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As multiple and heterogenous unmanned vehicle systems continue to play an increasingly important role in addressing complex missions in the real world, the need for effective cooperation among unmanned vehicles becomes paramount. The concept of autonomous cooperation, wherein unmanned vehicles cooperate without human intervention or human control, offers promising avenues for enhancing the efficiency and adaptability of intelligence of multiple-heterogeneous unmanned vehicle systems. Despite the growing interests in this domain, as far as the authors are concerned, there exists a notable lack of comprehensive literature on defining explicit concept and classifying levels of autonomous cooperation of multiple-heterogeneous unmanned vehicle systems. In this aspect, this article aims to define the explicit concept of autonomous cooperation of multiple-heterogeneous unmanned vehicle systems. Furthermore, we provide a novel criterion to assess the technical maturity of the developed unmanned vehicle systems by classifying the autonomous cooperative levels of multiple-heterogeneous unmanned vehicle systems.

This paper explores the conditions for determining fixed nodes in structured networks, specifically focusing on directed acyclic graphs (DAGs). We introduce several necessary and sufficient conditions for determining fixed nodes in $p$-layered DAGs. This is accomplished by defining the problem of maximum disjoint stems, based on the observation that all DAGs can be represented as hierarchical structures with a unique label for each layer. For structured networks, we discuss the importance of fixed nodes by considering their controllability against the variations of network parameters. Moreover, we present an efficient algorithm that simultaneously performs labeling and fixed node search for $p$-layered DAGs with an analysis of its time complexity. The results presented in this paper have implications for the analysis of controllability at the individual node level in structured networks.

This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops, we first establish a necessary and sufficient condition for strong structural controllability, based on the concepts of dedicated and sharing nodes. Subsequently, we define several conditions for strong structural controllability across various graph types by decomposing them into disjoint path graphs. We further extend our findings by introducing a composition rule, facilitating the analysis of strong structural controllability in larger networks. This rule allows us to determine the strong structural controllability of connected graphs called pactus graphs (a generalization of the well-known cactus graph) by consideration of the strong structural controllability of its disjoint component graphs. In this process, we introduce the notion of a component input node, which is a state node that functions identically to an external input node. Based on this concept, we present an algorithm with approximate polynomial complexity to determine the minimum number of external input nodes required to maintain strong structural controllability in a diffusively-coupled network with self-loops., Comment: 11 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2205.05275

Within the context of structured networks, this paper introduces the concept of the Fixed Strongly Structurally Controllable Subspace (FSSCS), enabling a comprehensive characterization of controllable subspaces. From a graph-theoretical viewpoint, the paper defines Fixed Strongly Structurally Controllable (FSSC) nodes based on the FSSCS concept and establishes the necessary and sufficient conditions for their identification. This paper proposes a method for determining the exact dimension of the Strongly Structurally Controllable Subspace (SSCS) in hierarchical directed acyclic graphs, employing a blend of graph-theoretical approaches and controllability matrix analyses. This approach not only facilitates the identification of FSSC nodes but also enhances our understanding of the robustness of node controllability against variations in network parameters within structured networks, marking a significant advancement in the field of strong structural controllability of individual nodes., Comment: The proofs of Lemma 1 and Theorem 3 have errors

This paper considers an optimal energy management problem for a network of interconnected microgrids. A model predictive control (MPC) approach is used to avoid capacity constraint violation and to cope with uncertainties of forecasted power demands. By employing a dual ascent method and a proximal alternative direction multiplier method (ADMM), respectively, two distributed methods are designed to allow every agent using only local information to determine its own optimal control decisions. The effectiveness of the proposed method is verified via numerical simulations.

We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge weights, and initial values. Focusing on the interaction topology of the network, we introduce the notion of topological clusters, which are sets of nodes that converge to an identical value due to the topological characteristics of the network, independent of the value of the edge weights. We then investigate properties of topological clusters and present a necessary and sufficient condition for a set of nodes to form a topological cluster. We also provide an algorithm for finding topological clusters. Examples show the validity of the analysis and algorithm.

