The classical proportional integral (PI) controller of SISO linear system is realized by DNA chemical reaction networks (CRNs) in the previous work. Up to now, few works have been done to realize PI controller of chaotic system through DNA CRNs. In this paper, a three-dimensional chaotic oscillatory system and a PI controller of three-dimensional chaotic oscillatory system are proposed by DNA CRNs. The CRNs of chaotic oscillatory system are made up of catalysis modules, degradation module and annihilation module then chemical reaction equations can be compiled into three-dimensional chaotic oscillatory system by the law of mass action to generate chaotic oscillatory signals. The CRNs of PI controller are designed by an integral module, a proportion module and an addition module, which can be compiled into PI controller for stabilizing chaotic oscillatory signals. The simulations of Matlab and Visual DSD are given to show our design achieving the PI control of a three-variable chaotic oscillatory system.

中文翻译：

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基于 DNA 化学反应网络的三维混沌振荡系统 PI 控制的稳定性


前期工作中，SISO线性系统的经典比例积分（PI）控制器是通过DNA化学反应网络（CRN）实现的。迄今为止，通过DNA CRNs实现混沌系统PI控制器的工作还很少。本文利用DNA CRNs提出了三维混沌振荡系统和三维混沌振荡系统的PI控制器。混沌振荡系统的CRN由催化模块、降解模块和湮灭模块组成，根据质量作用定律将化学反应方程编译成三维混沌振荡系统，产生混沌振荡信号。 PI控制器的CRN由积分模块、比例模块和加法模块组成，可以编译成PI控制器来稳定混沌振荡信号。 Matlab和Visual DSD的仿真表明我们的设计实现了三变量混沌振荡系统的PI控制。