MATJ5105 Introduction to Geometric Control Theory (JSS29) (2 op)
Opinnon taso:
Jatko-opinnot
Arviointiasteikko:
Hyväksytty - hylätty
Suorituskieli:
englanti
Vastuuorganisaatio:
Matematiikan ja tilastotieteen laitos
Opetussuunnitelmakaudet:
2017-2018, 2018-2019, 2019-2020
Kuvaus
Sisältö
After an introduction to the control theory framework and its terminology, three main topics will be discussed: controllability, optimal control, and stabilization. The goal is to present the standard tools of geometric control (Lie brackets, accessibility, Pontryagin Maximum Principle, ...) and also to illustrate them by means of some recent results. For controllability, applications to the bilinear Schrödinger equation will be presented. For stability, we shall discuss maximal Lyapunov exponents for bilinear control systems. For optimal control, some recent results on the regularity of optimal trajectories will be presented.
Suoritustavat
Obligatory attendance on lectures, and completing exercises.
Osaamistavoitteet
An overview of the questions considered in geometric control theory and of the tools which are used to tackle them. A subjective view of some of the active research areas in the field.
Esitietojen kuvaus
Basic theory of ODEs (existence, uniqueness, regular dependence with respect to parameters), elementary differential geometry (manifolds, vector fields, tangent and cotangent manifolds).
Suoritustavat
Tapa 1
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Osallistuminen opetukseen (2 op)
Tyyppi:
Osallistuminen opetukseen
Arviointiasteikko:
Hyväksytty - hylätty
Suorituskieli:
englanti