In this study, we propose a design methodology of distributed controllers for multi-agent systems on a class of directed interaction networks by extending the gradient-flow method. Although the gradient-flow method is a common design tool for distributed controllers, it is inapplicable to directed networks. First, we demonstrate how to construct a distributed controller for systems over a class of time-invariant directed graphs. Subsequently, we establish better convergence properties and performance enhancement than the conventional gradient-flow method. To illustrate its application in time-varying networks, we address the dynamic matching problem of two distinct groups of agents with different sensing ranges. This problem is a novel coordination task that involves pairing agents from two distinct groups to achieve a convergence of the paired agents' states to the same value. Accordingly, we apply the proposed method to this problem and provide sufficient conditions for successful matching. Lastly, numerical examples for systems on both time-invariant and time-varying networks demonstrate the effectiveness of the proposed method., Comment: 13 pages. https://ieeexplore.ieee.org/document/10453999

This paper designs a distributed least square solution method for a linear algebraic equation over a multiagent network. The coefficient matrix is divided into multiple blocks, and each agent only knows a subset of these blocks. The designed method is discrete-time and based on a proximal ADMM algorithm. By applying the designed method, each agent can find its corresponding part in one least square solution of the considered linear algebraic equation while using only its information and communicating with its neighbors. Numerical simulations verify the effectiveness of the designed method in MATLAB., Comment: I need to correct some unclear points in the paper

This paper is concerned with the stability analysis of encrypted observer-based control for linear continuous-time systems. Since conventional encryption has limited ability to deploy in continuous-time integral computation, our work presents systematically a new design of encryption for a continuous-time observer-based control scheme. To be specific, in this paper, both control parameters and signals are encrypted by the learning-with-errors (LWE) encryption to avoid data eavesdropping. Furthermore, we propose encrypted computations for the observer-based controller based on its discrete-time model, and present a continuous-time virtual dynamics of the controller for further stability analysis. Accordingly, we present novel stability criteria by introducing linear matrix inequalities (LMIs)-based conditions associated with quantization gains and sampling intervals. The established stability criteria with theoretical proofs based on a discontinuous Lyapunov functional possibly provide a way to select quantization gains and sampling intervals to guarantee the stability of the closed-loop system. Numerical results on DC motor control corresponding to several quantization gains and sampling intervals demonstrate the validity of our method.

This paper presents several conditions to determine strong sign controllability for diffusively-coupled undirected networks. The strong sign controllability is determined by the sign patterns (positive, negative, zero) of the edges. We first provide the necessary and sufficient conditions for strong sign controllability of basic components, such as path, cycle, and tree. Next, we propose a merging process to extend the basic componenets to a larger graph based on the conditions of the strong sign controllability. Furthermore, we develop an algorithm of polynomial complexity to find the minimum number of external input nodes while maintaining the strong sign controllability of a network.

This paper proposes matrix-scaled consensus algorithm, which generalizes the scaled consensus algorithm in \cite{Roy2015scaled}. In (scalar) scaled consensus algorithms, the agents' states do not converge to a common value, but to different points along a straight line in the state space, which depends on the scaling factors and the initial states of the agents. In the matrix-scaled consensus algorithm, a positive/negative definite matrix weight is assigned to each agent. Each agent updates its state based on the product of the sum of relative matrix scaled states and the sign of the matrix weight. Under the proposed algorithm, each agent asymptotically converges to a final point differing with a common consensus point by the inverse of its own scaling matrix. Thus, the final states of the agents are not restricted to a straight line but are extended to an open subspace of the state-space. Convergence analysis of matrix-scaled consensus for single and double-integrator agents are studied in detail. Simulation results are given to support the analysis., Comment: Accepted to the IEEE Conference on Decision and Control (CDC), 2022

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a process is called \textit{graph matching}) or checked for symmetry. Friendliness property of the associated adjacency matrices, specified by their spectral properties, is important in deriving a convex relaxation of the (intractable) discrete graph matching problem. In this work, we study unfriendliness properties of symmetric graphs by studying its relation to the underlying graph structure. It is revealed that a symmetric graph has two or more subgraphs of the same topology, and are adjacent to the same set of vertices. We then show that if adjacency matrices of symmetric graphs have distinct eigenvalues then there exist eigenvectors orthogonal to the vector of all ones, making them unfriendly. Relation of graph symmetry to uncontrollability of multi-agent systems under agreement dynamics with one controlled node is revisited. Examples of both synthetic and real-world graphs are also given for illustrations., Comment: 7 pages, manuscript accepted at the 2022 European Control Conference

