arXiv subjects

Minh Hoang Trinh

Publications and source records attributed to Minh Hoang Trinh.

At least 19 recordsLinked to original sources

arXiv2026

Warshall algorithm for matrix-weighted graphs

This paper proposes Warshall-type algorithms for determining connectedness and clustering in an undirected matrix-weighted graphs. While a path between two vertices guarantees their connectedness in a scalar-weighted graph, the existence of one or more paths between them does not necessarily guarantee that they belong to the same cluster in a matrix-weighted graph. First, a sufficient condition for pairwise connectedness is established via aggregating path kernels between them. Second, we introduce three block matrix logic operators that enables the connectedness condition to be compactly represented and manipulated with positive semidefinite matrices. The proposed Warshall algorithm simultaneously determines connectivity between every pair of vertices in the graph and provides an approximated graph partition. Third, a distributed version of the Warshall algorithm is developed. Proofs of correctness, together with computational complexity analysis and numerical examples, are provided to establish the validity of the proposed algorithms.

cs.DM↗

arXiv2026

Adaptive stabilization of a leaderless bearing-constrained formation with disturbances

In this paper, we consider the problem of regulating and maintaining a target formation characterized by a set of bidirectional bearing constraints under disturbances. The agents in the formation are modeled by single integrators with bounded continuous disturbances of which the upper bound is unavailable for the control design. Due to the time-varying disturbances, the target formation is time-varying. We propose adaptive sliding mode control laws to uniformly globally asymptotically stabilizes the moving target formation and reject the matched disturbances. In addition, to alleviate chattering phenomena from sliding mode control, smooth adaptive control laws are then designed to guarantee uniform global boundedness of the desired formation. Finally, simulation results are given to support the analysis.

cs.MA↗

arXiv2026

Dieu khien he da tac tu

Since the early 2000s, control of multiagent systems has attracted significant research interest, with applications ranging from natural collective behaviors and social dynamics to engineered systems such as autonomous vehicles, sensor networks, and smart grids. Although research on multi-agent systems has diversified into numerous specialized directions, textbooks -- including those in English -- that provide a systematic treatment of the fundamental principles of multi-agent system control remain scarce. The material presented in this book has been developed and used in teaching since 2021, initially as a concise Vietnamese-language reference for the courses Networked Control Systems and Control of Multi-Agent Systems at Hanoi University of Science and Technology. The book focuses on a selection of fundamental topics of broad and continuing interest in the field. The complexity of several topics is asymptotic to that encountered in research-level studies, however, the analysis is presented in a step-by-step manner to facilitate access to commonly used methods and tools. The material is divided into three main parts. Part I introduces multiagent systems and basic graph-theoretic concepts. Part II addresses the design and analysis of linear consensus algorithms. Part III covers selected applications and research directions, including formation control, network localization, distributed optimization, opinion dynamics, and matrix-weighted networks. Each chapter concludes with notes on notable researchers in this field, further reading, and exercises. This book cannot be completed without the encouragement, support and suggestions from families, colleagues and friends. The authors appreciate feedback from readers to further improve the content of the book.

cs.MA↗

arXiv2025

The networked input-output economic problem

In this chapter, an input-output economic model with multiple interactive economic systems is considered. The model captures the multi-dimensional nature of the economic sectors or industries in each economic system, the interdependencies among industries within an economic system and across different economic systems, and the influence of demand. To determine the equilibrium price structure of the model, a matrix-weighted updating algorithm is proposed. The equilibrium price structure is proved to be globally asymptotically achieved when certain joint conditions on the matrix-weighted graph and the input-output matrices are satisfied. The theoretical results are then supported by numerical simulations.

eess.SY↗

arXiv2025

Consensus seeking in diffusive multidimensional networks with a repeated interaction pattern and time-delays

This paper studies a consensus problem in multidimensional networks having the same agent-to-agent interaction pattern under both intra- and cross-layer time delays. Several conditions for the agents to asymptotically reach a consensus are derived, which involve the overall network's structure, the local interacting pattern, and the assumptions specified on the time delays. The validity of these conditions is proved by direct eigenvalue evaluation and supported by numerical simulations.

eess.SY↗

arXiv2024

Bearing-Constrained Leader-Follower Formation of Single-Integrators with Disturbance Rejection: Adaptive Variable-Structure Approaches

