arXiv subjects

Xudong Chen

Publications and source records attributed to Xudong Chen.

86 records · Page 5Linked to original sources

arXiv2017

Controlling and Stabilizing a Rigid Formation Using a Few Agents

We show in this paper that a small subset of agents of a formation of n agents in Euclidean space can control the position and orientation of the entire formation. We consider here formations tasked with maintaining inter-agent distances at prescribed values. It is known that when the inter-agent distances specified can be realized as the edges of a rigid graph, there is a finite number of possible configurations of the agents that satisfy the distance constraints, up to rotations and translations of the entire formation. We show here that under mild conditions on the type of control used by the agents, a subset of them forming a clique can work together to control the position and orientation of the formation as a whole. Mathematically, we investigate the effect of certain allowable perturbations of a nominal dynamics of the formation system. In particular, we show that any such perturbation leads to a rigid motion of the entire formation. Furthermore, we show that the map which assigns to a perturbation the infinitesimal generator of the corresponding rigid motion is locally surjective.

math.DS↗

arXiv2016

Optimal Capacity Allocation for Sampled Networked Systems

We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the average estimation error is minimized. We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.

eess.SY↗

arXiv2016

Global Stabilization of Triangulated Formations

Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the inter-agent distance conditions. It is well known that when the distance conditions are defined by a rigid graph, there is a finite number of target configurations modulo rotations and translations of the entire formation. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesirable configurations. The undesirable configurations become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We provide here a new point of view on this problem, and propose a partial solution by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations.

math.DS↗

arXiv2016

Swarm Aggregation under Fading Attractions

Gradient descent methods have been widely used for organizing multi-agent systems, in which they can provide decentralized control laws with provable convergence. Often, the control laws are designed so that two neighboring agents repel/attract each other at a short/long distance of separation. When the interactions between neighboring agents are moreover nonfading, the potential function from which they are derived is radially unbounded. Hence, the LaSalle's principle is sufficient to establish the system convergence. This paper investigates, in contrast, a more realistic scenario where interactions between neighboring agents have fading attractions. In such setting, the LaSalle type arguments may not be sufficient. To tackle the problem, we introduce a class of partitions, termed dilute partitions, of formations which cluster agents according to the inter- and intra-cluster interaction strengths. We then apply dilute partitions to trajectories of formations generated by the multi-agent system, and show that each of the trajectories remains bounded along the evolution, and converges to the set of equilibria.

eess.SY↗

arXiv2016

Voltage Graphs and Cluster Consensus with Point Group Symmetries

A cluster consensus system is a multi-agent system in which the autonomous agents communicate to form multiple clusters, with each cluster of agents asymptotically converging to the same clustering point. We introduce in this paper a special class of cluster consensus dynamics, termed the $G$-clustering dynamics for $G$ a point group, whereby the autonomous agents can form as many as $|G|$ clusters, and moreover, the associated $|G|$ clustering points exhibit a geometric symmetry induced by the point group. The definition of a $G$-clustering dynamics relies on the use of the so-called voltage graph. We recall that a $G$-voltage graph is comprised of two elements---one is a directed graph (digraph), and the other is a map assigning elements of a group~$G$ to the edges of the digraph. For example, in the case when $G = \{1, -1\}$, i.e., a cyclic group of order~$2$, a voltage graph is nothing but a signed graph. A $G$-clustering dynamics can then be viewed as a generalization of the so-called Altafini's model, which was originally defined over a signed graph, by defining the dynamics over a voltage graph. One of the main contributions of this paper is to identify a necessary and sufficient condition for the exponential convergence of a $G$-clustering dynamics. Various properties of voltage graphs that are necessary for establishing the convergence result are also investigated, some of which might be of independent interest in topological graph theory.

math.DS↗

arXiv2015

Exponential Convergence of the Discrete-Time Altafini Model

This paper considers the discrete-time version of Altafini's model for opinion dynamics in which the interaction among a group of agents is described by a time-varying signed digraph. Prompted by an idea from [1], exponential convergence of the system is studied using a graphical approach. Necessary and sufficient conditions for exponential convergence with respect to each possible type of limit states are provided. Specifically, under the assumption of repeatedly jointly strong connectivity, it is shown that (1) a certain type of two-clustering will be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced. An upper bound on the convergence rate is also provided.

