Piecewise parameterization for multifactor uncertain system and uncertain inventory-promotion optimization

The analytic solution provides a great deal of convenience for linear quadratic (LQ) model in industrial implementation. But, it usually dependents on the solution of Riccati differential equation. In many cases, this will increase the complexity and design cost of controller because we are not able to find the analytical solution of Riccati differential equation. In addition, the dynamic systems may be disturbed by more than one uncertain factor. Here, we discuss the piecewise parameterization for multifactor uncertain system and an uncertain inventory promotion optimization problem. First, we obtain an analytic optimal control of multifactor uncertain LQ model. For simplifying the expression of optimal control, a parametric multifactor uncertain LQ model is formulated. Moreover, a control variable piecewise parameterization method is presented for obtaining the optimal control parameters. Finally, an inventory promotion optimization problem under uncertain environment is considered for demonstrating the effectiveness of the formulated multifactor uncertain model and presented method.