Disturbance decoupling problem for multi-agent systems: A graph topological approach

Abstract

Çamlıbel, Mehmet Kanat (Dogus Author)This paper studies the disturbance decoupling problem for multi-agent systems with single integrator dynamics and a directed communication graph. We are interested in topological conditions that imply the disturbance decoupling of the network, and more generally guarantee the existence of a state feedback rendering the system disturbance decoupled. In particular, we will develop a class of graph partitions, which can be described as a "topological translation" of controlled invariant subspaces in the context of dynamical networks. Then, we will derive sufficient conditions in terms of graph partitions such that the network is disturbance decoupled, as well as conditions guaranteeing solvability of the disturbance decoupling problem. The proposed results are illustrated by a numerical example

On multi-consensus and almost equitable graph partitions

“…Remark 2 If π AE is an AEP of G, then, following the proof of Lemma 7 in (Monshizadeh et al, 2015), we have…”

“…Further insight into this invariance property is provided in (O'Clery et al, 2013). Moreover, the usefulness of such notions is widely documented in the recent literature: e.g., in (Monshizadeh et al, 2015), sufficient conditions in terms of AEPs are derived for diffusively coupled networked systems to be disturbance decoupled, and also conditions for guaranteeing the solvability of the disturbance decoupling problem under feedback are provided.…”

“…Hence, we tackle the problem of multi-consensus, being inspired by the most recent results on the relationship between a specific kind of graph partitionsnamely, the so-called almost equitable partitions (AEP) -and geometric control theory, especially by the invariance properties associated with such graph partitions (Cardoso et al, 2007;O'Clery et al, 2013;Schaub et al, 2016). Indeed, the almost equitability of a graph partition is an important graph-theoretical property which admits an interesting geometrical interpretation (Martini et al, 2010;Zhang et al, 2014;Monshizadeh et al, 2015;Aguilar and Gharesifard, 2016) and thus can be profitably used to set and solve networked analysis and control problems relying on a geometric approach. In particular, the mathematical foundation for the results presented in this paper has been laid by the seminal work by Caughman and Veerman (2006), where for the first time a block lower triangular structure is given for the Laplacian matrix of digraphs such that algebraic multiplicity of the zero eigenvalue is larger than one.…”

Input‐Output Decoupling of Boolean Control Networks

“…In 1964, Morgan considered the decoupling for systems whose state equations have special forms. In recent decades, the research effort focused on the decoupling for nonlinear systems , including disturbance decoupling problem for multi‐agent systems , static reduced decoupling problem for linear systems , disturbance decoupling problem for singular switched linear systems , input‐output energy decoupling of linear time‐invariant systems and so on. Decoupling problem is also unavoidable in gene regulatory networks and cell differentiation processes.…”

Almost equitable partitions and new necessary conditions for network controllability

“…Moreover, these partitions can account for a significant portion of the uncontrollable leader selections that could not have been detected by symmetry arguments alone. Using graph vertex partitions to study controltheoretic properties in multi-agent systems is not new and in fact is becoming an increasingly useful tool in the analysis and design of multi-agent control systems, see for instance [24,16,28,18,20] and references therein. Graph vertex partitions also take an important role in the study of synchrony and pattern formation in coupled cell networks [25,12].…”