Discrete-time non-smooth nonlinear MPC: Stability and robustness

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This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with model predictive controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and input-to-state stability (ISS), while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear. For a particular class of discontinuous piecewise affine systems, a new MPC set-up based on infinity norms is proposed, which is proven to be ISS to bounded additive disturbances. This ISS result does not require continuity of the system dynamics nor of the MPC value function. © 2007 Springer-Verlag Berlin Heidelberg.
Original languageEnglish
Pages (from-to)93-103
Number of pages11
JournalLecture Notes in Control and Information Sciences
Issue number1
Publication statusPublished - 19 Nov 2007


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