1. where α = (1-2µγ). Examinationofthe update equation indicates that it depends on future input values, us(k), and future output values, ys(k), and so cannot be implemented in real time. However, assuming the gradient of the cost function does not change significantly over the prediction horizon, s, the data vectors can be shifted back in time by s time steps and the update equation becomes: H(k +1) = αH(k)
2. Asmentioned above, thenumerical valueofα istypically slightly less than one. As the leakage factor approaches one, the control effort penalty decreases, resulting in a more aggressive controller. It is important to recall that α also depends on µ; i.e. α = 1-2µγ. For example, if µ is decreased but α remains the same,
3. 500 1000 1500 2000 105 110 115 120 125 130 135 140 145 frequency (Hz) M∞=0.275 M∞=0.32 M∞=0.38
4. 500 1000 1500 2000 105 baseline adaptive GPC