When a team of agents, such as unmanned aerial/underwater vehicles, are operating in $3$-dimensional space, their coordinated action in pursuit of a cooperative task generally requires all agents to either share a common coordinate system or know the orientations of their coordinate axes with regard to the global coordinate frame. Given the coordinate axes that are initially unaligned, this work proposes an orientation alignment scheme for multiple agents with a type of leader-following graph typologies using only inter-agent directional vectors, and the direction measurements to one or more landmarks of the first two agents. The directional vectors are expressed in the agents' body-fixed coordinate frames and the proposed alignment protocol works exclusively with the directional vectors without the need of a global coordinate frame common to all agents or the construction of the agents' orientation matrices. Under the proposed alignment scheme, the orientations of the agents converge almost globally and asymptotically to the orientation of the leader agent. Finally, numerical simulations are also given to illustrate the effectiveness of the proposed method., Comment: Preprint accepted by the 2022 American Control Conference

In this paper, we design a stochastic Model Predictive Control (MPC) traffic signal control method for an urban traffic network when the uncertainties in the estimation of the exogenous (in/out)-flows and the turning ratios of downstream traffic flows are taken into account. Assuming that the traffic model parameters are random variables with known expectations and variance, the traffic signal control and coordination problem is formulated as a quadratic program with linear and second-order cone constraints. In order to reduce computational complexity, we suggest a way to decompose the optimization problem corresponding to the whole traffic network into multiple subproblems. By applying Alternating Direction Method of Multipliers (ADMM), the optimal stochastic traffic signal splits are found in distributed manner. The effectiveness of the designed control method is validated via some simulations using VISSIM and MATLAB.

In this technical note, we first clarify a technical issue in the convergence proof of a free-will arbitrary time (FwAT) consensus law proposed recently in Pal et al. IEEE Trans. Cybern. (2020)[1], making the results questionable. We then propose free-will arbitrary time consensus protocols for multi-agent systems with first- and second-order dynamics, respectively, and with (possibly switching) connected interaction graphs. Under the proposed consensus laws, we show that an average consensus is achieved in a free-will arbitrary prespecified time. Further, the proposed consensus laws are distributed in the sense that information is only communicated locally between neighboring agents; unlike the average consensus in [1] that uses a deformed Laplacian., Comment: 7 pages

This letter proposes two finite-time bearing-based control laws for acyclic leader-follower formations. The leaders in formation move with a bounded continuous reference velocity and each follower controls its position with regard to three agents in the formation. The first control law uses only bearing vectors, and finite-time convergence is achieved by properly selecting two state-dependent control gains. The second control law requires both bearing vectors and communications between agents. Each agent simultaneously localizes and follows a virtual target. Finite-time convergence of the desired formation under both control laws is proved by mathematical induction and supported by numerical simulations. 10.1109/LCSYS.2021.3088299, Comment: Extended version of the L-CSS paper with omitted proofs and corrections

This paper presents a generalized robust stability analysis for bearing-based formation control and network localization systems. For an undirected network, we provide a robust stability analysis in the presence of time-varying exogenous disturbances in arbitrary dimensional space. In addition, we compute the explicit upper-bound set of the bearing formation and network localization errors, which provides valuable information for a system design., Comment: 10 pages

This article investigates discrete-time matrix-weighted consensus of multi-agent networks over undirected and connected graphs. We first present consensus protocols for the agents in common networks of symmetric matrix weights with possibly different update rates and switching network topologies. A special type of matrix-weighted consensus with non-symmetric matrix-weights that can render several consensus control scenarios such as ones with scaled/rotated updates and affine motion constraints is also considered. We employ Lyapunov stability theory for discrete-time systems and occasionally utilize Lipschitz continuity of the gradient of the Lyapunov function to show the convergence to a consensus of the agents in the system. Finally, simulation results are provided to illustrate the theoretical results., Comment: 10 pages. IEEE Transactions on Control of Network Systems, 2021

Motivated by the fact that intelligent traffic control systems have become inevitable demand to cope with the risk of traffic congestion in urban areas, this paper develops a distributed control strategy for urban traffic networks. Since these networks contain a large number of roads having different directions, each of them can be described as a multi-agent system. Thus, a coordination among traffic flows is required to optimize the operation of the overall network. In order to determine control decisions, we describe the objective of improving traffic conditions as a constrained optimization problem with respect to downstream traffic flows. By applying the gradient projection method and the minimal polynomial of a matrix pair, we propose algorithms that allow each road cell to determine its control decision corresponding to the optimal solution while using only its local information. The effectiveness of our proposed algorithms is validated by numerical simulations.

