A Unifying Framework for Strong Structural Controllability

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure

Strong Structural Controllability of Systems on Colored Graphs

This paper deals with structural controllability of leader-follower networks. The system matrix defining the network dynamics is a pattern matrix in which a priori given entries are equal to zero, while the remaining entries take nonzero values. The network is called strongly structurally controllable if for all choices of real values for the nonzero entries in the pattern matrix, the system is controllable in the classical sense. In this paper we introduce a more general notion of strong structural controllability which deals with the situation that given nonzero entries in the system's pattern matrix are constrained to take identical nonzero values. The constraint of identical nonzero entries can be caused by symmetry considerations or physical constraints on the network. The aim of this paper is to establish graph theoretic conditions for this more general property of strong structural controllability.Comment: 13 page

Analysis of Structural Properties of Complex and Networked Systems

Over the past decades, science and society have been experiencing systems that tend to be increasingly sophisticated and interconnected. Although it would be challenging to understand and control complex systems fully, the analysis and control of such systems can be partially realized only after applying some reasonable simplifications. In particular, for the analysis of certain control properties, such as controllability, a complex system can be simplified to a linear structured system capturing an essential part of the structural information in that system, such as the existence or absence of relations between components of the system. This thesis has studied the effect of the interconnection structure of complex systems on their control properties following a structural analysis approach. More explicitly, we have analyzed strong structural properties of complex systems. The main contributions have been split into two parts:1. We have introduced a new framework for linear structured systems in which the relations between the components of the systems are allowed to be unknown. This kind of systems has been formalized in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We have dealt with strong structural controllability and the solvability of the FDI problem of this kind of linear structured systems.2. We have introduced a novel framework for linear structured systems in which a priori given entries in the system matrices are restricted to take arbitrary but identical values. Several sufficient algebraic and graph theoretic conditions were established under which these systems are strongly structurally controllable.Finally, in the outlook subsection, we have suggested some future research problems concerning the analysis of strong structural properties of complex systems