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

K. Worthmann: Estimates of the Prediction Horizon Length in MPC: a Numerical Case Study
in: Proceedings of the IFAC Conference on Nonlinear Model Predictive Control 2012 (NMPC'12), Noordwijkerhout, the Netherlands, 2012, 0037.pdf

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Abstract:

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.

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