Model predictive control with time-delay in control input

The paper deals with syntheses of Model Predictive Control, taking into account time-delay incontrol input. The object is described by vector-matrix linear-difference equations:xt+1 = Axt+But−h+wt , x0= x0, ƒt= Hxt+ vt, yt=Gxt,where nxt  R is the object state, mut  R is the control input, pyt  R is the output,lƒt  R is the observation, h is the delay value. It is assumed that the object operates under constrainedconditions:a1 ≤ S1xt ≤ a2, ƒ1(xt) ≤ S2ut-h ≤ ƒ2(xt).A problem consists in finding such control, which provides the output vector of the system beclose to the reference one by taking into account all the constraints. A prediction is carried out onthe base of object states estimation obtained by the Kalman filter (extrapolator). The objectivefunction is chosen as convex quadratic. The results of simulation of the method proposed is givenfor an example of the goods production, storage and delivery to consumers' problem.

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