This paper is devoted to the problem of uncertainty in fractional-order Chaotic systems implemented by means of standard electronic components. The fractional order element (FOE) is typically substituted by one complex impedance network containing a huge number of discrete resistors and capacitors. In order to balance the complexity and accuracy of the circuit, a sparse optimization based parameter selection method is proposed. The random error and the uncertainty of system implementation are analyzed through numerical simulations. The effectiveness of the method is verified by numerical and circuit simulations, tested experimentally with electronic circuit implementations. The simulations and experiments show that the proposed method reduces the order of circuit systems and finds a minimum number for the combination of commercially available standard components.

本文致力于研究通过标准电子元件实现的分数阶混沌系统的不确定性问题。分数阶元件 (FOE) 通常被包含大量分立电阻器和电容器的复杂阻抗网络所取代。为了平衡电路的复杂度和精度，提出了一种基于稀疏优化的参数选择方法。通过数值模拟分析了系统实现的随机误差和不确定性。该方法的有效性通过数值和电路模拟得到验证，并通过电子电路实现进行实验测试。仿真和实验表明，该方法降低了电路系统的阶数，并找到了商用标准元件组合的最小数量。