On Phase and Anti-Phase Combination Synchronization of Time Delay Nonlinear Systems

Extensive studies have been done on the phenomenon of phase and anti-phase synchronization (APS) between one drive and one response systems. As well as, combination synchronization for chaotic and hyperchaotic systems without delay also has been investigated. Thus, this paper aims to introduce the concept of phase and anti-phase combination synchronization (PCS and APCS) between two drive and one response time delay systems, which are not studied in the literature as far as we know. The analysis of PCS and APCS are carried out using active control technique. An example is given to test the validity of the expressions of control forces to achieve the PCS and APCS of time delay systems. This example is between three different systems. When there is no control, the PCS does not occur where the phase difference is unbounded. The bounded phase difference appears when the control is applied which means that PCS is achieved. The special case which is the combination synchronization is studied as well.

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Phase synchronization in time-delay systems

Physical Review E ◽

10.1103/physreve.74.035205 ◽

2006 ◽

Vol 74 (3) ◽

Cited By ~ 50

Author(s):

D. V. Senthilkumar ◽

M. Lakshmanan ◽

J. Kurths

Keyword(s):

Time Delay ◽

Phase Synchronization ◽

Delay Systems ◽

Time Delay Systems

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Global phase synchronization in an array of time-delay systems

Physical Review E ◽

10.1103/physreve.82.016215 ◽

2010 ◽

Vol 82 (1) ◽

Cited By ~ 13

Author(s):

R. Suresh ◽

D. V. Senthilkumar ◽

M. Lakshmanan ◽

J. Kurths

Keyword(s):

Time Delay ◽

Phase Synchronization ◽

Delay Systems ◽

Time Delay Systems

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GLOBAL AND PARTIAL PHASE SYNCHRONIZATIONS IN ARRAYS OF PIECEWISE LINEAR TIME-DELAY SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412501787 ◽

2012 ◽

Vol 22 (07) ◽

pp. 1250178 ◽

Cited By ~ 4

Author(s):

R. SURESH ◽

D. V. SENTHILKUMAR ◽

M. LAKSHMANAN ◽

J. KURTHS

Keyword(s):

Time Delay ◽

Boundary Conditions ◽

Coupling Strength ◽

Phase Synchronization ◽

Linear Array ◽

Linear Time ◽

Piecewise Linear ◽

Delay Systems ◽

Time Delay Systems ◽

Partial Phase

In this paper, we report the phenomena of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization of local oscillators in the array as a function of the coupling strength (a second order transition). Several phase synchronized clusters are also formed during the transition to GPS at intermediate values of the coupling strength, as a prelude to full scale synchronization. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various qualitative and quantitative measures in three different frameworks, namely, using explicit phase, recurrence quantification analysis and the framework of localized sets.

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ROBUST ADAPTIVE FUZZY CONTROLLER DESIGN FOR A CLASS OF UNCERTAIN NONLINEAR TIME-DELAY SYSTEMS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488511007027 ◽

2011 ◽

Vol 19 (02) ◽

pp. 329-360 ◽

Cited By ~ 5

Author(s):

YAN-JUN LIU ◽

RUI WANG ◽

C. L. PHILIP CHEN

Keyword(s):

Time Delay ◽

Fuzzy Controller ◽

Control Technique ◽

Delay Systems ◽

Design Parameters ◽

Time Delay Systems ◽

Dynamic Surface ◽

Adaptive Fuzzy Controller ◽

Adaptive Fuzzy ◽

Approximation Errors

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques.

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Two term composite nonlinear feedback controller design for nonlinear time-delay systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217723703 ◽

2017 ◽

Vol 40 (12) ◽

pp. 3424-3432 ◽

Cited By ~ 5

Author(s):

Sonal Singh ◽

Shubhi Purwar ◽

Abhijit Kulkarni

Keyword(s):

Time Delay ◽

Transient Response ◽

Control Technique ◽

Delay Systems ◽

Time Delay Systems ◽

State Control ◽

Nonlinear Feedback ◽

Composite Nonlinear Feedback ◽

Fast Transient Response ◽

Fast Transient

A two term composite nonlinear feedback (2TCNF) control technique is developed here for nonlinear time delay systems in presence of input saturation. The proposed controller consists of two terms that are conventional composite nonlinear feedback (CNF) control and delay state control. CNF control has advantage of fast transient response and delay state control improves damping characteristics. The proposed controller thus has both these advantages and it tracks the reference smoothly. The closed loop asymptotic stability is guaranteed via Lyapunov–Krasovskii analysis. The efficiency of the proposed controller is tested on exothermic chemical reactor and validated through simulation results. Its performance is compared with the conventional CNF control. The superiority of 2TCNF is established in terms of less overshoot, fast transient response and reduced steady state error.

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