Synchronized Dynamics of Hyperchaotic Flows via an Improved Finite-Time Adaptive Controller Design

2020 ◽  
Vol 48 ◽  
pp. 49-62
Author(s):  
Edwin A. Umoh ◽  
Ogechukwu N. Iloanusi
Keyword(s):  
Uniform Convergence ◽  
Finite Time ◽  
Controller Design ◽  
Adaptive Controller ◽  
Coupled Systems ◽  
Convergence Time ◽  
Adaptive Controllers ◽  
System Parameters ◽  
Unknown System ◽  
Asymptotic Convergence Rate

We proposed a performance-improved finite-time adaptive synchronizing controllers and parameter update laws for coupling the dynamics of identical 4D hyperchaotic flows. The four-dimensional hyperchaotic flows consists of 12 terms and 11 system parameters and possessed very rich dynamics and larger parameter space. The performance of the proposed finite-time adaptive synchronizing controller was enhanced by the introduction of scalar quantities known as global controller strength coefficients and parameter update strength coefficients respectively, into the algebraically-derived control and parameter update structures, in order to constrained overshoots of the trajectories of the coupled systems and accelerate their rate of uniform convergence in finite time. Numerical simulation results obtained confirmed that the uniform asymptotic convergence rate of the coupling trajectories was faster, while the parameter update laws give a stable identification of the unknown system parameters in a global synchronizing time. A comparative analysis of the convergence time of the proposed adaptive controllers with recently published works indicated that the proposed controller has faster rates of uniform convergence of system trajectories.

Finite-time stabilization of stochastic coupled systems on networks by feedback control and its application

2019 ◽  
Vol 37 (3) ◽  
pp. 814-830
Author(s):  
Yongbao Wu ◽  
Wenxue Li ◽  
Jiqiang Feng
Keyword(s):  
Finite Time ◽  
Coupled Oscillators ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Convergence Time ◽  
Practical Application ◽  
Finite Time Stability ◽  
Finite Time Stabilization ◽  
Theoretical Results

Abstract In this paper, the finite-time stabilization of stochastic coupled systems on networks (SCSNs) is studied. Different from previous research methods, the method used in this paper combines Lyapunov method with graph theory, and some novel sufficient conditions are obtained to ensure finite-time stability for SCSNs. Meanwhile, the convergence time is closely related to topological structure in networks. As a practical application in physics, we address a concrete finite-time stabilization problem of stochastic coupled oscillators through our main results. In addition, a numerical example is presented to illustrate the effectiveness and feasibility of the theoretical results.

scholarly journals Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

2014 ◽  
Vol 24 (4) ◽  
pp. 409-446 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Lorenz System ◽  
Adaptive Controller ◽  
The Novel ◽  
Maximal Lyapunov Exponent ◽  
System Parameters ◽  
Quadratic Nonlinearities ◽  
Hyperchaotic Lorenz System ◽  
Unknown System

Abstract In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.

scholarly journals Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

2016 ◽  
Vol 26 (4) ◽  
pp. 471-495 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Adaptive Control ◽  
Lyapunov Exponents ◽  
Research Work ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
System Parameters ◽  
Quadratic Nonlinearities ◽  
Unknown System

AbstractThis research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1= 3.1575, L2= 0.3035, L3= 0 and L4= −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY= 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.

scholarly journals Adaptive Finite-Time Control for Spacecraft Rendezvous under Unknown System Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yuan Liu ◽  
Guojian Tang ◽  
Yuhang Li ◽  
Hang Li ◽  
Jing Ren ◽  
...  
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
External Disturbance ◽  
Finite Time Stability ◽  
System Parameters ◽  
Time Control ◽  
Control Objective ◽  
Relative Dynamics ◽  
Unknown System ◽  
Adaptive Smc

In this study, we investigated the sliding mode control (SMC) technology for the spacecraft rendezvous maneuver under unknown system parameters and external disturbance. With no knowledge of the mass and inertial matrix of the pursuer spacecraft, an adaptive SMC approach was devised using the hyperbolic tangent function to realize the control objective of reducing the chattering problem. In addition, the finite-time stability of the relative dynamics and the boundedness of the signals in the closed-loop system were derived under proposed method. The effectiveness and advantages of the proposed method were verified through theoretical analysis and numerical simulations.

A robust adaptive control design for active tuned mass damper systems of multistory buildings

2020 ◽  
pp. 107754632096623
Author(s):  
Rafet Can Ümütlü ◽  
Hasan Ozturk ◽  
Baris Bidikli
Keyword(s):  
Controller Design ◽  
Control Design ◽  
Adaptive Controller ◽  
Tuned Mass Damper ◽  
Robust Adaptive Control ◽  
System Parameters ◽  
Multistory Buildings ◽  
Mass Damper ◽  
Robust Adaptive ◽  
Control Purpose

In this study, a robust adaptive controller is designed to be used in an active tuned mass damper system that can be used to damp undesired vibrations that occurred on the multistory buildings during the earthquake. To realize the controller design, all of the system parameters are assumed to be unknown, and the adaptive structure of the designed controller is obtained by designing adaptive compensation rules for system parameters. A backstepping control design approach is utilized for the control design by considering the appropriateness of the system’s structure of multistory buildings having an active tuned mass damper system at the top of the structure. The proposed control design is supported with a Lyapunov-based stability analysis where it is proven that the designed controller is able to protect the overall system’s stability while reaching the main control purpose. In addition to these, in the simulation studies realized for a nine-story building under the effect of a major earthquake, it is shown that the designed controller can be used to reach the main control purpose efficiently.

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