Parametric Optimal Control Problem For Uncertain Linear Quadratic Models

In the fields of industrial production,health care and finance,there are many optimal con-trol problems which can be formulated as linear quadratic models.Because the complexity and uncertainty of the world,the control system is usually disturbed by some uncertain factors.For uncertain linear quadratic optimal control problem,the optimal control is given in a state feedback form and characterized by the solution of a Riccati differential equation.However,the control-relevant Riccati differential equation cannot be solved analytically in many cases.Hence,the coefficient of state variable in optimal control is usually a complex time-oriented function,which means that we need to design a more complicated controller for achieving con-trol objectives in engineering applications.It will increase the complexity and design cost of controller such that the optimal control is more difficult to be implemented.This thesis considers the parametric optimal control problems of uncertain linear quadratic models under expected value and optimistic value criterions,respectively.The optimal control can be simplified by introducing a control parameter.Different parametric optimization methods are designed for solving the optimal control parameter.The details of main work are proposed as follows.1.A parametric optimal control problem of one-dimensional uncertain linear quadratic model under expected value criterion is considered.First,we discuss one kind of uncertain lin-ear quadratic optimal control problem.Using the equation of optimality,an analytic expression of optimal control is deduced.By introducing a control parameter,we establish an uncertain linear quadratic optimal control model with control parameter.For solving the optimal control parameter,a parametric optimization method is designed.Finally,we study an application of proposed model in production planning optimal control problem.2.We discuss a parametric optimal control problem of multi-dimensional uncertain linear quadratic model under expected value criterion.By introducing a control parameter,a multi-dimensional uncertain linear quadratic optimal control model with control parameter is estab-lished.Then we define a norm in integral form and design a parametric optimization method for solving the optimal control parameter.Finally,we study an application of proposed model in inventory-promotion optimal control problem and analyze the error between two models.3.A parametric optimal control problem of multi-dimensional uncertain linear quadratic model under optimistic value criterion is investigated.First,we consider one kind of multi-dimensional uncertain linear quadratic optimal control problem.Then we formulate and dis-cuss a parametric optimal control problem of uncertain linear quadratic model under optimistic value criterion.The optimal control parameter is solved by using the presented parametric optimization method in chapter4.Finally,we study an application of proposed model in two-spool turbofan engine optimal control problem and analyze the error between two models under different confidence levels.4.We consider a piecewise parametric optimal control problems of uncertain linear quadrat-ic models under expected value and optimistic value criterions,respectively.Based on the chapter4 and chapter5,by introducing a piecewise control parameter,two uncertain linear quadratic optimal control models with piecewise control parameter are established.Applying the proposed parametric optimization method,the optimal piecewise control parameters are obtained.Finally,we study an application of proposed model in four-wheel steering vehicle optimal control problem.