Performance of NMPC Schemes without Stabilizing Terminal Constraints

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Altmüller, Nils ; Grüne, Lars ; Worthmann, Karl:
Performance of NMPC Schemes without Stabilizing Terminal Constraints.
Bayreuth , 2010

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Abstract

In this paper we investigate the performance of unconstrained nonlinear model predictive control (NMPC) schemes, i.e., schemes in which no additional terminal constraints or terminal costs are added to the finite horizon problem in order to enforce stability properties. The contribution of this paper is twofold: on the one hand in Section 3 we give a concise summary of recent results from [Grüne and Rantzer 2008, Grüne 2009, Grüne et al. 2009] in a simplified setting, restricting the reasoning to the special case of exponential controllability and classical NMPC feedback laws. On the other hand, in Section 4 we present a numerical case study for a control system governed by a semilinear parabolic PDE. This case study illustrates how our theoretical results can be used in order to explain the differences in the performance of NMPC schemes for distributed and boundary control.