Time-varying Communication Graphs Research Articles

Joint Robustness of Time-Varying Networks and Its Applications to Resilient Consensus

The notion of network robustness reported in some existing literature well characterizes the graph-theoretic properties of networked agent systems (NASs) with fixed communication graph for seeking resilient consensus. Yet, our systematic understanding of the graph properties for achieving resilient consensus of NASs with time-varying communication graphs remains limited. This study aims to investigate the resilient consensus problem of NASs with misbehaving agents and time-varying communication graphs under certain Mean-Subsequence-Reduced algorithms, with particular attention to formulating and revealing the graph-theoretic properties of the time-varying interaction graphs responsible for resilient consensus. Specifically, to achieve resilient consensus, each agent will first discard some extremely large and small values received from its neighbours and then generate the control input based upon the remaining neighbors' values at every time instant. To characterize the graph-theoretic properties of NASs subject to time-varying communication graphs for realizing resilient consensus in spite of the influence of misbehaving individuals, a new graph-theoretic property of the NASs, namely the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">joint robustness</i> , is introduced. This new property connects the network robustness of the fixed graph with the property of time-varying interaction graphs jointly containing a directed spanning tree. Several necessary and sufficient criteria for resilient consensus of NASs with first-order and second-order individual dynamics subject to time-varying communication graphs are respectively proven and analyzed in the framework of joint robustness. At last, the effectiveness of the analytical findings is validated by performing numerical simulations.

Distributed inertial online game algorithm for tracking generalized Nash equilibria.

This paper is concerned with the distributed generalized Nash equilibrium (GNE) tracking problem of noncooperative games in dynamic environments, where the cost function and/or the coupled constraint function are time-varying and revealed to each agent after it makes a decision. We first consider the case without coupled constraints and propose a distributed inertial online game (D-IOG) algorithm based on the mirror descent method. The proposed algorithm is capable of tracking Nash equilibrium (NE) through a time-varying communication graph and has the potential of achieving a low average regret. With an appropriate non-increasing stepsize sequence and an inertial parameter, the regrets can grow sublinearly if the deviation of the NE sequence grows sublinearly. Second, the time-varying coupled constraints are further investigated, and a modified D-IOG algorithm for tracking GNE is proposed based on the primal-dual and mirror descent methods. Then, the upper bounds of regrets and constraint violation are derived. Moreover, inertia and two information transmission modes are discussed. Finally, two simulation examples are provided to illustrate the effectiveness of the D-IOG algorithms.

Privacy-preserving Decentralized Federated Learning over Time-varying Communication Graph

Establishing how a set of learners can provide privacy-preserving federated learning in a fully decentralized (peer-to-peer, no coordinator) manner is an open problem. We propose the first privacy-preserving consensus-based algorithm for the distributed learners to achieve decentralized global model aggregation in an environment of high mobility, where participating learners and the communication graph between them may vary during the learning process. In particular, whenever the communication graph changes, the Metropolis-Hastings method [ 69 ] is applied to update the weighted adjacency matrix based on the current communication topology. In addition, the Shamir’s secret sharing (SSS) scheme [ 61 ] is integrated to facilitate privacy in reaching consensus of the global model. The article establishes the correctness and privacy properties of the proposed algorithm. The computational efficiency is evaluated by a simulation built on a federated learning framework with a real-world dataset.

Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm Over Time-Varying Digraphs With Unconstrained Actions

This paper presents a new distributed algorithm that leverages heavy-ball momentum and a consensus-based gradient method to find a Nash equilibrium (NE) in a class of non-cooperative convex games with unconstrained action sets. In this approach, each agent in the game has access to its own smooth local cost function and can exchange information with its neighbors over a communication network. The main novelty of our work is the incorporation of heavy-ball momentum in the context of non-cooperative games that operate on fully-decentralized, directed, and time-varying communication graphs, while also accommodating non-identical step-sizes and momentum parameters. Overcoming technical challenges arising from the dynamic and asymmetric nature of mixing matrices and the presence of an additional momentum term, we provide a rigorous proof of the geometric convergence to the NE. Moreover, we establish explicit bounds for the step-size values and momentum parameters based on the characteristics of the cost functions, mixing matrices, and graph connectivity structures. We perform numerical simulations on a Nash-Cournot game to demonstrate accelerated convergence of the proposed algorithm compared to that of the existing methods.

Distributed State Estimation Over Time-Varying Graphs: Exploiting the Age-of-Information

We study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-time-scale distributed observer that works under mild assumptions. Specifically, our communication model only requires strong-connectivity to be preserved over nonoverlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. We also develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a “freshness-index” that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.

