arXiv subjects

Weiguo Xia

Publications and source records attributed to Weiguo Xia.

11 recordsLinked to original sources

arXiv2026

Optimal Safety Control using High-Order Control Barrier Functions

This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.

eess.SY↗

arXiv2025

Coevolution of Actions and Opinions in Networks of Coordinating and Anti-Coordinating Agents

In this paper, we investigate the dynamics of coordinating and anti-coordinating agents in a coevolutionary model for actions and opinions. In the model, the individuals of a population interact on a two-layer network, sharing their opinions and observing others' action, while revising their own opinions and actions according to a game-theoretic mechanism, grounded in the social psychology literature. First, we consider the scenario of coordinating agents, where convergence to a Nash equilibrium (NE) is guaranteed. We identify conditions for reaching consensus configurations and establish regions of attraction for these equilibria. Second, we study networks of anti-coordinating agents. In this second scenario, we prove that all trajectories converge to a NE by leveraging potential game theory. Then, we establish analytical conditions on the network structure and model parameters to guarantee the existence of consensus and polarized equilibria, characterizing their regions of attraction.

cs.GT↗

arXiv2024

Distributed Traffic Signal Control of Interconnected Intersections: A Two-Lane Traffic Network Model

In this paper, we investigate traffic signal control in a network of interconnected intersections, aiming to balance lane-level vehicle densities through optimal green-time allocation. We develop a two-lane traffic flow model that explicitly captures lane-specific propagation dynamics, addressing key limitations of conventional road-level formulations. The proposed model offers a more granular and flexible representation of urban traffic, enabling controllers to react more accurately to lane-specific congestion patterns. Building on this model, we design a distributed model predictive control (MPC) framework and integrate it with the efficient alternating direction method of multipliers (ADMM) to enhance scalability and real-time performance. To accommodate time-varying traffic conditions, we further introduce a data-driven method for forecasting dynamic split ratios. Comprehensive VISSIM simulations on a six-intersection network in Dalian, China, demonstrate that the proposed approach outperforms existing signal control strategies in both traffic efficiency and computational speed, showing its promise for real-time deployment.

eess.SY↗

arXiv2020

Analysis of a Nonlinear Opinion Dynamics Model with Biased Assimilation

This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual's degree of bias when assimilating new opinions, and depending on the magnitude, an individual is said to have weak, intermediate, and strong bias. The opinions of the individuals lie between 0 and 1. It is shown that for strongly connected networks, the equilibria with all elements equal identically to the extreme value 0 or 1 is locally exponentially stable, while the equilibrium with all elements equal to the neutral consensus value of 1/2 is unstable. Regions of attraction for the extreme consensus equilibria are given. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is unstable for all strongly connected networks if individuals all have weak bias, becomes locally exponentially stable for complete and two-island networks if individuals all have strong bias, and its stability heavily depends on the network topology when individuals have intermediate bias. Analysis on star graphs and simulations show that additional equilibria may exist where individuals form clusters.

math.OC↗

arXiv2019

Formation control for multiple agents with local measurements: continuous-time and sampled-data-based cases

We study the formation control problem for a group of mobile agents in a plane, in which each agent is modeled as a kinematic point and can only use the local measurements in its local frame. The agents are required to maintain a geometric pattern while keeping a desired distance to a static/moving target. The prescribed formation is a general one which can be any geometric pattern, and the neighboring relationship of the N-agent system only has the requirement of containing a directed spanning tree. To solve the formation control problem, a distributed controller is proposed based on the idea of decoupled design. One merit of the controller is that it only uses each agent's local measurements in its local frame, so that a practical issue that the lack of a global coordinate frame or a common reference direction for real multi-robot systems is successfully solved. Considering another practical issue of real robotic applications that sampled data is desirable instead of continuous-time signals, the sampled-data based controller is developed. Theoretical analysis of the convergence to the desired formation is provided for the multi-agent system under both the continuous-time controller with a static/moving target and the sampled-data based one with a static target. Numerical simulations are given to show the effectiveness and performance of the controllers.

math.OC↗

arXiv2018

General formation control for multi-agent systems with double-integrator dynamics

We study the general formation problem for a group of mobile agents in a plane, in which the agents are required to maintain a distribution pattern, as well as to rotate around or remain static relative to a static/moving target. The prescribed distribution pattern is a class of general formations that the distances between neighboring agents or the distances from each agent to the target do not need to be equal. Each agent is modeled as a double integrator and can merely perceive the relative information of the target and its neighbors. A distributed control law is designed using the limit-cycle based idea to solve the problem. One merit of the controller is that it can be implemented by each agent in its Frenet-Serret frame so that only local information is utilized without knowing global information. Theoretical analysis is provided of the equilibrium of the N-agent system and of the convergence of its converging part. Numerical simulations are given to show the effectiveness and performance of the proposed controller.

