On input-to-state stability of min-max nonlinear model predictive control

M. Lazar, D. Munoz de la Pena, W.P.M.H. Heemels, T. Alamo

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Abstract

In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and other disturbance inputs. The min–max model predictive control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for robust stability of the resulting closed-loop system using the input-to-state stability (ISS) framework. First, we show that only input-to-state practical stability can be ensured in general for closed-loop min–max MPC systems; and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new conditions for guaranteeing ISS of min–max MPC closed-loop systems, using a dual-mode approach. An example illustrates the presented theory.
Original languageEnglish
Pages (from-to)39-48
Number of pages10
JournalSystems and Control Letters
Volume57
Issue number1
DOIs
Publication statusPublished - 2008

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