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In this paper, we formulate an input-output economic model with multiple interactive economic systems. 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. We prove that the equilibrium price structure can be globally asymptotically achieved given that certain joint conditions on the matrix-weighted graph and the input-output matrices are satisfied. The theoretical results are then supported by numerical simulations., Comment: 14 pages, 3 figures, preprint

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., Comment: 14 pages (double-column), 7 figures, submitted to a journal

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 globally asymptotically achieve a consensus are derived, which involve the overall network's structure, the local interacting pattern, and the values of the time delays. The validity of these conditions is proved by direct eigenvalue evaluation and supported by numerical simulations., Comment: 6 pages, 7 figures, submitted to a journal

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., Comment: 14 pages, 6 figures

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., Comment: preprint, 6 pages, 2 figures. Published in the Proceeding of the 12th International Conference on Control, Automation and Information Sciences (ICCAIS). arXiv admin note: text overlap with arXiv:2303.14733

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., Comment: 17 pages, 8 figures, preprint submitted to a journal

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 $\epsilon$-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., Comment: 32 pages, 6 figures, preprint

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

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 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

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