No Arabic abstract
This paper examines the structural controllability for a group of agents, called followers, connected to each other based on the consensus law under commands of multiple leaders, which are agents with superior capabilities, over a fixed communication topology. It is proved that the graph-theoretic sufficient and necessary condition for the set of followers to be structurally controllable under the leaders commands is leader-follower connectivity of the associated graph topology. This shrinks to graph connectivity for the case of solo leader. In the approach, we explicitly put into account the dependence among the entries of the system matrices for a consensus network using the linear parameterization technique introduced in [1].
In this paper we consider the problem of controlling a limited number of target nodes of a network. Equivalently, we can see this problem as controlling the target variables of a structured system, where the state variables of the system are associated to the nodes of the network. We deal with this problem from a different point of view as compared to most recent literature. Indeed, instead of considering controllability in the Kalman sense, that is, as the ability to drive the target states to a desired value, we consider the stronger requirement of driving the target variables as time functions. The latter notion is called functional target controllability. We think that restricting the controllability requirement to a limited set of important variables justifies using a more accurate notion of controllability for these variables. Remarkably, the notion of functional controllability allows formulating very simple graphical conditions for target controllability in the spirit of the structural approach to controllability. The functional approach enables us, moreover, to determine the smallest set of steering nodes that need to be actuated to ensure target controllability, where these steering nodes are constrained to belong to a given set. We show that such a smallest set can be found in polynomial time. We are also able to classify the possible actuated variables in terms of their importance with respect to the functional target controllability problem.
The problem of analyzing the performance of networked agents exchanging evidence in a dynamic network has recently grown in importance. This problem has relevance in signal and data fusion network applications and in studying opinion and consensus dynamics in social networks. Due to its capability of handling a wider variety of uncertainties and ambiguities associated with evidence, we use the framework of Dempster-Shafer (DS) theory to capture the opinion of an agent. We then examine the consensus among agents in dynamic networks in which an agent can utilize either a cautious or receptive updating strategy. In particular, we examine the case of bounded confidence updating where an agent exchanges its opinion only with neighboring nodes possessing similar evidence. In a fusion network, this captures the case in which nodes only update their state based on evidence consistent with the nodes own evidence. In opinion dynamics, this captures the notions of Social Judgment Theory (SJT) in which agents update their opinions only with other agents possessing opinions closer to their own. Focusing on the two special DS theoretic cases where an agent state is modeled as a Dirichlet body of evidence and a probability mass function (p.m.f.), we utilize results from matrix theory, graph theory, and networks to prove the existence of consensus agent states in several time-varying network cases of interest. For example, we show the existence of a consensus in which a subset of network nodes achieves a consensus that is adopted by follower network nodes. Of particular interest is the case of multiple opinion leaders, where we show that the agents do not reach a consensus in general, but rather converge to opinion clusters. Simulation results are provided to illustrate the main results.
In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: 1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology, quite different from the familiar notion of consensus or formation controllability; 2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; 3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient. For a networked system with single-input/single-output (SISO) LTI nodes, we present precise necessary and sufficient conditions for the controllability of a general network topology.
In linear control theory, a structured system is a system whose entries of its system matrices are either fixed zero or indeterminate. This system is structurally controllable, if there exists a realization of it that is controllable, and is strongly structurally controllable (SSC), if for any nonzero values of the indeterminate entries, the corresponding system is controllable. This paper introduces a new controllability notion, termed partial strong structural controllability (PSSC), which naturally extends SSC and bridges the gap between structural controllability and SSC. Dividing the indeterminate entries into two categories, generic entries and unspecified entries, a system is PSSC, if for almost all values of the generic entries in the parameter space except for a set of measure zero, and any nonzero (complex) values of the unspecified entries, the corresponding system is controllable. We highlight that this notion generalizes the generic property embedded in the conventional structural controllability for single-input systems. We then give algebraic and (bipartite) graph-theoretic necessary and sufficient conditions for single-input systems to be PSSC. Conditions for multi-input systems are subsequently given for a particular case. We also extend our results to the case where the unspecified entries can take either nonzero values or zero/nonzero values. Finally, we show the established results can induce a new graph-theoretic criterion for SSC in maximum matchings over the system bipartite graph representations.
This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our approach differs from well-known structural controllability conditions for linear systems or consensus networks, where controllability conditions are based on edge connectivity (i.e., zero or nonzero edges). Our results first provide a process for merging controllable graphs into a larger controllable graph. Then, based on this process, we provide a graph decomposition process for evaluating the topological controllability of a given network.