Behavioral control in the presence of disturbances

This paper deals with the issue of control with a constraint that in the controlled system certain variables remain free. By free, we mean that the variables are allowed to assume any trajectory. These variables can be interpreted as disturbances. The question of which controlled behaviors are a priori possible such that the controlled behaviors do not impose any constraints on the disturbance variables is addressed and solved. Certain generalities are imposed on the problem in the sense that a controller can act on only certain variables called control variables, while the performance specification is in terms of a different variable called the to-be-controlled variable. Another issue that we deal with is the notion of compatibility of such controllers. Further, the issue of controllability of the controller itself is dealt with, for the specific control problems of pole placement and stabilization. We use the behavioral approach to address these issues. In this setup control is considered as interconnection of two systems without distinguishing the variables of each system into inputs and outputs.