Control variable parameterization and optimization method for stochastic linear quadratic models

The linear quadratic (LQ) optimal control model is widely used in industrial production, medical treatment, finance and other fields. For the stochastic dynamic system, the optimal control of LQ optimal control problem is given in an analytic solution. However, the analytic optimal control is governed by a time-dependent Riccati differential equation, which is often complex and difficult to be solved accurately. Hence, the analytic optimal control may be inconvenient to be implemented in practice. Here, we discuss a parametric optimal control problem of stochastic LQ model. Firstly, the optimal control of a stochastic LQ model is derived. For obtaining an approximate control strategy with a simplified expression, we formulate a parametric stochastic LQ control model, and a control variable parameterization and optimization method is presented to solve optimal control parameter. Finally, for showing effectiveness and practicability of the control variable parameterization and optimization method, an inventory control problem under stochastic environment is discussed.(c) 2021 Elsevier Ltd. All rights reserved.