Finite-Horizon Minimal Realizations for Model Predictive Control of Large-Scale Systems

In model predictive control (MPC) for large-scale applications, the computational limitations for on-line optimization often lead to the use of (relatively) short prediction horizons. In this paper, we show that as a result, the controller optimizes over only a fraction of the dynamics of the large-scale system. Based on this observation, which we will formalize, we propose a method to construct reduced-order models of minimal order, by exploiting the system-theoretic concept of finite-horizon observability, that exactly match the response of the large-scale system within a finite horizon. These so-called finite-horizon minimal realizations are used to implement equivalent MPC schemes with reduced computational effort (or the same computational effort but with a larger prediction horizon) without sacrificing accuracy/performance (as the equivalent optimization problem has the same optimizers as the original MPC problem). By computing finite-horizon minimal realizations, we can determine the dynamics as "seen" by the MPC, which can provide useful design insights, in particular, when tuning the prediction horizon. We demonstrate the strengths of our results in a numerical case study.