ME 598-JB: Approximation Techniques in Controller Synthesis for Distributed Parameter Systems

Class Description:

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.

Course content:

  1. Boundary backstepping control – numerical kernel computation for hyperbolic, parabolic, and Navier-Stokes equations.
  2. Weak form of control problem formulation.
  3. 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.
  4. Riccati operator equation approximation and moving horizon control.
  5. Transfer function approximations in the H∞ control of infinite-dimensional systems.
  6. Lyapunov design using wavelet-based multi-scale Lyapunov functionals.
  7. 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.

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