Stability and Robustness Analysis of Commensurate Fractional-order Networks

Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems

The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuat…

Robustness and convergence of fractional systems and their applications to adaptive systems

Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results due to Cong et al. We establish theorems that generalize in several ways many previous results in the specialized literature, including those of Cong et al. We use the proposed theorems in adaptive systems, proving convergence and robustness of such schemes, that up to date remain unsolved problems, showing the wide scope of application of our results.

一种研究非 commensurate 分数阶微分系统稳定性的构造性方法

A constructive approach for investigating the stability of incommensurate fractional differential systems

本文提出构造性方法研究非等阶分数阶微分系统稳定性，先给出有理阶系统稳定充要判据，再证明一般阶系统分数阶谱与有理逼近等价，进而证明非线性系统平衡点稳定性，数值仿真验证了理论结果。

Fractional-Order Model Predictive Control for Neurophysiological Cyber-Physical Systems: A Case Study using Transcranial Magnetic Stimulation

Fractional-order dynamical systems are used to describe processes that exhibit temporal long-term memory and power-law dependence of trajectories. There has been evidence that complex neurophysiological signals like electroencephalogram (EEG) can be modeled by fractional-order systems. In this work, we propose a model-based approach for closed-loop Transcranial Magnetic Stimulation (TMS) to regulate brain activity through EEG data. More precisely, we propose a model predictive control (MPC) approach with an underlying fractional-order system (FOS) predictive model. Furthermore, MPC offers, by …

基于弱形式与帕累托子集选择的鲁棒数据驱动分数阶微分方程发现

Robust data-driven discovery of fractional differential equations via weak formulations and Pareto-based subset selection

Weak-Pareto方法结合弱形式与帕累托子集选择，可从含噪数据中鲁棒发现分数阶微分方程，在多基准测试中表现优于无正则化方法及同期神经基线。