arXiv subjects

Nhat-Minh Le-Phan

Publications and source records attributed to Nhat-Minh Le-Phan.

6 recordsLinked to original sources

arXiv2026

Angle-Based Formation Tracking of Underactuated Planar Agents

This paper addresses the angle-based formation tracking problem for a class of heterogeneous planar underactuated agents subject to disturbances. A representative example is a group of underactuated surface vessels (USVs) operating in the surge-sway-yaw plane, in which each vessel has three degrees of freedom but only two independent control inputs, which are surge force and yaw moment. The desired formation is characterized by a set of longitudinal offset points, referred to as hand points, together with prescribed angular constraints among triplets of these points. The formation tracking problem is studied on a leader-follower interaction graph, assuming the leader moves at constant velocity. Under the assumption that relative velocity measurements are available, the first control law achieves asymptotic formation tracking with internal stability guarantees. Moreover, a second algorithm that does not rely on relative velocity information is introduced, which successfully drives the followers' hand points to their desired configuration. Numerical simulations involving USVs are presented to validate the effectiveness of the proposed approaches.

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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.

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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.

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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.

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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.

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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.

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