000219000 001__ 219000
000219000 005__ 20190509132556.0
000219000 0247_ $$2doi$$a10.5075/epfl-thesis-7012
000219000 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis7012-1
000219000 02471 $$2nebis$$a10674239
000219000 037__ $$aTHESIS
000219000 041__ $$aeng
000219000 088__ $$a7012
000219000 245__ $$aMoment-sum-of-squares hierarchies for set approximation and optimal control
000219000 269__ $$a2016
000219000 260__ $$bEPFL$$c2016$$aLausanne
000219000 300__ $$a190
000219000 336__ $$aTheses
000219000 502__ $$aDr Alireza Karimi (président) ; Prof. Colin Neil Jones (directeur de thèse) ; Prof. Aude Billard, Prof. Jean Bernard Lasserre, Prof. Anders Rantzer (rapporteurs)
000219000 520__ $$aThis thesis uses the idea of lifting (or embedding) a nonlinear controlled dynamical system into an infinite-dimensional space of measures where this system is equivalently described by a linear equation. This equation and problems involving it are subsequently approximated using well-known moment-sum-of-squares hierarchies.  First, we address the problems of region of attraction, reachable set and maximum controlled invariant set computation, where we provide a characterization of these sets as an infinite-dimensional linear program in the cone of nonnegative measures and we describe a hierarchy of finite-dimensional semidefinite-programming (SDP) hierarchies providing a converging sequence of outer approximations to these sets.  Next, we treat the problem of optimal feedback controller design under state and input constraints. We provide a hierarchy of SDPs yielding an asymptotically optimal sequence of rational feedback controllers. In addition, we describe hierarchies of SDPs yielding approximations to the value function attained by any given rational controller, from below and from above, as well as a hierarchy of SDPs providing approximations from below to the optimal value function, hence obtaining performance certificates for the designed controllers as well as for any given rational controller.  Finally, we describe a method to verify properties of a closed loop interconnection of a nonlinear dynamical system and an optimization-based controller (e.g., a model predictive controller) for deterministic and stochastic nonlinear dynamical systems. Properties such as global stability, the $\ell_2$ gain or performance with respect to a given infinite-horizon cost function can be certified.  The methods presented are easy to implement using freely available software packages and are documented by a number of numerical examples.
000219000 6531_ $$aregion of attraction
000219000 6531_ $$areachable set
000219000 6531_ $$amaximum controlled invariant set
000219000 6531_ $$aoptimal control
000219000 6531_ $$amoment hierarchy
000219000 6531_ $$asum-of-squares
000219000 6531_ $$asemidefinite programming
000219000 6531_ $$acontroller verification
000219000 6531_ $$alifting
000219000 6531_ $$aembedding
000219000 700__ $$0246186$$g219039$$aKorda, Milan
000219000 720_2 $$aJones, Colin Neil$$edir.$$g207237$$0246471
000219000 8564_ $$uhttps://infoscience.epfl.ch/record/219000/files/EPFL_TH7012.pdf$$zn/a$$s7064420$$yn/a
000219000 909C0 $$xU12397$$0252490$$pLA3
000219000 909CO $$pthesis$$pthesis-bn2018$$pDOI$$ooai:infoscience.tind.io:219000$$qDOI2$$qGLOBAL_SET$$pSTI
000219000 917Z8 $$x108898
000219000 917Z8 $$x108898
000219000 917Z8 $$x108898
000219000 918__ $$dEDPR$$cIGM$$aSTI
000219000 919__ $$aLA3
000219000 920__ $$b2016$$a2016-6-10
000219000 970__ $$a7012/THESES
000219000 973__ $$sPUBLISHED$$aEPFL
000219000 980__ $$aTHESIS