Amir Ajorlou

A Class of Bounded Distributed Control Strategies for Connectivity Preservation in Multi-Agent Systems

This technical note proposes a general class of distributed potential-based control laws with the connectivity preserving property for single-integrator agents. The potential functions are designed in such a way that when an edge in the information flow graph is about to lose connectivity, the gradient of the potential function lies in the direction of that edge, aiming to shrink it. The results are developed for a static information flow graph first, and then are extended to the case of dynamic edge addition. Connectivity preservation for problems involving static leaders is covered as well. The potential functions are chosen to be smooth, resulting in bounded control inputs. Other constraints may also be imposed on the potential functions to satisfy various design criteria such as consensus, containment, and formation convergence. The effectiveness of the proposed control strategy is illustrated by simulation for examples of consensus and containment.

Brief paper: Leader localization in multi-agent systems subject to failure: A graph-theoretic approach

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied. A graphical condition for structural controllability based on the information flow graph of the system is provided. The notions of p-link and q-agent controllability in a multi-leader setting are then introduced, which provide quantitative measures for the controllability of a system subject to failure in the agents and communication links. The problem of leader localization is introduced, which is concerned with finding the minimum number of agents whose selection as leaders results in a p-link or q-agent controllable network. Polynomial-time algorithms are subsequently presented to solve the problem for both cases of undirected and directed information flow graphs.

Technical communique: Sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms

This paper is concerned with the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents. In the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents has a contracting property. A set-valued LaSalle-like approach is subsequently employed to show the convergence of the agents to a common point. The results are shown to be more general than the ones reported in the literature in some cases. An illustrative example demonstrates how the proposed convergence conditions can be verified.

Connectivity Preservation in Nonholonomic Multi-Agent Systems: A Bounded Distributed Control Strategy

This technical note is concerned with the connectivity preservation of a group of unicycles using a novel distributed control scheme. The proposed local controllers are bounded, and are capable of maintaining the connectivity of those pairs of agents which are initially within the connectivity range. This means that if the network of agents is initially connected, it will remain connected at all times under this control law. Each local controller is designed in such a way that when an agent is about to lose connectivity with a neighbor, the lowest-order derivative of the agents position that is neither zero nor perpendicular to the edge connecting the agent to the corresponding neighbor, makes an acute angle with this edge, which is shown to result in shrinking the edge. The proposed methodology is then used to develop bounded connectivity preserving control strategies for the consensus problem as one of the unprecedented contributions of this work. The theoretical results are validated by simulation.

On the structural controllability of multi-agent systems subject to failure: A graph-theoretic approach

This paper considers the structural controllability of a leader-follower multi-agent system. Graphical conditions for structural controllability based on the information flow graph of the system are provided. Then, the notions of p-link and q-agent controllability are introduced as quantitative measures for the controllability of the system subject to failure in communication links or agents. Necessary and sufficient conditions for the system to remain structurally controllable in the case of the failure of some of the communication links or loss of some agents are derived in terms of the topology of the information flow graph. Moreover, a polynomial-time algorithm for determining the maximum number of failed communication links under which the system remains structurally controllable is presented (which can be analogously developed for the case of agents loss). Finally, the proposed algorithm is extended to the case of loss of agents.

Characterization of link failures in multi-agent systems under the agreement protocol

The concept of detectability for a link with respect to an agent in a multi-agent system is introduced in this work. Link failures in the network are characterized in terms of their detectability, depending on how a link failure affects the response of a particular node in the system, and whether the link failure can be determined by observing that nodes response. Sufficient conditions for detectability are provided and it is pointed out that link failures are detectable for a class of directed graphs with rooted out-branchings. The conceptually related notion of distinguishable directed information flow graphs is also introduced, and its importance in a multi-agent system is discussed. Simulation studies reveal that the obtained analytical results hold for randomly initialized network configurations.

A class of bounded distributed controllers for connectivity preservation of unicycles

This paper is concerned with the connectivity preservation of a group of nonholonomic agents using a novel distributed control scheme. The proposed controllers are bounded, and are capable of maintaining the connectivity of those pairs of agents which are initially within the connectivity range. This means that if the underlying network of agents is initially connected, it will remain connected at all times. The main idea is to design the controller in such a way that when an agent is about to lose connectivity with a neighbor, the lowest-order derivative of the agents position that is neither zero nor perpendicular to the edge connecting the agent to the corresponding neighbor makes an acute angle with this edge, forcing it to shrink. The results are first developed for a static information flow graph and are then extended to the case of dynamic edge addition. The control laws are derived based on a set of potential functions which are smooth, resulting in bounded control inputs. The effectiveness of the proposed control scheme is illustrated by a consensus example.

Leader selection in multi-agent systems subject to partial failure

This paper studies the structural controllability of a leader-follower multi-agent system. A controllability condition is first provided based on the topology of the information flow graph. Conditions for controllability preservation in a multiple-leader system subject to failure in the agents and communication links are then investigated. The problem of optimal leader selection is introduced, which is concerned with finding the minimum number of agents whose selection as leaders increase the reliability of the network in terms of controllability. A polynomial-time algorithm is subsequently presented to solve the problem for undirected information flow graphs.

Convergence analysis for a class of nonlinear consensus algorithms

In this paper, sufficient conditions for the convergence of a class of continuous-time nonlinear consensus algorithms for single integrator agents are proposed. More precisely, in the consensus algorithms studied here, the control input of each agent is assumed to be a state-dependent combination of the relative positions of its neighbors in the information flow graph. It is shown that under some mild assumptions, the contraction of the convex hull of the agents can be guaranteed. A set-valued Lasalle-like approach is then employed to derive the convergence from the contracting property. The proposed convergence criteria are verified for two different consensus algorithms via simulations.

Detectability of multiple link failures in multi-agent systems under the agreement protocol

The detectability of single link failures in a multi-agent network under the agreement protocol has been the subject of a previous study. This work expands the available results by considering the effect of multiple link losses. The analytical results offer sufficient graphical conditions for the detectability of a group of edges in the network information flow digraph. To this end, a powerful extension of the all-minors matrix tree theorem in algebraic graph theory is proved which relates the minors of the Laplace-transformed Laplacian of a directed graph to the number of shortest paths between its vertices. The results reveal an intricate relationship between the detectability of link failures and the inter-nodal paths in the network digraph.