This paper studies a leader-follower formation tracking problem where the leaders are moving at the same unknown bounded velocity. A distance-based control law is proposed for follower agents to maintain the desired distances in the formation and move at the leaders' velocity. The control law consists of a component to handle the uncertainty of the leaders' velocity and a component to achieve the desired distances in finite time. Numerical simulations are also provided to support the theoretical results., Comment: accepted to ICCAS 2020

This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and \textit{asymmetric} graphs, there is a unique permutation matrix that maps the vertices in one graph to the vertices in the other. Based on a convex relaxation of graph matching in Aflalo et al. (2015), we propose a distributed computation of graph matching as a distributed convex optimization problem subject to equality constraints and a global set constraint, using a network of multiple agents whose interaction graph is connected. Each agent in the network only knows one column of each of the adjacency matrices of the two graphs, and all agents collaboratively learn the graph matching by exchanging information with their neighbors. The proposed algorithm employs a projected primal-dual gradient method to handle equality constraints and a set constraint. Under the proposed algorithm, the agents' estimates of the permutation matrix converge to the optimal permutation globally and exponentially fast. Finally, simulation results are given to illustrate the effectiveness of the method., Comment: 10 pages, 2 figures, an extended version of a paper submitted to CDC20

In this paper, we develop a hybrid distance-angle rigidity theory that involves heterogeneous distances (or unsigned angles) and signed constraints for a framework in the 2-D and 3-D space. The new rigidity theory determines a (locally) unique formation shape up to a translation and a rotation by a set of distance and signed constraints, or up to a translation, a rotation and additionally a scaling factor by a set of unsigned angle and signed constraints. Under this new rigidity theory, we have a clue to resolve the flip (or reflection) and flex ambiguity for a target formation with hybrid distance-angle constraints. In particular, we can completely eliminate the ambiguity issues if formations are under a specific construction which is called \myemph{signed Henneberg construction} in this paper. We then apply the rigidity theory to formation shape control and develop a gradient-based control system that guarantees an exponential convergence close to a desired formation by inter-neighbor measurements. Several numerical simulations on formation shape control with hybrid distance-angle constraints are provided to validate the theoretical results.

A distributed pose localization framework based on direction measurements is proposed for a type of \textit{leader-follower} multi-agent systems in $\mathbb{R}^3$. The novelty of the proposed localization method lies in the elimination of the need for using distance measurements and relative orientation measurements for the network pose localization problem. In particular, a network localization scheme is developed based directly on the measured direction constraints between an agent and its neighboring agents in the network. The proposed position and orientation localization algorithms are implemented through differential equations which simultaneously compute poses of all followers by using locally measured directional vectors and angular velocities, and actual pose knowledge of some leader agents, allowing some tracking of time-varying orientations. Further, we establish an almost global asymptotic convergence of the estimated positions and orientations of the agents to the actual poses in the stationary case., Comment: 13 pages, 6 figures

This paper focuses on the problem of estimating bearing vectors between the agents in a two dimensional multi-agent network based on subtended angle measurements, called edge localization problem. We propose an edge localization graph to investigate the solvability of this problem and a distributed estimation method via orientation estimation of virtual agents to solve the problem. Under the proposed method, the estimated bearing vector exponentially converges to the real one with a common bias if and only if the edge localization graph has an oriented spanning tree. Furthermore, the estimated variables exponentially converge to the true values if the edge localization graph has an oriented spanning tree with a root knowing the bearing vector from it to one of its neighbors., Comment: 12 pages, 12 figures, Brief version of a paper named "Distributed Bearing Vector Estimation in Multi-agent Networks" published in Automatica

This paper studies the problem of multi-agent cooperative localization of a common reference coordinate frame in $\mathbb{R}^3$. Each agent in a system maintains a body-fixed coordinate frame and its actual \textit{frame transformation} (translation and rotation) from the global coordinate system is unknown. The mobile agents aim to determine their \textit{trajectories of rigid-body motions} (or the frame transformations, i.e., rotations and translations) with respect to the global coordinate frame up to a common frame transformation by using local measurements and information exchanged with neighbors. We present two frame localization schemes which compute the rigid-body motions of the agents with asymptotic stability and finite-time stability properties, respectively. Under both localization laws, the estimates of the frame transformations of the agents converge to the actual frame transformations almost globally and up to an unknown constant transformation bias. Finally, simulation results are provided., Comment: 9 pages, 4 figures, Extended version of a paper accepted at Ifac NecSys 2019

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.

This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized by a general set of pure inter-agent distances and angles. As the first result of its applications, the paper provides analysis of locally exponential stability for formation systems with pure distance/angle constraints in the $2$- and $3$-dimensional spaces. Then, as the second result, if there are three agents in the $2$-dimensional space, almost globally exponential stability for formation systems is ensured. Through numerical simulations, the validity of analyses is illustrated.

