A note on the canonical controller in the behavioral system-theoretic approach

This paper aims at gaining some insights into the structure of the canonical controller introduced by A.J. Van der Schaft in the behavioral approach to system theory. One of the striking feature of this controller is its nice property of achieving exactly the specified behavior when interconnected to a plant for which it has been designed. We carry out a study of this controller by instantiating its general behavioral equation in the classical single-input/single output unity-feedback configuration. In doing so, insights into the action of the controller are obtained and reveal that the canonical controller, in that setting, acts essentially as a “plant-inverting” controller. We give also an independant result which shows how any controller which achieves a specification can be designed with experimental plant input/output data without an explicit knowledge of the behavioral equations of the controlled plant. Such a result might be of certain importance for some classes of dynamical plants and also for dealing with real-time (online) fault-tolerant controller design.