Asymptotic features of Hessian Matrix in Receding Horizon Model Predictive Control with Medium Sized Prediction Frames

Abstract

In this paper, Receding Horizon Model Predictive Control (RH-MPC) having a quadratic objective function is studied through the Singular Value Decomposition (SVD) and Singular Vectors of its Hessian Matrix. Contrary to the previous work, non-equal and medium sized control and prediction horizons are considered and it is shown that the Singular Values converge to the open loop magnitude response of the system and singular vectors contain the phase information. Earlier results focused on classical formulation of Generalized Predictive Control (GPC), whereas, current work proves the applicability to modern formulation. Although, method can easily be extended to MIMO systems, only SISO system examples are presented.