Disturbance decoupling (i.e., disturbance localization) is one of the first examples of feedback synthesis through the geometric state-space theory. The goal of disturbance decoupling is to design a controller such that any external disturbance has absolutely no influence on the controlled output of the system. ARC 24 presents an optimization-based perspective for incorporating disturbance decoupling constraints into controller synthesis, which paves the way for utilizing numerical optimization tools. The constraints arising from the following sets of static state feedback are considered: (1) The set of all disturbance decoupling controllers; (2) The set of all disturbance decoupling and stabilizing controllers. These sets are inner approximated by means of matrix equations or inequalities. The concepts and methods of the existing geometric approach are tailored to the optimization-based perspective and, where possible, are unified. Our subspaces-friends repository on GitHub is used for numerical examples.
We have been driven by two primary motivations in investigating inner approximations of the sets above: (1) Enable the formulation of a variety of equality (and inequality) constrained optimization problems, where cost functions, such as a norm of the state feedback, can be minimized over a large subset of the set of all disturbance decoupling (and stabilizing) controllers; (2) Introduce the disturbance decoupling constraints to members of the control systems community who might not be quite familiar with the elegant geometric state-space theory, similar to us. This can add another dimension to research endeavors in resilient control of networked multi-agent systems. ACC 24 is a multi-agent system example in which cooperative output regulation and disturbance decoupling are considered simultaneously.