math.OC↗

arXiv2015

Distributed Evaluation and Convergence of Self-Appraisals in Social Networks

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable.

eess.SY↗

arXiv2015

A Stackelberg Game for Multi-Period Demand Response Management in the Smart Grid

This paper studies a multi-period demand response management problem in the smart grid where multiple utility companies compete among themselves. The user-utility interactions are modeled by a noncooperative game of a Stackelberg type where the interactions among the utility companies are captured through a Nash equilibrium. It is shown that this game has a unique Stackelberg equilibrium at which the utility companies set prices to maximize their revenues (within a Nash game) while the users respond accordingly to maximize their utilities subject to their budget constraints. Closed-form expressions are provided for the corresponding strategies of the users and the utility companies. It is shown that the multi- period scheme, compared with the single-period case, provides more incentives for the users to participate in the game. A necessary and sufficient condition on the minimum budget needed for a user to participate is provided.

math.OC↗

arXiv2015

A Remark on Formation Control with Triangulated Laman Graphs: Genericity of Equivariant Morse Functions

This paper, as a continuing work of [1], focus on establishing the fact that if we equip a reciprocal multi-agent (RMA) system with a triangulated Laman graph (TLG), then the associated potential function is generically an equivariant Morse function, i.e, there are only finitely many critical orbits each of which is nondegenerate. Though this assumption on the potential function of being an equivariant Morse function has been used, and in fact indispensable, in several occasions. But it is actually still an open question whether it is true for a given RMA system. Thus, in this paper we will provide a confirmative answer to the question for the class of RMA systems with TLGs. The main result, as well as the analysis of this paper, has many implications for other difficult problems.

eess.SY↗

arXiv2015

Controllability of Formations over Time-varying Graphs

In this paper, we investigate the controllability of a class of formation control systems. Given a directed graph, we assign an agent to each of its vertices and let the edges of the graph describe the information flow in the system. We relate the strongly connected components of this graph to the reachable set of the formation control system. Moreover, we show that the formation control model is approximately path-controllable over a path-connected, open dense subset as long as the graph is weakly connected and satisfies some mild assumption on the numbers of vertices of the strongly connected components.

eess.SY↗

arXiv2015

Decentralized Formation Control with A Quadratic Lyapunov Function

In this paper, we investigate a decentralized formation control algorithm for an undirected formation control model. Unlike other formation control problems where only the shape of a configuration counts, we emphasize here also its Euclidean embedding. By following this decentralized formation control law, the agents will converge to certain equilibrium of the control system. In particular, we show that there is a quadratic Lyapunov function associated with the formation control system whose unique local (global) minimum point is the target configuration. In view of the fact that there exist multiple equilibria (in fact, a continuum of equilibria) of the formation control system, and hence there are solutions of the system which converge to some equilibria other than the target configuration, we apply simulated annealing, as a heuristic method, to the formation control law to fix this problem. Simulation results show that sample paths of the modified stochastic system approach the target configuration.

eess.SY↗

arXiv2015

Consensus with Linear Objective Maps

A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics.

eess.SY↗

arXiv2015

Formation Control with Triangulated Laman Graphs

Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is well known that when the distance conditions are defined via a rigid graph, there is a finite number of target configurations modulo rotations and translations. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesired equilibria. The undesired equilibria become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We propose here a partial solution to this problem by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations.

eess.SY↗

arXiv2010

Thermal Transport Properties of Bechgaard Salts (TMTSF)2PF6 and (TMTSF)2ClO4: Implication of Spin-Charge Separation

We report thermal transport measurements performed on the quasi-one-dimensional Bechgaard salts (TMTSF)2ClO4 and (TMTSF)2PF6 along the a-direction. For both salts, magnon-drag effects are found to contribute considerably to thermopower above 80 K. These results imply spin-charge separation in the metallic state for both salts. Moreover, a linear temperature-dependent thermal conductivity is found to be unaffected by anion disorder below an anion ordering transition temperature TAO~25 K in (TMTSF)2ClO4.

cond-mat.str-el↗