?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F2252%2F&rft.title=Non-smooth+model+predictive+control%3A+stability+and+applications+to+hybrid+systems&rft.creator=Lazar%2C+Mircea&rft.creator=Heemels%2C+W.P.M.H.&rft.creator=Weiland%2C+Siep&rft.creator=Bemporad%2C+Alberto&rft.subject=TL+Motor+vehicles.+Aeronautics.+Astronautics&rft.description=+In+this+report+we+investigate+the+stability+of+hybrid+systems+in+closed-loop+with+Model+Predictive+Controllers+(MPC)+and+we+derive+a+priori+sufficient+conditions+for+Lyapunov+asymptotic+stability+and+exponential+stability.+A+general+theory+is+presented+which+proves+that+Lyapunov+stability+is+achieved+for+both+terminal+cost+and+constraint+set+and+terminal+equality+constraint+hybrid+MPC%2C+even+though+the+considered+Lyapunov+function+and+the+system+dynamics+may+be+discontinuous.+For+particular+choices+of+MPC+criteria+and+constrained+Piecewise+Affine+(PWA)+systems+as+the+prediction+models+we+develop+novel+algorithms+for+computing+the+terminal+cost+and+the+terminal+constraint+set.+For+a+quadratic+MPC+cost%2C+the+stabilization+conditions+translate+into+a+linear+matrix+inequality+while%2C+for+an+%E2%88%9E-norm+based+MPC+cost%2C+they+are+obtained+as+%E2%88%9E-norm+inequalities.+It+is+shown+that+by+using+%E2%88%9E-norms%2C+the+terminal+constraint+set+is+automatically+obtained+as+a+polyhedron+or+a+finite+union+of+polyhedra+by+taking+a+sublevel+set+of+the+calculated+terminal+cost+function.+New+algorithms+are+developed+for+calculating+polyhedral+or+piecewise+polyhedral+positively+invariant+sets+for+PWA+systems.+In+this+manner%2C+the+on-line+optimization+problem+leads+to+a+mixed+integer+quadratic+programming+problem+or+to+a+mixed+integer+linear+programming+problem%2C+which+can+be+solved+by+standard+optimization+tools.+Several+examples+illustrate+the+effectiveness+of+the+developed+methodology.&rft.publisher=University+of+Technology%2C+Eindhoven&rft.date=2005-09&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F2252%2F1%2FTR_Bemporad_2005_Eindoven.pdf&rft.identifier=++Lazar%2C+Mircea+and+Heemels%2C+W.P.M.H.+and+Weiland%2C+Siep+and+Bemporad%2C+Alberto++Non-smooth+model+predictive+control%3A+stability+and+applications+to+hybrid+systems.++Technical+Report++%23+%2F2005++++University+of+Technology%2C+Eindhoven+++++++(Unpublished)+++