Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the Observability and Controllability of Large-Scale IoT Networks: Reducing Number of Unmatched Nodes via Link Addition
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we study large-scale networks in terms of observability and controllability. In particular, we compare the number of unmatched nodes in two main types of Scale-Free (SF) networks: the Barab{a}si-Albert (BA) model and the Holme-Kim (HK) model. Comparing the two models based on theory and simulation, we discuss the possible relation between clustering coefficient and the number of unmatched nodes. In this direction, we propose a new algorithm to reduce the number of unmatched nodes via link addition. The results are significant as one can reduce the number of unmatched nodes and therefore number of embedded sensors/actuators in, for example, an IoT network. This may significantly reduce the cost of controlling devices or monitoring cost in large-scale systems.
rate research
Read More
Observability is a fundamental concept in system inference and estimation. This paper is focused on structural observability analysis of Cartesian product networks. Cartesian product networks emerge in variety of applications including in parallel and distributed systems. We provide a structural approach to extend the structural observability of the constituent networks (referred as the factor networks) to that of the Cartesian product network. The structural approach is based on graph theory and is generic. We introduce certain structures which are tightly related to structural observability of networks, namely parent Strongly-Connected-Component (parent SCC), parent node, and contractions. The results show that for particular type of networks (e.g. the networks containing contractions) the structural observability of the factor network can be recovered via Cartesian product. In other words, if one of the factor networks is structurally rank-deficient, using the other factor network containing a spanning cycle family, then the Cartesian product of the two nwtworks is structurally full-rank. We define certain network structures for structural observability recovery. On the other hand, we derive the number of observer nodes--the node whose state is measured by an output-- in the Cartesian product network based on the number of observer nodes in the factor networks. An example illustrates the graph-theoretic analysis in the paper.
It is known that determining the observability and reconstructibility of Boolean control networks (BCNs) are both NP-hard in the number of nodes of BCNs. In this paper, we use the aggregation method to overcome the challenging complexity problem in verifying the observability and reconstructibility of large-scale BCNs with special structures in some sense. First, we define a special class of aggregations that are compatible with observability and reconstructibility (i.e, observability and reconstructibility are meaningful for each part of the aggregation), and show that even for this special class of aggregations, the whole BCN being observable/reconstructible does not imply the resulting sub-BCNs being observable/reconstructible, and vice versa. Second, for acyclic aggregations in this special class, we prove that all resulting sub-BCNs being observable/reconstructible implies the whole BCN being observable/reconstructible. Third, we show that finding such acyclic special aggregations with sufficiently small parts can tremendously reduce computational complexity. Finally, we use the BCN T-cell receptor kinetics model to illustrate the efficiency of these results. In addition, the special aggregation method characterized in this paper can also be used to deal with the observability/reconstructibility of large-scale linear (special classes of nonlinear) control systems with special network structures.
Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all of the present theory was developed for linear networks without symmetries, here we present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks.
Finite-state systems have applications in systems biology, formal verification and synthesis problems of infinite-state (hybrid) systems, etc. As deterministic finite-state systems, logical control networks (LCNs) consist of a finite number of nodes which can be in a finite number of states and update their states. In this paper, we investigate the synthesis problem for controllability and observability of LCNs by state feedback under the semitensor product framework. We show that state feedback can never enforce controllability of an LCN, but sometimes can enforce its observability. We prove that for an LCN $Sig$ and another LCN $Sig$ obtained by feeding a state-feedback controller into $Sig$, (1) if $Sig$ is controllable, then $Sig$ can be either controllable or not; (2) if $Sig$ is not controllable, then $Sig$ is not controllable either; (3) if $Sig$ is observable, then $Sig$ can be either observable or not; (4) if $Sig$ is not observable, $Sig$ can also be observable or not. We also prove that if an unobservable LCN can be synthesized to be observable by state feedback, then it can also be synthesized to be observable by closed-loop state feedback (i.e., state feedback without any input). Furthermore, we give an upper bound for the number of closed-loop state-feedback controllers that are needed to verify whether an unobservable LCN can be synthesized to be observable by state feedback.
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact-controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact-controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
