Control Systems Theory

A fundamental problem in control theory is to automatically generate the control input that acts on the behaviour of such system in the best possible way. This is done by minimizing a cost criterion or performance index which penalises i) the deviations of key measurements from their desired values and ii) the control effort, because energy has its price: this is in particular the goal of optimal control. This very general setting has generated a large amount of literature connecting this problem with a broad circle of ideas encompassing Passivity, Spectral factorization, Riccati equations, and Stochastic realization. In recent years these ideas have been connected to Negative Imaginary Systems that models an important form o passivity in the case of systems where sensors and actuators a co-located.
The study of these topics is a fundamental step for the design of control systems with high performances.

The main topic addressed in this field are:

  • Positive real and negative imaginary functions
  • Matricial Equations
  • All pass functions
  • Spectral Factorization
  • Spectral Analysis and Estimation


People: Augusto Ferrante (contact person), Giorgio Picci, Giacomo Baggio