Stability Based on PI Control of Three-Dimensional Chaotic Oscillatory System via DNA Chemical Reaction Networks

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.