Nonlinear MPC: the Impact of Sampling on Closed Loop Stability |
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| Authors: | Karl Worthmann Marcus Reble Lars Grüne Frank Allgöwer |
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| Institution: | 1. Institut für Mathematik, Technische Universität Ilmenau, Weimarer Str.25, 98693 Ilmenau, Germany;2. Institute for Systems Theory and Automatic Control, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany;3. Mathematical Institute, University of Bayreuth, Universitätsstr. 30, 95440 Bayreuth, Germany |
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| Abstract: | In this paper we consider model predictive control (MPC) schemes without stabilizing terminal constraints and/or costs for continuous time systems. While the estimates on the required prediction horizon length such that asymptotic stability of the MPC closed loop is guaranteed yield, in general, satisfactory results their applicability is limited due to the fact that the respective proofs assume that the input function can be switched arbitrarily often on compact time intervals. We present a technique which allows to determine a suitable discretization accuracy such that the obtained performance bound is preserved while the control signal is only switched at the sampling instants of the corresponding sampled data system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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