Min-max nonlinear model predictive control with guaranteed input-to-state stability

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

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Abstract

Abstract—In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and 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 via the input-to-state stability framework. First, we show that only input-to-state practical stability can be ensured in general for perturbed nonlinear systems in closed-loop with min-max MPC schemes and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new sufficient conditions that guarantee input-to-state stability of the min-max MPC closedloop system, via a dual-mode approach. Keywords—Min-max, Nonlinear model predictive control, Input-to-state stability, Input-to-state practical stability
Original languageEnglish
Title of host publicationProceedings of the 17th Symposium on Mathematical Theory of Networks and Systems(MTNS 2006), July 24-28, 2006, Kyoto, Japan,
Pages108-114
Publication statusPublished - 2006
Event17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006) - Kyoto, Japan
Duration: 24 Jul 200628 Jul 2006
Conference number: 17th

Conference

Conference17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006)
Abbreviated titleMTNS 2006
CountryJapan
CityKyoto
Period24/07/0628/07/06

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    Lazar, M., Munoz de la Pena, D., Heemels, W. P. M. H., & Alamo, T. (2006). Min-max nonlinear model predictive control with guaranteed input-to-state stability. In Proceedings of the 17th Symposium on Mathematical Theory of Networks and Systems(MTNS 2006), July 24-28, 2006, Kyoto, Japan, (pp. 108-114)