Course Objective: Gaining proficiency in the use of the approximation methods in the main control design techniques for distributed parameter systems (DPS).
Prerequisites: ECE515 or equivalent. Some knowledge of real analysis and partial differential equations.
- Boundary backstepping control – numerical kernel computation for hyperbolic, parabolic, and Navier-Stokes equations.
- Weak form of control problem formulation.
- Approximation and finite-dimensionalization methods: Galerkin and POD approximation, modal expansion, multiresolution basis decomposition, Perron-Frobenius reduction, method of moments, finite lattice structures, parabolization of Navier-Stokes equation, inertial manifolds.
- Riccati operator equation approximation and moving horizon control.
- Transfer function approximations in the H∞ control of infinite-dimensional systems.
- Lyapunov design using wavelet-based multi-scale Lyapunov functionals.
- Applications to multi-phase flow systems, moving boundary problems, and beam networks.
Text: R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear System Theory, Springer-Verlag, 1995; a list of relevant books will be provided; current research papers will be given in class.