math.OC↗

arXiv2018

Random Asynchronous Iterations in Distributed Coordination Algorithms

Distributed coordination algorithms (DCA) carry out information processing processes among a group of networked agents without centralized information fusion. Though it is well known that DCA characterized by an SIA (stochastic, indecomposable, aperiodic) matrix generate consensus asymptotically via synchronous iterations, the dynamics of DCA with asynchronous iterations have not been studied extensively, especially when viewed as stochastic processes. This paper aims to show that for any given irreducible stochastic matrix, even non-SIA, the corresponding DCA lead to consensus successfully via random asynchronous iterations under a wide range of conditions on the transition probability. Particularly, the transition probability is neither required to be independent and identically distributed, nor characterized by a Markov chain.

math.OC↗

arXiv2017

Persistent Flows and Non-Reciprocal Interactions in Deterministic Networks

This paper studies deterministic consensus networks with discrete-time dynamics under persistent flows and non-reciprocal agent interactions. An arc describing the interaction strength between two agents is said to be persistent if its weight function has an infinite $l_1$ norm. We discuss two balance conditions on the interactions between agents which generalize the arc-balance and cut-balance conditions in the literature respectively. The proposed conditions require that such a balance should be satisfied over each time window of a fixed length instead of at each time instant. We prove that in both cases global consensus is reached if and only if the persistent graph, which consists of all the persistent arcs, contains a directed spanning tree. The convergence rates of the system to consensus are also provided in terms of the interactions between agents having taken place. The results are obtained under a weak condition without assuming the existence of a positive lower bound of all the nonzero weights of arcs and are compared with the existing results. Illustrative examples are provided to show the critical importance of the nontrivial lower boundedness of the self-confidence of the agents.

eess.SY↗

arXiv2017

On Convergence Rate of a Continuous-Time Distributed Self-Appraisal Model with Time-Varying Relative Interaction Matrices

This paper studies a recently proposed continuous-time distributed self-appraisal model with time-varying interactions among a network of $n$ individuals which are characterized by a sequence of time-varying relative interaction matrices. The model describes the evolution of the social-confidence levels of the individuals via a reflected appraisal mechanism in real time. We first show by example that when the relative interaction matrices are stochastic (not doubly stochastic), the social-confidence levels of the individuals may not converge to a steady state. We then show that when the relative interaction matrices are doubly stochastic, the $n$ individuals' self-confidence levels will all converge to $1/n$, which indicates a democratic state, exponentially fast under appropriate assumptions, and provide an explicit expression of the convergence rate.

math.OC↗

arXiv2016

Structural balance and opinion separation in trust-mistrust social networks

Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent results have shown that structural balance is necessary for polarization in networks with fixed, strongly connected neighbor relationships when the opinion dynamics are described by DeGroot-type averaging rules. We develop this line of research in this paper in two steps. First, we consider fixed, not necessarily strongly connected, neighbor relationships. It is shown that if the network includes a strongly connected subnetwork containing mistrust, which influences the rest of the network, then no opinion clustering is possible when that subnetwork is not structurally balanced; all the opinions become neutralized in the end. In contrast, it is shown that when that subnetwork is indeed structurally balanced, the agents of the subnetwork evolve into two polarized camps and the opinions of all other agents in the network spread between these two polarized opinions. Second, we consider time-varying neighbor relationships. We show that the opinion separation criteria carry over if the conditions for fixed graphs are extended to joint graphs. The results are developed for both discrete-time and continuous-time models.

cs.SI↗

arXiv2015

Products of Generalized Stochastic Sarymsakov Matrices

In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the infinitely long left-product of the elements from a compact subset converges to a rank-one matrix. In this paper, we show that a larger subset with these two properties can be derived by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved either by introducing an "SIA index", whose value is one for Sarymsakov matrices, and then looking at those stochastic matrices with larger SIA indices, or by considering matrices that are not even SIA. Besides constructing a larger set, we give sufficient conditions for generalized Sarymsakov matrices so that their products converge to rank-one matrices. The new insight gained through studying generalized Sarymsakov matrices and their products has led to a new understanding of the existing results on consensus algorithms and will be helpful for the design of network coordination algorithms.

math.OC↗