Scale-Free Cooperative Control of Inverter-Based Microgrids With General Time-Varying Communication Graphs

This paper presents a method for controlling the voltage of inverter-based Microgrids by proposing a new scale-free distributed cooperative controller. The main contribution of this paper is that the proposed distributed cooperative controller is scale-free where is independent of any information about the communication system and the number of distributed generators, as such it works for any Microgrids with any size. Moreover, the communication network is modeled by a general time-varying graph which enhances the resilience of the proposed protocol against communication link failure, data packet loss, and arbitrarily fast plug and play operation in the presence of arbitrarily finite communication delays as the protocol does not require the knowledge of the upper bound on the delay. The stability analysis of the proposed protocol is provided. The proposed method is simulated on the CIGRE medium voltage Microgrid test system. The simulation results demonstrate the feasibility of the proposed scale-free distributed nonlinear protocol for regulating voltage of Microgrids in the presence of communication failures, data packet loss, noise, and degradation.

Distributed data-driven UAV formation control via evolutionary games: Experimental results

This work proposes a novel data-driven distributed formation-control approach based on multi-population evolutionary games, which is structured in a leader-follower scheme. The methodology considers a time-varying communication graph that describes how the multiple agents share information to each other. We present stability guarantees for configurations given by time-varying interaction networks, making the proposed method suitable for real-world problems where communication constraints change along the time. Additionally, the proposed formation controller allows for an agent to leave or enter the group without the need to modify the behaviors of other agents in the group. This game-theoretical approach is evaluated through numerical simulations and real outdoors experimental results using a fleet of aerial autonomous vehicles, showing the control performance.

Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators

This paper investigates the problem of finding a fixed point for a global nonexpansive operator under time-varying communication graphs in real Hilbert spaces, where the global operator is separable and composed of an aggregate sum of local nonexpansive operators. Each local operator is only privately accessible to each agent, and all agents constitute a network. To seek a fixed point of the global operator, it is indispensable for agents to exchange local information and update their solution cooperatively. To solve the problem, two algorithms are developed, called distributed Krasnosel’skiĭ–Mann (D-KM) and distributed block-coordinate Krasnosel’skiĭ–Mann (D-BKM) iterations, for which D-BKM is a block-coordinate version of D-KM in the sense of randomly choosing and computing only one block-coordinate of local operators at each time for each agent. It is shown that the proposed two algorithms can both converge weakly to a fixed point of the global operator. Meanwhile, the designed algorithms are applied to recover the classical distributed gradient descent (DGD) algorithm, devise a new block-coordinate DGD algorithm, handle a distributed shortest distance problem in the Hilbert space for the first time, and solve linear algebraic equations in a novel distributed approach. Finally, the theoretical results are corroborated by a few numerical examples.

Game of the Byzantine Generals on Time-Varying Graphs

In this paper, we propose a game of the Byzantine Generals, which is a coordination game of agents seeking consensus by strategically transmitting information on a sequence of time-varying communication graphs. The first scenario of the game is where the generals cannot communicate with others at the same "level" in the communication graph. The second scenario is where those generals can. In either scenario, we examine the influences of the number of traitors and the decision rule held by the generals on equilibrium predictions of the game.

Distributed Online Optimization With Long-Term Constraints

In this article, we consider distributed online convex optimization problems, where the distributed system consists of various computing units connected through a time-varying communication graph. In each time step, each computing unit selects a constrained vector, experiences a loss equal to an arbitrary convex function evaluated at this vector, and may communicate to its neighbors in the graph. The objective is to minimize the system-wide loss accumulated over time. We propose a decentralized algorithm with regret and cumulative constraint violation in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(T^{\max \lbrace c,1-c\rbrace })$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(T^{1-c/2})$</tex-math></inline-formula> , respectively, for any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c\in (0,1)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is the time horizon. When the loss functions are strongly convex, we establish improved regret and constraint violation upper bounds in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(\log (T))$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(\sqrt{T\log (T)})$</tex-math></inline-formula> . These regret scalings match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problem (for both convex and strongly convex loss functions). In the case of bandit feedback, the proposed algorithms achieve a regret and constraint violation in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(T^{\max \lbrace c,1-c/3 \rbrace })$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(T^{1-c/2})$</tex-math></inline-formula> for any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c\in (0,1)$</tex-math></inline-formula> . We numerically illustrate the performance of our algorithms for the particular case of distributed online regularized linear regression problems on synthetic and real data.

Proximal Dynamics in Multiagent Network Games

We consider dynamics and protocols for agents seeking an equilibrium in a network game with proximal quadratic cost coupling. We adopt an operator-theoretic perspective to show global convergence to a network equilibrium, under the assumption of convex cost functions with proximal quadratic couplings, time-invariant and time-varying communication graph along with convex local constraints, and a time-invariant communication graph along with convex local constraints and separable convex coupling constraints. We show that proximal dynamics generalize opinion dynamics in social networks and are applicable to distributed tertiary control in power networks.

