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.

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.

Controlling Chaos Using Input–Output Linearization Approach

1997 ◽  
Vol 07 (07) ◽  
pp. 1659-1664 ◽  
Author(s):  
Xinghuo Yu
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Zero Dynamics ◽  
Input Output ◽  
Controlling Chaos ◽  
Periodic Signals ◽  
Simulation Results ◽  
The Lorenz System ◽  
Partial States ◽  
Input Output Linearization

In this article the input–output linearization approach is used for controlling chaos. It is shown that by using only partial states, the entire chaotic system is stabilizable, provided the zero dynamics is stable. Generally speaking, trajectories of chaotic systems do not grow exponentially and are usually bounded. In particular, for dissipative chaotic systems the stable zero dynamics can always be found. Hence the stabilization as well as tracking periodic signals are possible. The Lorenz system is used to inform the discussion. Simulation results are presented to show the effectiveness of the approach.

Nonlinear Control of Semi-Active MacPherson Suspension System

2012 ◽  
Author(s):  
Olugbenga M. Anubi ◽  
Carl D. Crane
Keyword(s):  
Closed Loop ◽  
Control Design ◽  
Mr Damper ◽  
Suspension System ◽  
Time Domain Simulation ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
Space Frequency ◽  
Simulation Results ◽  
Active Damper

This paper presents the control design and analysis of a non-linear model of a MacPherson suspension system equipped with a magnetorheological (MR) damper. The model suspension considered incorporates the kinematics of the suspension linkages. An output feedback controller is developed using an ℒ2-gain analysis based on the concept of energy dissipation. The controller is effectively a smooth saturated PID. The performance of the closed-loop system is compared with a purely passive MacPherson suspension system and a semi-active damper, whose damping coefficient is tunned by a Skyhook-Acceleration Driven Damping (SH-ADD) method. Simulation results show that the developed controller outperforms the passive case at both the rattle space, tire hop frequencies and the SH-ADD at tire hop frequency while showing a close performance to the SH-ADD at the rattle space frequency. Time domain simulation results confirmed that the control strategy satisfies the dissipative constraint.

Logic-Based Switching Adaptive Control of DC-DC Buck Converter

2012 ◽  
Vol 229-231 ◽  
pp. 2209-2212
Author(s):  
Bao Bin Liu ◽  
Wei Zhou
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Buck Converter ◽  
Uncertain Parameters ◽  
Small Signal ◽  
Closed Loop System ◽  
Unknown Parameters ◽  
Signal Model ◽  
Small Signal Model ◽  
Control Scheme

Logic-based switching adaptive control scheme is proposed for the model of DC-DC buck converter in presence of uncertain parameters and power supply disturbance. All uncertain parameters and the disturbance are estimated together through constructing Lyapunov function. And a switching mechanism is used to ensure global asymptotic stability of the closed-loop system. The results of simulation show that even if there are multiple unknown parameters in the small-signal model, the control system of DC-DC buck converter can estimate unknown parameters quickly and accurately.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

scholarly journals Distributed Fuzzy Adaptive Control for Heterogeneous Nonlinear Multiagent Systems with Similar Composite Structure

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yongqing Fan ◽  
Tiantian Xiao ◽  
Zhen Li
Keyword(s):  
Adaptive Control ◽  
Graph Theory ◽  
Multiagent Systems ◽  
Lyapunov Stability ◽  
Closed Loop ◽  
Zero Set ◽  
Closed Loop System ◽  
Fuzzy Adaptive Control ◽  
Different Dimensions ◽  
Fuzzy Adaptive

A distributed fuzzy adaptive control with similar parameters is constructed for a class of heterogeneous multiagent systems. Unlike many existing works, the dimensions of each multiagent dynamic system are considered to be nonidentical in this paper. Firstly, similar properties for different dimensions of multiagent systems are introduced, and some similar parameters among multiagent systems are also proposed. Secondly, a distributed fuzzy adaptive control on the basis of similar parameters is designed for the consensus of leader-follower multiagent systems. Following the graph theory and Lyapunov stability approach, it is concluded that UUB (uniformly ultimately bounded) of all signals in the closed-loop system can be guaranteed, and the consensus tacking error converges to a small compact zero set. Finally, a simulation example with different dimensions is provided to illustrate the effectiveness of the proposed method.

scholarly journals Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jinsheng Xing ◽  
Naizheng Shi
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Closed Loop ◽  
Loop System ◽  
Asymptotically Stable ◽  
Bilinear Model ◽  
Closed Loop System ◽  
Fuzzy Modelling ◽  
Control Scheme

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

Speed Model Predictive Control Based on the Track Error Rate

2013 ◽  
Vol 336-338 ◽  
pp. 839-842
Author(s):  
Jin Huang ◽  
Cheng Zhi Yang ◽  
Ji Feng Wang
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Matlab Simulation ◽  
Closed Loop System ◽  
Index Function ◽  
Dynamical Characteristics ◽  
Simulation Results ◽  
Controlled Object

In order to make the controlled object have better dynamical characteristics, through introducing the differential item of error into optimal performance index function of tracking error, an improved algorithm of model predictive control is discussed in this paper. The theoretical analysis and Matlab simulation results show that it has better controlled quality and stronger robustness for closed-loop system.

Stable Nonlinear Control Allocation for Aircraft with Multiple Control Effectors

2011 ◽  
Vol 138-139 ◽  
pp. 404-409 ◽  
Author(s):  
Heng Li ◽  
Jin Yong Yu ◽  
You An Zhang
Keyword(s):  
Closed Loop ◽  
Dynamic Control ◽  
Lyapunov Stability Theory ◽  
Invariant Set ◽  
Control Law ◽  
Control Allocation ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Multiple Control ◽  
Simulation Results

With respect to aircraft with redundant multiple control effectors, a nonlinear controller, which is composed of a virtual control law and a dynamic control allocation with position constraints of each effector, is designed. Based on Lyapunov stability theory and LaSalle invariant set theorem, asymptotic stabilities of upper control subsystem, dynamic control allocation subsystem and overall closed-loop system are proved respectively. Simulation results show the effectiveness of the proposed method.

scholarly journals Adaptive Compensator of Single State Elastoplastic Friction Model

2011 ◽  
Vol 8 (2) ◽  
pp. 66
Author(s):  
A. A. Abouelsoud ◽  
J. Abdo ◽  
R. Zaier
Keyword(s):  
Closed Loop ◽  
Friction Model ◽  
Adaptive Observer ◽  
Nonlinear Friction ◽  
Closed Loop System ◽  
Adaptive Compensator ◽  
Single State ◽  
Contact Surfaces ◽  
Simulation Results ◽  
Lyapunov Second Method

 A nonlinear friction is an unavoidable phenomenon frequently experienced in mechanical system between two contact surfaces. An adaptive compensator is designed to achieve tracking of a desired velocity trajectory in the presence of friction force described by a single state elastoplastic friction model. The adaptive compensator includes an adaptive observer and a computed force controller. The closed loop system is shown to be stable using Lyapunov second method. Simulation results show the effectiveness of the proposed compensator. 

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