Fixed Mode Elimination by Minimum Communication Within an Estimator-Based Framework for Distributed Control

A distributed control scheme is considered, where each subsystem estimates a part of the state space and uses a state feedback-based controller to actuate a subset of the system’s inputs. The estimated parts of the state space are overlapping and thus provide some information about the neighboring subsystems to the local controllers. The number of communication links which are added to improve performance is a design choice. However, a minimum of communication is needed if there are fixed modes (FMs), which are eigenvalues of the closed-loop system that cannot be changed under the given structural constraints. Mild conditions on the overlapping structure are given under which there exists a communication topology of measurements or estimates to eliminate all FMs. The problem of finding the minimum communication to eliminate all FMs is formulated as a minimum cost coverage problem with submodular constraints. Based on this result, an algorithm for the FM elimination is proposed and compared to the greedy algorithm. A numerical example illustrates the results.