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The goal is to present the standard tools of geometric control Lie brackets, accessibility, Pontryagin Maximum Principle, 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. Learning outcomes: An overview of the questions considered in geometric control theory and of the tools which are used to tackle them.

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A subjective view of some of the active research areas in the field. Prerequisites: Basic theory of ODEs existence, uniqueness, regular dependence with respect to parameters , elementary differential geometry manifolds, vector fields, tangent and cotangent manifolds. Time: 5.

International Conference on Continuous Optimization

Introduction, motivation 2. A short introduction to stochastic differential equations Existence and uniqueness strong solutions , a priori estimate, examples Black-Scholes model, etc. Backward stochastic differential equations Martingale representation property, a priori estimate, existence and uniqueness, comparison theorem 4.

SDEs and BSDEs with mean reflexion Introduction, existence and uniqueness, links with mean field PDEs Learning outcomes: The main objective of these lectures is to develop the theory of backward stochastic differential equations as introduced by Pardoux and Peng in which is now a standard tool of stochastic calculus.

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Figures from this paper. References Publications referenced by this paper. Analytic extension of differentiable functions defined in closed sets by means of continuous linear operators Leonhard Frerick , Dietmar Vogt. Jurdjevic", World Scientific.

Irena Lasiecka

Ordinary Differential Equations Dan B. Marghitu , S. A stable control structure for binary distillation columns F. Observability for systems with more outputs than inputs and asymptotic observers J. Gauthier , I. Gauthier , Lukas Kupka. Finite singularities of nonlinear systems.