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- Master ACYSON : Algorithmique, Calcul Symbolique et Optimisation Numérique
- Nonsmooth Dynamical Systems (Master 2 ACSYON). Lectures available soon. The aim of this course is to study a large class of nonsmooth dynamical systems including: piecewise-linear systems, differential inclusions, Filippov inclusions, Linear Complementarity Systems, Evolution Variational Inequalities, Moreau's sweeping Process with applications in mechanics and electrical circuits. The course is organised as follows:
- Tools from convex and nonsmooth analysis
- Motivating examples in mechanics and electrical circuits
- Formulation of Nonsmooth Dynamical Systems
- Existence and Uniqueness results
- Numerical Schemes for solving Nonsmooth Dynamical Systems
- Introduction to the software SICONOS for the simulation of NDS
- Numerical Optimizations (Master 2 ACSYON). Lectures available soon. This course introduces the students to the theory and numerical algorithms for continuous nonlinear optimization (constrained and unconstrained). The course covers the following topics: exact and inexact line-search, trust-region; conjugate-gradient, Newton, quasi-Newton; linear programming; quadratic programming; penalty and augmented Lagrangian methods; sequential quadratic programming; and interior-point methods. The primary programming tool for this course is Matlab and ampl.
- Convex Analysis (Master 1 ACSYON). Lectures available soon. Convex analysis is a branch of applied mathematics devoted to the study of properties of convex sets and convex functions, with applications essentially drawn from optimization. This course will focus on the fundamentals of convex analysis in finite dimensional spaces. It is connected to the optimization and practical numerical optimization courses. The topics covered are
- Basic convexity concepts in R^n;
- Topological properties of convex sets in R^n;
- Separation of convex sets;
- Convex functions.
- R. T. Rockafellar, Convex Analysis, Princeton University Press (1979) pp. xviii+451.
- J.B. Hiriart-Urruty, C. Lemaréchal, Fundamentals of Convex Analysis, Springer (2001)
- Stability of Dynamical Systems (Master 1 ACSYON). PDF Lectures available soon. Dynamic system theory provides a paradigm for modelling and studying phenomena that undergo evolution in time. Stability theory concerns the behaviour of the system trajectories of a dynamic system when the system initial state is near an equilibrium state. The main objective of this course is to present and develop necessary mathematical tools for stability analysis of nonlinear dynamic systems described by ordinary differential equations, with an emphasis on Lyapunov-based methods. The other goal is to introduce the student into various applied fields in which the dynamic systems appear such as electronics, mechanics, biology, etc. The topics covered are:
- Introduction to applied dynamical systems;
- Lyapounov stability;
- Invariance principle;
- Attractivity results;
- Application to problems in control theory.
- Hassan K. Khalil, Nonlinear Systems, Third Edition, Prentice Hall, 2002, ISBN 0-13-067389-7
- W. M. Haddad, V. S. Chellaboina, Nonlinear Dynamical Systems and Control, Princeton University Press (2008)