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Optimization & Control


by Dr Laurent CORDIER

The course objectives are to provide students with the concepts and tools (numerical, physical and mathematical) needed to cope with flow and transfer control. First, the analysis and control of linear systems will be presented and optimal and robust control will be detailed. Model reductions needed to cope with non linear dynamics will then be described (Proper Orthogonal Decomposition, balanced modes, global modes). Finally, the course will present an in-depth analysis of the tools on the configuration of the linearized channel flow (Orr-Sommerfeld/Squire) for which the concept of optimal perturbation is introduced.

  1. Linear Systems Analysis
    • Dynamical System State Representation.
    • Linear State Representation.
    • Commandability and Observability.
    • Balanced Representation.
  2. Open Loop Optimal Control.
    • Sensitivity.
    • Adjoint Methods. Lagrange Multiplicators.
    • Optimal Control.
    • Discreete and Continuous Adjuncts.
    • Example of Burgers Equation.
  3. Linear Control of a Closed Loop with complete information
    • Poles Placement.
    • Lineair Quadratic Control (LQR). Riccati Equations.
    • Heat Equation example.
  4. Linear Closed Loop Control with State Estimation.
    • Stochastic Processes.
    • Estimation and Kalman Filter.
    • Linear Gaussian Control (LQG). Separation Principle.
  5. Models Reduction.
    • Proper Orthogonal Decomposition
    • Balanced POD
    • Global Modes
  6. Illustration on Orr-Sommerfeld/Squire System.

         
        Passive and Active Flow Control