Estimates of the Prediction Horizon Length in MPC: a Numerical Case Study

In this paper we are concerned with estimates of the prediction horizon length in nonlinear model predictive control (MPC) without terminal constraints or costs for systems governed by ordinary differential equations. A growth bound — which is known to be the crucial condition in order to determine a horizon length for which asymptotic stability or a desired performance of the MPC closed loop is guaranteed — is numerically deduced for an example of a synchronous generator. Then, the system dynamics are discretized and the computations are repeated for the resulting sampled data system. We investigate how the obtained estimates are related — in particular, for sampling periods tending to zero. Furthermore, it is shown that a suitable design of the running costs in the sampled data setting can lead to improved performance bounds and, thus, can ensure stability for significantly shorter prediction horizons.