scholarly journals Robust Parametric Control of Lorenz System via State Feedback

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Da-Ke Gu ◽  
Da-Wei Zhang ◽  
Yin-Dong Liu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Lorenz System ◽  
Feedback Gain ◽  
Eigenvalues And Eigenvectors ◽  
Constant Matrix ◽  
Parametric Control ◽  
Generalized Sylvester Matrix Equation ◽  
Parametric Expression ◽  
The Lorenz System

This paper considers the parametric control to the Lorenz system by state feedback. Based on the solutions of the generalized Sylvester matrix equation (GSE), the unified explicit parametric expression of the state feedback gain matrix is proposed. The closed loop of the Lorenz system can be transformed into an arbitrary constant matrix with the desired eigenstructure (eigenvalues and eigenvectors). The freedom provided by the parametric control can be fully used to find a controller to satisfy the robustness criteria. A numerical simulation is developed to illustrate the effectiveness of the proposed approach.

ADAPTIVE CONTROL OF UNCERTAIN LORENZ SYSTEM USING DECOUPLED BACKSTEPPING

2004 ◽  
Vol 14 (04) ◽  
pp. 1439-1445 ◽  
Author(s):  
S. S. GE
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Lorenz System ◽  
Physical Property ◽  
Asymptotic Convergence ◽  
Closed Loop System ◽  
Feedback Form ◽  
Controlling Chaos ◽  
Simulation Results ◽  
The Lorenz System

In this letter, we reconsider the problem of controlling chaos in the well-known Lorenz system. Firstly, the difficulty in controlling the Lorenz system is discussed in the general strict-feedback form. Then, singularity-free adaptive control is presented for the Lorenz system with three key parameters unknown by exploiting the physical property of the system using decoupled backstepping design. The proposed controller guarantees the asymptotic convergence of the output and the boundedness of all the signals in the closed-loop system. Simulation results are conducted to show the effectiveness of the approach.

scholarly journals Dynamic Mathematical Models’ System and Synchronization

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Malik Bader Alazzam ◽  
Abdulsattar Abdullah Hamad ◽  
Ahmed S AlGhamdi
Keyword(s):  
Chronic Disease ◽  
Risk Behaviors ◽  
State Feedback ◽  
Lorenz System ◽  
Dynamic Modelling ◽  
Delivery Systems ◽  
Prevention System ◽  
Health Related ◽  
Hybrid Synchronization ◽  
The Lorenz System

We created the equilibrium, which includes sickness outcomes, health and risk behaviors, environmental factors, and health-related assets and delivery systems, and it should be incorporated in system Dyc (dynamic) modelling of chronic disease prevention. System Dyc has the ability to model a variety of interconnected illnesses and dangers, as well as the interaction between delivery systems and afflicted people, as well as state and national policies. This paper proposes a unique idea. Hybrid synchronization utilizes four positive LYP (Lyapunov) exponents based on state feedback management with two identical systems of the Lorenz system 6D HYCH system.

ADAPTIVE BACKSTEPPING CONTROL OF UNCERTAIN LORENZ SYSTEM

2001 ◽  
Vol 11 (04) ◽  
pp. 1115-1119 ◽  
Author(s):  
C. WANG ◽  
S. S. GE
Keyword(s):  
Closed Loop ◽  
Lorenz System ◽  
Backstepping Design ◽  
Closed Loop System ◽  
Adaptive Backstepping ◽  
Feedback Form ◽  
Controlling Chaos ◽  
Simulation Results ◽  
The Lorenz System ◽  
Adaptive Backstepping Design

In this paper, we consider the problem of controlling chaos in the well-known Lorenz system. Firstly we show that the Lorenz system can be transformed into a kind of nonlinear system in the so-called general strict-feedback form. Then, adaptive backstepping design is used to control the Lorenz system with three key parameters unknown. By exploiting the property of the system, the resulting controller is singularity free, and the closed-loop system is stable globally. Simulation results are conducted to show the effectiveness of the approach.

A New Method of Calculating the State Feedback Gain Vector of Vibration Control System

2012 ◽  
Vol 229-231 ◽  
pp. 424-427
Author(s):  
Ming Yang ◽  
De Chen Zhang ◽  
Xin Xiang Zhou
Keyword(s):  
Vibration Control ◽  
Uncertain Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Random Perturbation ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Vibration System ◽  
Deterministic Systems ◽  
Closed Loop Systems

Using the random model, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the standard deviations for responses of the closed-loop systems with the uncertain parameters is presented by using the random perturbation. This method is applied to a vibration system to illustrate the application. The numerical results show that the present method is effective.

A General Formula for Controlling Hopf Bifurcation

2002 ◽  
Author(s):  
Pei Yu
Keyword(s):  
Hopf Bifurcation ◽  
General Formula ◽  
State Feedback ◽  
Lorenz System ◽  
Subcritical Hopf Bifurcation ◽  
The Lorenz System

An explicit general formula is proposed for controlling Hopf bifurcation using state feedback. This method can be used to either delay (or even eliminate) an existing Hopf bifurcation or change a subcritical Hopf bifurcation to supercritical. The Lorenz system is used to illustrate the application of the formula.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

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