Relationship Between Integer Order Systems and Fractional Order Systems and Its Two Applications

Existence of periodic solutions and stability of fractional order dynamic systems are two important and difficult issues in fractional order systems(FOS) field. In this paper, the relationship between integer order systems(IOS) and fractional order systems is discussed. A new proof method based on the above involved relationship for the non existence of periodic solutions of rational fractional order linear time invariant systems is derived. Rational fractional order linear time invariant autonomous system is proved to be equivalent to an integer order linear time invariant non-autonomous system. It is further proved that stability of a fractional order linear time invariant autonomous system is equivalent to the stability of another corresponding integer order linear time invariant autonomous system. The examples and state figures are given to illustrate the effects of conclusion derived.

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

Study on Four Disturbance Observers for FO-LTI Systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant U+0028 FO-LTI U+0029 systems, where the disturbance includes time series expansion disturbance and sinusoidal disturbance. On one hand, the reduced order extended state observer U+0028 ROESO U+0029 and reduced order cascade extended state observer U+0028 ROCESO U+0029 are proposed for the case that the system state can be measured directly. On the other hand, the extended state observer U+0028 ESO U+0029 and the cascade extended state observer U+0028 CESO U+0029 are presented for another case when the system state cannot be measured directly. It is shown that combination of ROCESO and CESO can achieve a highly effective observation result. In addition, the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods. © 2014 Chinese Association of Automation.

分数阶微分算子的最优有理逼近算法

在分析经典逼近算法不足的基础上,提出了一种新的分数阶微分算子的实现算法——最优有理逼近算法.推导了最优有理逼近算法的公式,通过数值优化,得出了频带增益的最优轨迹.该算法避免了改进的Oustaloup算法考察频带对称的问题,并具有更高的逼近精度.频域和时域的数值实例验证了使用本算法的优势.

基于线性规划的分数阶系统有理函数逼近方法

针对分数阶系统在进行有理函数近似时,往往会存在得到的有理函数阶次较高、近似精度低或优化速度慢等问题,本文基于频域误差极小化原理,提出了一种利用低阶有理传递函数逼近分数阶系统的方法.该方法将分数阶系统和其有理逼近函数之间的误差极小化运算转化为一个线性规划问题进行求解,避免了求解方程组和非线性问题的复杂运算.仿真验证结果表明,与Charef近似法及Oustaloup近似法相比,在整个需要逼近的频段内,利用该方法得到的有理逼近函数能够以较低的阶次达到较好的近似效果.该方法不仅适用于具有分数次幂极点的系统,也适用于由分数阶微分算子组成的一般形式的分数阶系统,且降低了计算复杂度,提高了优化速度.