A parametric optimization approach for uncertain linear quadratic models

As it is well known, the optimal control of linear quadratic model is given in a feedback form, which is determined by the solution of a Riccati equation. However, the corresponding Riccati equation cannot be solved analytically in many cases. Even if an analytic solution can be obtained, it might be a complex time-oriented function. In this paper, we introduce an approximate model with parameter for simplifying the form of optimal control of uncertain linear quadratic model. First, we discuss an optimal control problem of uncertain linear quadratic model and deduce an analytic expression of optimal control. Then we formulate an approximate model with parameter and present a parametric optimization method for solving the optimal parameter. Finally, a production planning problem is given to illustrate the efficiency of the proposed approximate model and parametric optimization approach.