On input-to-state stability of min–max nonlinear model predictive control |
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Authors: | M. Lazar, D. Mu oz de la Pe a, W.P.M.H. Heemels,T. Alamo |
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Affiliation: | aDepartment of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;bDepartamento de Inginería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, Sevilla 41092, Spain;cDepartment of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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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. |
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Keywords: | Min– max Nonlinear model predictive control Input-to-state stability |
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