Linear Quadratic Models

Abstract

The linear quadratic model has been developed in [10]. See also [2, 20, 22]. We highlight here the results. We take

$$\displaystyle\begin{array}{rcl} f(x,m,v)& =& \dfrac{1} {2}\left [{x}^{{\ast}}Qx + {v}^{{\ast}}Rv +{ \left (x - S\int \xi m(\xi )d\xi \right )}^{{\ast}}\bar{Q}\left (x - S\int \xi m(\xi )d\xi \right )\right ]{}\end{array}$$

(6.1)

$$\displaystyle\begin{array}{rcl} g(x,m,v)& = Ax +\bar{ A}\int \xi m(\xi )d\xi + Bv&{}\end{array}$$

(6.2)

$$\displaystyle\begin{array}{rcl} h(x,m)& = \dfrac{1} {2}\left [{x}^{{\ast}}Q_{T}x +{ \left (x - S_{T}\int \xi m(\xi )d\xi \right )}^{{\ast}}\bar{Q_{T}}\left (x - S_{T}\int \xi m(\xi )d\xi \right )\right ].&{}\end{array}$$

(6.3)