Nonlinear Optimal Control for Supply Chain Networks Under Time-Delays

The paper proposes a nonlinear optimal control method for treating the control and stabilization problem of supply chain networks and inventories under time-delays. The state-space model of the supply chain network is considered to have as state variables the customer’s demand and the inventories of the manufacturer, of the retailers and of the distributors. The control inputs of the model are the manufacturer’s production and the retailer’s ordering quantities. The model is subject to time-delays. It is proven that the dynamic model of the supply chain is differentially flat and a nonlinear optimal control method is applied to it. To implement this control method, approximate linearization is performed with the use of Taylor-series expansion while an algebraic Riccati equation has to be solved at each sampling instance. The proposed control method avoids complicated changes of state variables and state-space model transformations while the control inputs it computes are applied directly on the initial nonlinear model of the controlled system. It achieves optimality because of enabling convergence of the state variables of the supply chain network to the targeted setpoints under minimal variations of the control inputs. The article’s nonlinear optimal control method is novel when compared to past approaches for treating the optimal control problem in nonlinear dynamical systems. Unlike Nonlinear Model Predictive Control (NMPC), the proposed nonlinear optimal control scheme ensures convergence to optimum without dependence on initialization and empirical selection of the controller’s parameters.