Journal of Convex Analysis 15 (2008), No. 4, 905--917
Copyright Heldermann Verlag 2008
Nonlinear Contractive Model Predictive Control via Polytopic Robust Controllable Sets
Jian Wan
Institut d'Informātica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain
jwan@eia.udg.es
Josep Vehí
Institut d'Informātica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain
vehi@eia.udg.es
Ningsu Luo
Institut d'Informātica i Aplicacions, Universitat de Girona, Campus Montilivi, 17071 Girona, Spain
ningsu@eia.udg.es
A general framework for computing polytopic robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed polytopic robust controllable sets is introduced in this paper. The resulting one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solvers of set inversion and constrained minimax optimization via interval analysis are applied to compute robust controllable sets and one-step control inputs in a reliable way. The computed robust controllable sets are unions of boxes and polytope geometry is applied to approximate a union of boxes innerly by one polytope.
Keywords: Nonlinear discrete-time systems, model predictive control, robust controllable sets, interval analysis, polytope geometry.
MSC: 65G40, 93B05, 93B51
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