Control and synchronization of the hyperchaotic closed-loop supply chain network by PI sliding mode control

In this paper, a closed-loop supply chain is modeled based on hyperchaotic dynamics. Then, synchronization of the two hyperchaotic closed loop supply chains is performed with a proportional integral (PI) sliding mode controller design method. Using Lyapunov stability theory, it has been proved that the PI sliding mode controller can converge the synchronization error to zero in a limited time. The most important issue in the design of control strategies is the behavior of the control signal. In other words, it affects the cost of design and implementation. Numerical simulation results show that the control signal has low amplitude and fluctuations. so, the PI sliding mode control method can be implemented in the real world. Based on the numerical simulation results, the use of two controllers is proposed to reduce design costs.