一类分段连续系统的连续近似
Continuous approximations of a class of piece-wise continuous systems
AI总结：
本文为分段连续系统提供了连续近似的数学基础，利用微分包含理论对分段函数进行局部或全局近似，从而建模整数或分数阶的分段连续时间动力系统，解决分数阶微分方程断点右侧数值方法不足的问题。
摘要：
本文为一类具有分段连续函数的系统提供了连续近似的严谨数学基础。通过利用微分包含理论，可以对底层分段函数进行局部或全局近似。近似结果可用于建模整数或分数阶的分段连续时间动力系统。通过克服分数阶微分方程断点右侧数值方法的不足，可以轻松实现诸如混沌控制、同步、反控制等系统建模所涉及的不可达过程。本文给出了几个例子并研究了三种比较应用。
英文摘要：
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise functions can be locally or globally approximated. The approximation results can be used to model piece-wise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for diffrential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