This paper studies the problem of stabilizing a leader-follower formation specified by a set of bearing constraints and being disturbed by some unknown uniformly bounded disturbance{s}. A set of leaders are positioned at their desired positions, while each follower is modeled by a single integrator with an additive time-varying disturbance. Adaptive variable-structure control laws using displacements or only bearing vectors are provided to stabilize the desired formation. Thanks to the adaptive mechanisms, the proposed control laws require neither information of the bearing Laplacian nor the disturbances' directions and upper bounds. It is further proved that when the leaders are moving with a same bounded uniformly continuous velocity, the moving target formation can still be achieved under the proposed control laws. Simulation results are also given to support the stability analysis.

eess.SY↗

arXiv2024

Bearing-Only Solution for Fermat-Weber Location Problem: Generalized Algorithms

This paper presents novel algorithms for the Fermat-Weber Location Problem, guiding an autonomous agent to the point that minimizes the weighted sum of Euclidean distances to some beacons using only bearing measurements. The existing results address only the simple scenario where the beacons are stationary and the agent is modeled by a single integrator. In this paper, we propose a number of bearing-only algorithms that let the agent, which can be modeled as either a single-integrator or a double-integrator, follow the Fermat-Weber point of a group of stationary or moving beacons. The theoretical results are rigorously proven using Lyapunov theory and supported with simulation examples.

eess.SY↗

arXiv2024

Matrix-Scaled Consensus over Undirected Networks

In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix scaling weights. First, the algebraic properties of the matrix-scaled Laplacian and the geometry of the matrix-scaled consensus space are studied. Second, we examine matrix-scaled consensus algorithms for networks of single-integrators with or without constant parametric uncertainties. Nonlinear and finite-time matrix-scaled consensus algorithms are also proposed. Third, observer-based matrix-scaled consensus algorithms for homogeneous or heterogeneous linear-time invariant agents are designed. The convergence of the proposed algorithms is asserted by rigorous mathematical analysis and supported by numerical simulations.

eess.SY↗

arXiv2024

Randomized Matrix Weighted Consensus

In this paper, randomized gossip-type matrix-weighted consensus algorithms are proposed for both leaderless and leader-follower topologies. First, we introduce the notion of expected matrix-weighted network, which captures the multi-dimensional interactions between any two agents in a probabilistic sense. Under some mild assumptions on the distribution of the expected matrix weights and the upper bound of the updating step size, the proposed asynchronous pairwise update algorithms drive the network to achieve a consensus in expectation. An upper bound of the $ε$-convergence time of the algorithm is then derived. Furthermore, the proposed algorithms are applied to the bearing-based network localization and formation control problems. The theoretical results are supported by several numerical examples.

eess.SY↗

arXiv2024

Bearing-Based Network Localization Under Randomized Gossip Protocol

In this paper, we consider a randomized gossip algorithm for the bearing-based network localization problem. Let each sensor node be able to obtain the bearing vectors and communicate its position estimates with several neighboring agents. Each update involves two agents, and the update sequence follows a stochastic process. Under the assumption that the network is infinitesimally bearing rigid and contains at least two beacon nodes, we show that when the updating step-size is properly selected, the proposed algorithm can successfully estimate the actual sensor nodes' positions with probability one. The randomized update provides a simple, distributed, and cost-effective method for localizing the network. The theoretical result is supported with a simulation of a 1089-node sensor network.

eess.SY↗

arXiv2023

Finite-time bearing-based maneuver of acyclic leader-follower formations

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

math.OC↗

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.

math.OC↗

arXiv2021

Decentralized sliding-mode control laws for the bearing-based formation tracking problem

This paper studies the time-varying bearing-based tracking of leader-follower formations. The desired constraints between agents are specified by bearing vectors, and several leaders are moving with a bounded reference velocity. Each followers can measure the relative positions of its neighbors, its own velocities, and receive information from their neighbors. Under the assumptions that the desired formation is infinitesimally bearing rigid and the local reference frames of followers are aligned with each other, two control laws are presented in this paper based on sliding mode control approach. Stability analyses are given based on Lyapunov stability theory and supported by numerical simulations.

cs.MA↗

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.

math.OC↗

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.

eess.SY↗

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.

math.OC↗

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.

cs.SI↗

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.

eess.SY↗