Controllability of partial differential equations

Yacine Chitour (1) , Emmanuel Trélat (2)

1 L2S - Laboratoire des signaux et systèmes
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This is the notes of a FAP 2005 course (for CTS PhD and posdoc students, and for researchers) about controllability of partial differential equations, with the following items:
# m-dissipative operators in a Hilbert space.
# Semi-group theory in a Banach space.
# Theorems of Hille-Yosida and Lumer-Phillips.
# Stability. Main types of solutions.
# Examples: heat equation, wave equation.
# Nonlinear parabolic problems.
# Controllability and observability of linear evolution problems.
# HUM theory.
# Riccati equation in infinite dimension.
# Controllability of the heat and wave equations.
# Other examples.

Domaines: Optimisation et contrôle [math.OC]

Yacine Chitour, Emmanuel Trélat. Controllability of partial differential equations. Lecture Notes in Control and Information Sciences 328. Advanced Topics in Control Systems Theory, Springer, pp.171--198, 2006, ⟨10.1007/11583592_5⟩. ⟨hal-00086402⟩