Distributed Control for Identical Dynamically Coupled Systems: A Decomposition Approach

Abstract

Abstract-We consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems. If the state space matrices of these systems satisfy a certain structural property, then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant. This procedure is basically a multiobjective optimization under Linear Matrix Inequality constraints, with system norms as performance indices. The explicit expressions for computing these controllers are given for both or 2 performance, and both for static state feedback and dynamic output feedback (in discrete time). At the end of the paper, two application examples illustrate the effectiveness of the approach.

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

“…Stability of the closed-loop system is completely determined by eigenvalues of A. Massioni and Verhaegen proposed a procedure to design distributed controllers for systems that have a similar structure to (2) in [13]. Unlike this work, we would like to design A so that the eigenvalue distribution of A becomes desirable.…”

Observer‐based controller design with disturbance feedforward framework for formation control of satellites

“…As in [8,9,12], the term Z i j ∈ R 2 denotes the relative position output measurement between the i th and the j th satellites belonging to the neighbourhood set J i of the i th satellite. The coordinates x 1i := x i and x 3i := y i describe the position of the i th follower satellite relative to the leader satellite.…”

“…A disadvantage is that the formation does not tolerate failures at the leader level, since the leader's trajectory is independent of the motion of the associated followers. Recently graph theoretic methods have been widely applied to formation problems: see for example [8,9,10,11,12,13,14] and the references therein. In [8], a swarm of satellites around a planet on a circular orbit, modelled as Clohessy-Wiltshire (CW) equations, is considered, and disturbance terms are assumed to be absent.…”

“…[11] provides a detailed look at consensus protocols for a similar problem. According to [8,10,11,12,14], formation flying of multiple satellites can be modeled as a spatially distributed network of vehicles which collaborate to perform a unique mission requirement. Graph theoretic methods, that are discussed in detail in [20], have been exploited in [10] to address the formation flying problem from the perspective of synchronization of a network of Lagrangian systems.…”

Distributed Fault Detection Using Relative Information in Linear Multi-Agent Networks ★ ★The work from Daniel Silvestre was supported by the project FCT [UID/EEA/50009/2013] and with grant SFRH//BD/71206/2010, from Fundação para a Ciência e a Tecnologia. J. Hespanha was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under grants No. W911NF-09-1-0553 and W911NF-09-D-0001. C. Silvestre was supported by project MYRG117(Y1-L3)-FST12-MKM of the University of Macau.

“…The motivation for this work is to provide tools to facilitate the distributed fault detection task in a system with sub-systems with a shared objective and only sharing relative information. The importance of this problem is reported in [1] and later in [2], where the detection is crucial as a single malfunctioning node can severely impact the overall network performance. Applications span the areas of mobile robots, cooperating unmanned vehicles tasks such as surveillance and reconnaissance, distributed state estimation, among others (see [3] and the references therein).…”