Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/392019-05-22T07:19:15Z2019-05-22T07:19:15ZPerformance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementationsGrüne, LarsMechelli, Lucapop508278Pirkelmann, SimonVolkwein, Stefanpop214121123456789/458302019-05-17T01:14:34Z2019Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations
Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan
In this paper performance indices for economic model predictive controllers (MPC) are considered. Since existing relative performance measures, designed for stabilizing controllers, fail in the economic setting, we propose alternative absolute quantities. We show that these can be applied to assess the performance of the closed loop trajectories on-line while the controller is running. The advantages of our approach are demonstrated by simulations involving a convection-diffusion-system. The method is also combined with proper orthogonal decomposition, thus demonstrating the possibility for both efficient and performant MPC for systems governed by partial differential equations.
2019Grüne, LarsMechelli, LucaPirkelmann, SimonVolkwein, Stefan510In this paper performance indices for economic model predictive controllers (MPC) are considered. Since existing relative performance measures, designed for stabilizing controllers, fail in the economic setting, we propose alternative absolute quantities. We show that these can be applied to assess the performance of the closed loop trajectories on-line while the controller is running. The advantages of our approach are demonstrated by simulations involving a convection-diffusion-system. The method is also combined with proper orthogonal decomposition, thus demonstrating the possibility for both efficient and performant MPC for systems governed by partial differential equations.WORKINGPAPERurn:nbn:de:bsz:352-2-ywxqb2eru5d19engKonstanzer Schriften in Mathematik3832019-05-16T15:03:43+02:00123456789/392019-05-16T13:03:43ZGlobal existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluidsSroczinski, Matthiaspop210756123456789/457162019-04-26T01:14:41Z2019Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occurring in the relativistic dynamics of dissipative fluids
Sroczinski, Matthias
2019Sroczinski, Matthias510DOCTORAL_THESISurn:nbn:de:bsz:352-2-1mmwauoubh2at4eng2019-04-25T11:58:00+02:00123456789/392019-04-25T09:58:00ZSpectrahedral and semidefinite representability of orbitopesKobert, Timpop211986123456789/457152019-04-25T01:14:47Z2019Spectrahedral and semidefinite representability of orbitopes
Kobert, Tim
Polar orbitopes are a rich class of orbitopes such as the symmetric and skewsymmetric Schur-Horn orbitopes, the Fan orbitopes and the tautological orbitope of the special orthogonal group. Our main result in Chapter 3.1 is to show that every polar orbitope under a connected group is a spectrahedron (Theorem 3.1.19). It follows that the polar orbitopes under connected groups are basic closed semialgebraic und their faces are exposed. Another consequence is that every polar orbitope is a spectrahedral shadow (Theorem 3.1.26). Our main result for Chapter 4 is Theorem 4.3.4. The theorem generalizes the fact, that every orbitope under the torus is a spectrahedral shadow and gives new examples of orbitopes under the bitorus, which are spectrahedra. Chapter 5.1 is concerned with finding orbitopes, which are not spectrahedral shadows. Our main result here, is to prove that many 30-dimensional orbitopes under the bitorus are not spectrahedral shadows (Theorem 5.2.2).
2019Kobert, Tim510Polar orbitopes are a rich class of orbitopes such as the symmetric and skewsymmetric Schur-Horn orbitopes, the Fan orbitopes and the tautological orbitope of the special orthogonal group. Our main result in Chapter 3.1 is to show that every polar orbitope under a connected group is a spectrahedron (Theorem 3.1.19). It follows that the polar orbitopes under connected groups are basic closed semialgebraic und their faces are exposed. Another consequence is that every polar orbitope is a spectrahedral shadow (Theorem 3.1.26). Our main result for Chapter 4 is Theorem 4.3.4. The theorem generalizes the fact, that every orbitope under the torus is a spectrahedral shadow and gives new examples of orbitopes under the bitorus, which are spectrahedra. Chapter 5.1 is concerned with finding orbitopes, which are not spectrahedral shadows. Our main result here, is to prove that many 30-dimensional orbitopes under the bitorus are not spectrahedral shadows (Theorem 5.2.2).DOCTORAL_THESISurn:nbn:de:bsz:352-2-15qzbd2l8d9fi3eng2019-04-24T14:55:49+02:00123456789/392019-04-24T12:55:49ZGeneration of semigroups for the thermoelastic plate equation with free boundary conditionsDenk, Robertpop75824Shibata, Yoshihiro123456789/456142019-04-11T01:14:32Z2019Generation of semigroups for the thermoelastic plate equation with free boundary conditions
Denk, Robert; Shibata, Yoshihiro
2019Denk, RobertShibata, Yoshihiro510JOURNAL_ARTICLEeng10.3934/eect.20190162163-248030131382Evolution Equations & Control Theory2019-04-10T13:26:27+02:00123456789/39Evolution Equations & Control Theory ; 8 (2019), 2. - S. 301-313. - eISSN 2163-2480unknown2019-04-10T11:26:27Ztrue