems

2013 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Discrete Dynamical Systems ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Tin this paper, a theory for switchability and singularity of discontinuous, discrete dynamical systems. G-functions for the discrete dynamical systems are introduced through the boundary, and the necessary and sufficient conditions for the switchability of discrete mappings are presented.

ON FLOW BARRIERS AND SWITCHABILITY IN DISCONTINUOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (01) ◽  
pp. 1-76 ◽  
Author(s):  
ALBERT C. J. LUO
Keyword(s):  
Dynamical Systems ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Friction Model ◽  
Necessary And Sufficient Conditions ◽  
Separation Boundary ◽  
Boundary Flow ◽  
Pass Through ◽  
Necessary And Sufficient ◽  
And Control

In this paper, the theory of flow barriers in discontinuous dynamical systems is systematically presented as a new theory for the first time, which helps one rethink the existing theories of stability and control in dynamical systems. The concept of flow barriers in discontinuous dynamical systems is introduced, and the passability of a flow to the separation boundary with flow barriers is presented. Because the flow barriers exist on the separation boundary, the switchability of a flow to such a separation boundary is changed accordingly. The coming and leaving flow barriers in passable flows are discussed first, and the necessary and sufficient conditions for a flow to pass through the boundary with flow barrier are developed. Flow barriers for sink and source flows are also discussed. Once the sink flow is formed, the boundary flow will exist. When the boundary flow disappears from the boundary, the boundary flow barrier on the boundary may exist, which is independent of vector fields in the corresponding domains. Thus, the necessary and sufficient conditions for formations and vanishing of the boundary flow are developed. A periodically forced friction model is presented as an example for a better understanding of flow barrier existence in physical problems. The flow barrier theory presented in this paper may provide a theoretic base to further develop control theory and stability.

scholarly journals Stability of fractional order fuzzy cellular neural networks with distributed delays via hybrid feedback controllers

2021 ◽  
Author(s):  
Ajendra Sing ◽  
Jitendra Nath Rai
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Control Technique ◽  
Fuzzy Cellular Neural Networks ◽  
Feedback Controllers ◽  
Lyapunov Approach ◽  
Analysis Techniques

Abstract This article studies the Global Mittag-Leffler stability of fractional order fuzzy cellular neural networks via hybrid feedback controllers. Based on hybrid feedback control technique Lyapunov approach, and some novel analysis techniques of fractional calculation, some sufficient conditions are obtained to guarantee the Global Mittag-lefflers stability. Finally, two simulation example are given to illustrate the effectiveness of the proposed method.

scholarly journals Robust set stabilization of Boolean control networks with impulsive effects

2018 ◽  
Vol 23 (4) ◽  
pp. 553-567 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Algebraic Form ◽  
Control Networks ◽  
Set Stabilization ◽  
Necessary And Sufficient

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.

On Weak Asymptotic Periodicity

2020 ◽  
Vol 30 (02) ◽  
pp. 2050030
Author(s):  
Karol Gryszka
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Property ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Conjugacy ◽  
Asymptotic Periodicity ◽  
Necessary And Sufficient

We introduce the asymptotic property associated with recurrence-like behavior of orbits in dynamical systems in general metric spaces. We define a notion of weak asymptotic periodicity and determine its elementary properties and relations including the invariance by topological conjugacy. We use the equicontinuity and the topology of the space to describe necessary and sufficient conditions for the existence of such a behavior.

Controllability of nonlinear stochastic fractional higher order dynamical systems

2019 ◽  
Vol 22 (4) ◽  
pp. 1063-1085
Author(s):  
R. Mabel Lizzy ◽  
K. Balachandran ◽  
Yong-Ki Ma
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Necessary And Sufficient Condition ◽  
Bounded Operators ◽  
Semilinear Systems ◽  
Operator Functions ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
The Given

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

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