Fuzzy Robust Control for an Uncertain Switched Dual-Channel Closed-Loop Supply Chain Model

In this paper, we construct a type of dynamic discrete switched dual-channel closed-loop supply chain (CLSC) model with a time delay in remanufacturing and the uncertainties of cost parameters, gratuitous return rate, remanufacturing/disposal rates, preference rate of the customer to the Internet channel, and the customer's demand under the Internet based on cost switching. This model consists of a material recovery subsystem with a third-party reverse logistics provider (3PRLP) and a manufacturer remanufacturing recovery subsystem, as well as a cost-based switching signal vector. The reverse logistics includes the remanufacturing part and the gratuitous return. Furthermore, we analyze the robust operation in the CLSC system and bring forward a relative strategy with the fuzzy robust control method. A sufficient condition for the quadratic asymptotic stability is presented and stabilizing switching laws of the output-dependent form are designed in order to inhibit the operation fluctuation caused by the processes in the CLSC system. The parallel distributed compensation technique is employed to design the fuzzy controllers for the Takagi-Sugeno fuzzy model. Then, the controller gains can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. A firm cost of the CLSC operation is obtained through the fuzzy robust control strategy. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.