Loading...

Controllability of Networked Systems based on Structural Features of Proximity Graphs

Mousavi, Shima | 2018

675 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51635 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Haeri, Mohammad
  7. Abstract:
  8. Recently, there has been a surge of research activities in the area of networks in the systems and control community. One foundational class of questions on networked systems pertains to their controllability. While there are classical tests to check the controllability of linear time-invariant (LTI) systems, their applications to large-scale networks is numerically infeasible. Indeed, finding a minimum cardinality set of input nodes that ensure the controllability of a network is NP-hard. Moreover, when the interaction strengths along the edges of a network are unknown, the classical controllability test cannot be applied. To overcome these issues, an alternative set of approaches involves adopting graph-theoretic techniques and connecting the controllability of a network to its topological features. Such an approach to the network controllability problem can also provide a framework for designing topologies that have favorable system theoretic properties. In some works on network controllability, a specific dynamics such as the Laplacian dynamics has been considered for the network. In this case, the system matrix is a constant matrix with all entries predetermined.In some other works, a family of system matrices assuming a certain structure are considered. The controllability analysis of such families of networks leads to the structural and strong structural controllability results. In the first part of this thesis, we examine the controllability of the Laplacian networks defined over cographs that appear in modelling a wide range of networks. We present a necessary and sufficient condition for the controllability of cographs and provide an efficient method for selecting a minimal set of input nodes from which a cograph is controllable. In the second part of the thesis, we develop a balancing set approach for the controllability analysis of a family of undirected networks.Moreover, by introducing the notion of a generalized zero forcing set, the structural controllability of undirected networks is discussed. In this direction, a method is proposed that facilitates synthesis of structural and strong structural controllable networks. In the next part, a one-to-one correspondence between the strong structural controllability of zero and nonzero modes of a network and the notions of loop and strong zero forcing sets is established. As the next contribution, we propose a framework for growing undirected and directed networks that preserves their modal strong structural controllability. Finally, we investigate the robustness of strong structural controllability of networks with respect to structural perturbations, including edge deletions and additions. To this aim, we introduce a new construct referred to as the perfect graph associated with a network with a given set of control nodes. Moreover, we obtain a characterization of critical edge sets, the maximal sets of edges whose any subset can be respectively added to, or removed from a network, while preserving strong structural controllability. Finally, procedures for combining networks to obtain strong structural controllable network-of-networks are proposed
  9. Keywords:
  10. Network Controllability ; Structural Controllability ; Strong Structural Controllability ; Laplacian Dynamic ; Cograph Structure ; Controllability Robustness ; Zero-Forcing Sets

 Digital Object List

 Bookmark

No TOC