Stochastic Dual Averaging for Decentralized Online Optimization on Time-Varying Communication Graphs

We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized stochastic variants ( $\mathsf{SODA}\hbox{-}\mathsf{C}$ and $\mathsf{SODA}\hbox{-}\mathsf{PS}$ ) of Nesterov's dual averaging method $(\mathsf{DA})$ , where each agent only uses a coordinate of the noise-corrupted gradient in the dual-averaging step. We show that the expected regret bounds for both algorithms have sublinear growth of $O(\sqrt{T})$ , with the time horizon $T$ , in scenarios when the underlying communication topology is time-varying. The sublinear regret can be obtained when the stepsize is of the form $1/\sqrt{t}$ and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients, and the variance of the noisy gradients is bounded. We also provide simulation results of the proposed algorithms on sensor networks to complement our theoretical analysis.

Wardrop equilibrium on time-varying graphs

Several problems in transportation and communication networks lead to the notion of Wardrop equilibrium. There exists a large number of algorithms to find Wardrop equilibria, both centralized and distributed. This paper presents a distributed control algorithm, which converges to a Wardrop equilibrium, derived from the algorithm presented in Fischer and Vöcking (2009). The innovation lies in the fact that convergence results are obtained considering that communications occur over time-varying communication graphs, with mild assumptions on the graph connectivity in time (uniform connectivity).

Distributed Extremum Seeking in Multi-Agent Systems with Arbitrary Switching Graphs

This paper studies the problem of averaging-based extremum seeking in dynamical multi-agent systems with time-varying communication graphs. We consider a distributed consensus-optimization problem where the plants and the controllers of the agents share information via time-varying graphs, and where the cost function to be minimized corresponds to the summation of the individual response maps generated by the agents. Although the problem of averaging-based extremum seeking control in multi-agent dynamical systems with time-invariant graphs has been extensively studied, the case where the graph is time-varying remains unexplored. In this paper we address this problem by making use of recent results for generalized set-valued hybrid extremum seeking controllers, and the framework of switched differential inclusions and common Lyapunov functions. For the particular consensus-optimization problem considered in this paper, a semi-global practical stability result is established. A numerical example in the context of dynamic electricity markets illustrates the results.

Distributed continuous-time approximate projection protocols for shortest distance optimization problems

In this paper, we investigate a distributed shortest distance optimization problem for a multi-agent network to cooperatively minimize the sum of the quadratic distances from some convex sets, where each set is only associated with one agent. To deal with this optimization problem with projection uncertainties, we propose a distributed continuous-time dynamical protocol, where each agent can only obtain an approximate projection and communicate with its neighbors over a time-varying communication graph. First, we show that no matter how large the approximate angle is, system states are always bounded for any initial condition, and uniformly bounded with respect to all initial conditions if the inferior limit of the stepsize is greater than zero. Then, in both cases of nonempty and empty intersection of convex sets, we provide stepsize and approximate angle conditions to ensure the optimal convergence, respectively. Moreover, we also give some characterizations about the optimal solutions for the empty intersection case.

Leader-following control of multiple nonholonomic systems over directed communication graphs

This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours’ state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.

Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle

In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that $\pi/4$ is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations.

Convergence of random sleep algorithms for optimal consensus

In this paper, we propose a random sleep algorithm for a network to cooperatively find a point within the intersection of some convex sets, each of which is known only to a particular node. At each step, each node first chooses to project its own set or not at random by a Bernoulli decision independently. When a node has chosen to project its set, we assume that it can detect only the projection direction rather than the exact projection point, based on which the node obtains an estimate for the projection point. Then the agents update their states by averaging the estimates with their neighbors. Under directed and time-varying communication graph, sufficient and/or necessary stepsize conditions are presented for the considered algorithm converging to a consensus within the intersection set.

Robust Consensus for Continuous-Time Multiagent Dynamics

This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to $L_\infty$ and $L_1$ norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions. The results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance. The $\epsilon$-convergence time is obtained for the consensus computation on directed and $K$-bidirectional graphs.

Multi-agent Systems Reaching Optimal Consensus with Time-varying Communication Graphs

AbstractIn this paper, an optimal consensus problem for continuous-time multi-agent systems is formulated and solved with time-varying interconnection topologies. Based on a sharp connectivity assumption, the considered multi-agent network with simple nonlinear distributed control rules achieves not only a consensus, but also an optimal one by agreeing within the global optimal solution set of a sum of objective functions corresponding to multiple agents. Convergence analysis is presented, by establishing several key properties of a class of distance functions and invariant sets with the help of convex analysis and non-smooth analysis.