ast t future Reference r(t+k) Predicted outputs y(t+kt) output horizon t+l Manipulated u(t+k Inputs input horizon Figure 1-2 The MPC problem at the the sampling instant t An mPc pling instant for some time; k is the current sampling instant. The current measured output, 3, and a Figure 1-2 shows the state of a hypothetical SISO MPC system which has been operatin previous measurements, yk-l,yk.2,,are known and are the filled circles in Figure 1-2(a) The current measured disturbance, d, and its past values are also known(not shown1 Introduction 1-8 Figure 1-2 The MPC problem at the the sampling instant t. An MPC sampling instant Figure 1-2 shows the state of a hypothetical SISO MPC system which has been operating for some time; k is the current sampling instant. The current measured output, yk , and previous measurements, yk-1, yk-2, ..., are known and are the filled circles in Figure 1-2 (a). The current measured disturbance, dk , and its past values are also known (not shown). (b) (a) input horizon output horizon t t+1 past future t t+1 t+m t+p Predicted outputs y(t+k|t) t+m t+p Manipulated (t u k+ ) Inputs Reference r(t+k) umin umax