Résumé:
This comprehensive course material bridges classical control theory with modern challenges
in distributed systems governed by partial differential equations (PDEs). It systematically
explores controllability and observability principles for both finite-dimensional systems
(ODEs) and infinite-dimensional systems (PDEs), emphasizing rigorous mathematical tools
such as the Kalman rank condition, Gramian-based methods, and the Hilbert Uniqueness
Method (HUM). Key topics include:
Controllability: From Kalman criteria for linear time-invariant (LTI) systems to
boundary control of wave/heat equations.
Observability: Duality principles, spectral techniques, and geometric control
conditions (GCC) for PDEs.
Optimal Control: Adjoint methods, PDE-constrained optimization for elliptic,
parabolic, and hyperbolic systems.
The text integrates theoretical proofs with computational and real-world applications,
designed for mathematicians, engineers, and scientists, it equips readers with tools to analyze,
control, and optimize spatially distributed systems.
