Séminaire de Petteri Laakkonen, 27/01/2016

An algebraic formulation of the internal model principle and the solvability of the robust regulation problem

Petteri Laakkonen (University of Tampere, Finland)

Wednesday 27th of January, at 10am, Plenary room, INRIA

Abstract: Robustness of a controller means that it achieves its control goal despite some small inaccuracies – e.g. modeling errors or inaccurate  parameter estimations – in the system to be controlled. In the robust
regulation problem we require the controller to achieve two control goals simultaneously: stabilization of the closed loop and regulation. By regulation we mean that the error between the measured behavior of
the system and a given reference signal – the desired behavior – is zeroed out asymptotically. Stability is often a robust property under reasonable assumptions. On the other hand, the famous internal model
principle states that including a reduplicated model of the reference signal dynamics into the controller guarantees that the controller achieves regulation for all systems it stabilizes. Thus, a robustly regulating controller is achieved by finding a robustly stabilizing controller that contains an internal model.

This talk presents an algebraic approach to the robust regulation. In particular, the aim is to study the internal model principle. The problem is formulated first, and then the internal model principle is presented in algebraic terms. This allows us to give a necessary and sufficient condition for the existence of a robustly regulating controller. Parameterization of all robustly regulating controllers is also discussed.