Clustering Switching Regions for Feedback Controllers: A Convex Approach

Abstract

Coalitional control groups dynamically local controllers into clusters that jointly determine their control actions to maximize control performance while minimizing the cooperation burden. This work presents linear matrix inequalities decision methods to set state-space regions where the switchings between network topologies satisfy properties of interest. In particular, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convexity</i> guarantees ellipsoidal switching sets with back-switchings avoided via a dwell time. Also, the convexity property is exploited to analyze the need for coordination at different points of the state space, leading to coordination effort zones. Moreover, by considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">invariance</i> , new ellipsoids that confine the state between topologies transitions are provided. Finally, we introduce additional conditions to attain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">submodularity</i> and, hence, reduce the effort to find optimal solutions. A numerical example is given to illustrate the feasibility of the proposed approach.