A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems With One Control Input

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Pitcha Khamsuwan ◽  
Suwat Kuntanapreeda
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Direct Method ◽  
Output Feedback Control ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Input ◽  
Unified Chaotic Systems ◽  
System Output

This paper focuses on stabilization of fractional-order unified chaotic systems. In contrast to existing methods in literature, the proposed method requires only the system output for feedback and uses only one control input. The controller consists of a state feedback control law and a dynamic estimator. Sufficient stability conditions are derived using a fractional-order extension of the Lyapunov direct method and a new lemma of the Caputo fractional derivative. The conditions are expressed in the form of linear matrix inequalities (LMIs). All the parameters of the controller can be simultaneously obtained by solving the LMIs. Numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed method.

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

2014 ◽  
Author(s):  
Chuong Hoang Nguyen ◽  
Alexander Leonessa
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Output Feedback ◽  
Reference System ◽  
Reference Model ◽  
Output Feedback Control ◽  
State Feedback Control ◽  
Control Input ◽  
Actual System ◽  
System Output

In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, a predictor, a reference model, and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output, and the reference system trajectories all converge to each other.

OUTPUT FEEDBACK CONTROL OF UNIFIED CHAOTIC SYSTEMS BASED ON FEEDBACK PASSIVITY

2010 ◽  
Vol 20 (05) ◽  
pp. 1519-1525 ◽  
Author(s):  
TEERAWAT SANGPET ◽  
SUWAT KUNTANAPREEDA
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Output Feedback Control ◽  
Control Law ◽  
Control Laws ◽  
Unified Chaotic Systems ◽  
System Output ◽  
Simulation Results ◽  
Passivity Based Control ◽  
System States

Recently, the concept of feedback passivity-based control has drawn attention to chaos control. In all existing papers, the implementations of passivity-based control laws require the system states for feedback. In this paper, a passivity-based control law which only requires the knowledge of the system output is proposed. Simulation results are provided to show the effectiveness of the proposed solution.

scholarly journals Robust Mixed H2/H∞ State Feedback Controller Development for Uncertain Automobile Suspensions with Input Delay

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 359
Author(s):  
Nan Liu ◽  
Hui Pang ◽  
Rui Yao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Actuator Saturation ◽  
Output Feedback Control ◽  
Active Suspension ◽  
Feedback Controller ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Feedback Controller

In order to achieve better dynamics performances of a class of automobile active suspensions with the model uncertainties and input delays, this paper proposes a generalized robust linear H2/H∞ state feedback control approach. First, the mathematical model of a half-automobile active suspension is established. In this model, the H∞ norm of body acceleration is determined as the performance index of the designed controller, and the hard constraints of suspension dynamic deflection, tire dynamic load and actuator saturation are selected as the generalized H2 performance output index of the designed controller to satisfy the suspension safety requirements. Second, a generalized H2/H∞ guaranteed cost state-feedback controller is developed in terms of Lyapunov stability theory. In addition, the Cone Complementarity Linearization (CCL) algorithm is employed to convert the generalized H2/H∞ output-feedback control problem into a finite convex optimization problem (COP) in a linear matrix inequality framework. Finally, a numerical simulation case of this half-automobile active suspension is presented to illustrate the effectiveness of the proposed controller in frequency-domain and time-domain.

scholarly journals New Results on Synchronization of Fractional-Order Memristor‐Based Neural Networks via State Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xiaofan Li ◽  
Yuan Ge ◽  
Hongjian Liu ◽  
Huiyuan Li ◽  
Jian-an Fang
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Nonsmooth Analysis ◽  
State Feedback ◽  
Direct Method ◽  
Young Inequality ◽  
State Feedback Control ◽  
Feedback Controllers ◽  
Theoretical Results

This paper addresses the synchronization issue for the drive-response fractional-order memristor‐based neural networks (FOMNNs) via state feedback control. To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. Then, by adopting nonsmooth analysis, fractional Lyapunov’s direct method, Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization of the drive-response FOMNNs. Lastly, for illustrating the effectiveness of the obtained theoretical results, an example is given.

scholarly journals Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo ◽  
Guanjun Li ◽  
Heng Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Control ◽  
Control Input ◽  
Saturated Control ◽  
Laplace Transform Technique

In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 <α≤ 1 and 1 <α< 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method.

Feedback Linearizing Control of Surge in an Axial Compression System: Theory and Experimental Validation

1995 ◽  
Author(s):  
O. O. Badmus ◽  
S. Chowdhury ◽  
C. N. Nett
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Controller Design ◽  
Dynamic Pressure ◽  
Axial Compressor ◽  
State Feedback Control ◽  
Effective Length ◽  
Control Input ◽  
System Input ◽  
System Output

This paper presents experimental demonstration of surge stabilization in an axial compressor rig with a feedback linearizing controller. The controller design approach is model-based, and hence a nonlinear surge model for the facility is first validated. The surge model is a modification of the classic one-dimensional incompressible fluid surge model, with an effective length function incorporated, to account for the increased path-length of the fluid in the compressor due to the imparted tangential forces of the blade. This model, which adequately describes the observed surge dynamics both in terms of amplitude and frequency of oscillation, is then used to develop the feedback control law. The feedback linearizing control input implicitly linearizes the dynamics between the system input, throttle area parameter, and the system output, inlet dynamic pressure. A linear state feedback control input, implemented on the feedback linearized system thus ensures stabilization of the surge dynamics in the original nonlinear model. Finally, the nonlinear based observer is included in closed loop implementation to enhance the tracking of the system output, and also to minimize the adverse effect of measurement noise, thereby improving closed loop system performance.

Chaos Synchronization of Fractional-Order Chaotic Systems With Input Saturation

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Pitcha Khamsuwan ◽  
Teerawat Sangpet ◽  
Suwat Kuntanapreeda
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Direct Method ◽  
Input Saturation ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Sufficient Stability ◽  
Local Sector ◽  
The Stability ◽  
Synchronization Scheme

This paper deals with the problem of master-slave synchronization of fractional-order chaotic systems with input saturation. Sufficient stability conditions for achieving the synchronization are derived from the basis of a fractional-order extension of the Lyapunov direct method, a new lemma of the Caputo fractional derivative, and a local sector condition. The stability conditions are formulated in linear matrix inequality (LMI) forms and therefore are readily solved. The fractional-order chaotic Lorenz and hyperchaotic Lü systems with input saturation are utilized as illustrative examples. The feasibility of the proposed synchronization scheme is demonstrated through numerical simulations.

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems: Experimental Results

2014 ◽  
Author(s):  
Chuong Hoang Nguyen ◽  
Alexander Leonessa
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Output Feedback ◽  
Reference System ◽  
State Feedback Control ◽  
Experimental Results ◽  
Control Input ◽  
Test Bed ◽  
Full State ◽  
System Output

Experimental results are presented to validate a recently developed adaptive output feedback controller for a general class of unknown MIMO linear systems. The control approach relies on three components, a predictor, a reference model, and a controller. Specifically, since the predictor is designed to predict the system’s output for any admissible control input, controlling the uncertain system is reduced to controlling the predictor, which is a virtual system with known dynamics and full state available. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory while accounting for the actuator amplitude and rate saturation constraints. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output, and the reference system trajectories all converge to each other. Theorems and the step-by-step implementation of the control strategy are presented. Finally, the control’s efficacy is illustrated by a real time implementation of the proposed algorithm on an actual helicopter test bed.

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