To model the interdependent couplings of multiple topics, we develop a set of rules for opinion updates of a group of agents. The rules are used to design or assign values to the elements of interdependent weighting matrices. The cooperative and anti-cooperative couplings are modeled in both the inverse-proportional and proportional feedbacks. The behaviors of cooperative opinion dynamics are analyzed using a null space property of state-dependent matrix-weighted Laplacian matrices and a Lyapunov candidate. Various consensus properties of state-dependent matrix-weighted Laplacian matrices are predicted according to the intra-agent network topology and inter-dependency topical coupling topologies.

In this paper, and inspired by the recent discrete-time model in [1,2], we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a `logic' matrix, which is distinct from the Laplacian matrix capturing interactions between individuals. For each of Model 1 and Model 2, we obtain a necessary and sufficient condition for the network to reach to a consensus on each separate topic. The condition on Model 1 involves a combination of the eigenvalues of the logic matrix and Laplacian matrix, whereas the condition on Model 2 requires only separate conditions on the logic matrix and Laplacian matrix. Further investigations of Model 1 yields two sufficient conditions for consensus, and allow us to conclude that one way to guarantee a consensus is to reduce the rate of interaction between individuals exchanging opinions. By placing further restrictions on the logic matrix, we also establish a set of Laplacian matrices which guarantee consensus for Model 1. The two models are also expanded to include stubborn individuals, who remain attached to their initial opinions. Sufficient conditions are obtained for guaranteeing convergence of the opinion dynamics system, with the final opinions generally being at a persistent disagreement. Simulations are provided to illustrate the results., Comment: Extended version of a journal paper submission, with detailed proofs and additional discussion and simulations

In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We apply the new concepts to a three-agent formation control problem with a gradient control law, and prove instability of the control system at any incorrect equilibrium point and convergence to a desired target formation. Also, we propose a modified Henneberg construction, which is a technique to generate minimally rigid (or weakly rigid) graphs. Finally, we extend the concept of the weak rigidity in R^2 to the concept in R^3., Comment: Submitted for a publication

Given a network of multiple agents, the pointing consensus problem asks all agents to point toward a common target. This paper proposes a simple method to solve the pointing consensus problem in the plane. In our formulation, each agent does not know its own position, but has information about its own heading vector expressed in a common coordinate frame and some desired relative angles to the neighbors. By exchanging the heading vectors via a communication network described by a rooted out-branching graph and controlling the angle between the heading vectors, we show that all agents' heading vectors asymptotically point towards the same target for almost all initial conditions. Simulations are provided to validate the effectiveness of the proposed method., Comment: 6 pages, 6 figures, accepted to the American Control Conference 2018, Milwaukee, WI

This paper considers the economic dispatch problem for a network of power generators and customers. In particular, our aim is to minimize the total generation cost under the power supply-demand balance and the individual generation capacity constraints. This problem is solved in a distributed manner, i.e., a dual gradient-based continuous-time distributed algorithm is proposed in which only a single dual variable is communicated with the neighbors and no private information of the node is disclosed. The proposed algorithm is simple and no specific initialization is necessary, and this in turn allows on-line change of network structure, demand, generation constraints, and even the participating nodes. The algorithm also exhibits a special behavior when the problem becomes infeasible so that each node can detect over-demand or under-demand situation of the power network. Simulation results on IEEE 118 bus system confirm robustness against variations in power grids.

This paper studies a constrained optimization problem over networked systems with an undirected and connected communication topology. The algorithm proposed in this work utilizes singular perturbation, dynamic average consensus, and saddle point dynamics methods to tackle the problem for a general class of objective function and affine constraints in a fully distributed manner. It is shown that the private information of agents in the interconnected network is guaranteed in our proposed strategy. The theoretical guarantees on the optimality of the solution are provided by rigorous analyses. We apply the new proposed solution into energy networks by a demonstration of two simulations., Comment: 8 pages

This paper presents a consensus algorithm under misaligned orientations, which is defined as (i) misalignment to global coordinate frame of local coordinate frames, (ii) biases in control direction or sensing direction, or (iii) misaligned virtual global coordinate frames. After providing a mathematical formulation, we provide some sufficient conditions for consensus or for divergence. Besides the stability analysis, we also conduct some analysis for convergence characteristics in terms of locations of eigenvalues. Through a number of numerical simulations, we would attempt to understand the behaviors of misaligned consensus dynamics., Comment: 23 pages, 9 figures