arXiv subjects

Hyo-Sung Ahn

Publications and source records attributed to Hyo-Sung Ahn.

At least 37 records · Page 2Linked to original sources

arXiv2022

Matrix-Scaled Consensus

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.

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arXiv2022

Strong Sign Controllability of Diffusively-Coupled Networks

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.

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arXiv2022

Further analysis on structure and spectral properties of symmetric graphs

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.

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arXiv2022

Direction-only Orientation Alignment of Leader-Follower Networks

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.

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arXiv2021

Free-Will Arbitrary Time Consensus Protocols with Diffusive Coupling

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.

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arXiv2020

Distance-Based Formation Tracking with Unknown Bounded Reference Velocities

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.

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arXiv2020

Distributed Bearing-based Formation Control and Network Localization with Exogenous Disturbances

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.

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arXiv2020

Edge Localization in Two Dimensional Space via Orientation Estimation

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.

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arXiv2020

Discrete-Time Matrix-Weighted Consensus

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.

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arXiv2020

Distributed traffic control for a large-scale urban network

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.

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arXiv2020

Generalized weak rigidity: Theory, and local and global convergence of formations

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.

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arXiv2020

Distributed Computation of Graph Matching in Multi-Agent Networks

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.

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arXiv2020

Continuous-time Opinion Dynamics on Multiple Interdependent Topics

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.

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arXiv2019

Hybrid distance-angle rigidity theory with signed constraints and its applications to formation shape control

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.

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arXiv2019

Pose Localization of Leader-Follower Networks with Direction Measurements

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.

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arXiv2019

Multi-agent Localization of A Common Reference Coordinate Frame: An Extrinsic Approach

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.

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arXiv2019

Topological Controllability of Undirected Networks of Diffusively-Coupled Agents

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.

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arXiv2019

Cooperative opinion dynamics on multiple interdependent topics: Modeling and analysis

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.

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