scholarly journals Adaptive Inverse Optimal Control of a Novel Fractional-Order Four-Wing Hyperchaotic System with Uncertain Parameter and Circuitry Implementation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Chaojun Wu ◽  
Gangquan Si ◽  
Yanbin Zhang ◽  
Ningning Yang
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
State Feedback ◽  
Feedback Controller ◽  
Uncertain Parameter ◽  
Hyperchaotic System ◽  
Inverse Optimal Control ◽  
State Feedback Controller ◽  
Oscillation Circuit ◽  
Order Four

An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF) is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.

Control of Chaos via Fractional-Order State Feedback Controller

2010 ◽  
pp. 511-519 ◽  
Author(s):  
Seyed Hassan Hosseinnia ◽  
Reza Ghaderi ◽  
Abolfazl Ranjbar ◽  
Farzad Abdous ◽  
Shaher Momani
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Feedback Controller ◽  
Control Of Chaos ◽  
State Feedback Controller ◽  
Order State

Controlling the Fractional-Order Chaotic System Based on Inverse Optimal Control Approach

2011 ◽  
Vol 474-476 ◽  
pp. 108-113
Author(s):  
Xin Gao
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chaotic System ◽  
State Feedback ◽  
Fractional Order System ◽  
Order System ◽  
Inverse Optimal Control ◽  
Control Approach ◽  
Linear State ◽  
Optimal Control Approach

In this paper, we numerically investigate the chaotic behaviors of a fractional-order system. We find that chaotic behaviors exist in the fractional-order system with an order being less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders ranging from 2.7 to 3. Finally, a simple, but effective, linear state feedback controller is proposed for controlling the fractional-order chaotic system based on an inverse optimal control approach. Numerical simulations show the effectiveness and feasibility of the proposed controller.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

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