https://hal-centralesupelec.archives-ouvertes.fr/hal-01720260Ahmadi-Moshkenani, ParisaParisaAhmadi-MoshkenaniITK NTNU - Department of Engineering Cybernetics [Trondheim] - NTNU - Norwegian University of Science and Technology [Trondheim] - NTNU - Norwegian University of Science and TechnologyJohansen, TorTorJohansenITK NTNU - Department of Engineering Cybernetics [Trondheim] - NTNU - Norwegian University of Science and Technology [Trondheim] - NTNU - Norwegian University of Science and TechnologyOlaru, SorinSorinOlaruDISCO - Dynamical Interconnected Systems in COmplex Environments - L2S - Laboratoire des signaux et systèmes - UP11 - Université Paris-Sud - Paris 11 - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en AutomatiqueL2S - Laboratoire des signaux et systèmes - UP11 - Université Paris-Sud - Paris 11 - CentraleSupélec - CNRS - Centre National de la Recherche ScientifiqueCombinatorial Approach towards Multi-Parametric Quadratic Programming based on Characterizing Adjacent Critical RegionsHAL CCSD2018[SPI.AUTO] Engineering Sciences [physics]/AutomaticOlaru, Sorin2018-03-01 01:20:462023-03-24 14:53:062018-03-01 17:11:17enJournal articleshttps://hal-centralesupelec.archives-ouvertes.fr/hal-01720260/document10.1109/TAC.2018.2791479application/pdf1—Several optimization-based control design techniques can be cast in the form of parametric optimization problems. The multi-parametric quadratic programming (mpQP) represents a popular class often related to the control of constrained linear systems. The complete solution to mpQP takes the form of explicit feedback functions with a piecewise affine structure, valid in polyhedral partitions of the feasible parameter space known as critical regions. The recently proposed combinatorial approach for solving mpQP has shown better efficiency than geometric approaches in finding the complete solution to problems with high dimensions of the parameter vectors. The drawback of this method, on the other hand, is that it tends to become very slow as the number of constraints increases in the problem. This paper presents an alternative method for enumerating all optimal active sets in a mpQP based on theoretical properties of adjacent critical regions and their corresponding optimal active sets. Consequently, it results in excluding a noticeable number of feasible but not optimal candidate active sets from investigation. Therefore, the number of linear programs that should be solved decreases noticeably and the algorithm becomes faster. Simulation results confirm the reliability of the suggested method in finding the complete solution to the mpQPs while decreasing the computational time compared favourably with the best alternative approaches.