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 modelled based on hyperchaotic dynamics. then, synchronization of the two hyperchaotic closed-loop supply chains is performed with a proportionalintegral (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 or controlling the chaotic closed-loop supply chain with minimal control strategies, discussing the cost of the hyperchaotic supply chain network control method. 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.