Use of exponential data weighting in model predictive control design

The usual design procedures in model predictive control (MPC) use a rectangular type of moving horizon window. The length of the window equals the prediction horizon assumed in the algorithm. This is known to affect the closed-loop stability. The results obtained in this paper further shows that the prediction horizon also affects the numerical condition of the MPC algorithms that contain integrators. Specifically, for a large control horizon, the numerical condition of the MPC algorithm deteriorates rapidly as the prediction horizon increases. Thus, instead of a rectangular window, this paper proposes the use of an exponentially weighted moving horizon window in model predictive control design. By using a classical result in Toeplitz matrix, the paper shows that the condition number of the Hessian matrix is bounded if an appropriate exponential weight is used in the design