USING THECONTROL HORIZON. THE POSITIVE INTEGER NUMBERM < PIS CAL...

1. Using thecontrol horizon. The positive integer numberM < Pis called thecontrolquadratic programming problem of the formhorizonif the following condition hold:J

_k

(

x

_k

, ˜u

_k

, ˜u

_k+1

, ..., ˜u

_k+P−1

) =

u¯

^T

Hu¯

+

2f

^T

u¯

+

g→ ^minu˜

_k+M−1

=

u˜

_k+M

=

...

=

u˜

_k+P−1

.

u

∈

Ω

⊂

E

^mP

. (19)

¯

HereHis a positive definite matrix andΩis a convex set defined by the system of linear con-Thus, the number of independent variables is decreased frommPtomM. This approachstraints. On-line solution of the optimization problem (19) at each sampling instant generallyallows to essentially reduce the optimization problem order. However, if the controlleads to nonlinear feedback control law.horizonMis too small, the closed-loop stability can be compromised and the quality ofNote that the optimization problem (19) can be solved analytically for the unconstrained case.the processes can decrease.The result is the linear controller