Distributed robust optimization for multi-agent systems with guaranteed finite-time convergence

A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded uncertainty under a uniformly strongly connected network. Firstly, a distributed lower bounding procedure is developed, which is based on an outer iterative approximation of the DRCO through the discretization of the compact uncertainty set into a finite number of points. Secondly, a distributed upper bounding procedure is proposed, which is based on iteratively approximating the DRCO by restricting the constraints right-hand side with a proper positive parameter and enforcing the compact uncertainty set at finitely many points. The lower and upper bounds of the global optimal objective for the DRCO are obtained from these two procedures. Thirdly, two distributed termination methods are proposed to make all agents stop updating simultaneously by exploring whether the gap between the upper and the lower bounds reaches a certain accuracy. Fourthly, it is proved that all the agents finite-time converge to a feasible consensus solution that satisfies global optimality within a certain accuracy. Finally, a numerical case study is included to illustrate the effectiveness of the distributed algorithm.Comment: Submitted for publication in Automatic

Distributed Estimation and Control of Algebraic Connectivity over Random Graphs

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph. Using results from stochastic approximation theory, we prove that the proposed method converges almost surely (a.s.) to the desired value of connectivity even in the presence of imperfect communication scenarios. The estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network, in order to maximize the network connectivity in the presence of realistic Medium Access Control (MAC) protocols or simply to drive the connectivity toward a desired target value. Numerical results corroborate our theoretical findings, thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.Comment: To appear in IEEE Transactions on Signal Processin

Distributed consensus of discrete time-varying linear multi-agent systems with event-triggered intermittent control

The consensus problem of discrete time-varying linear multi-agent systems (MASs) is studied in this paper. First, an event-triggered intermittent control (ETIC) protocol is designed, aided by a class of auxiliary functions. Under this protocol, some sufficient conditions for all agents to achieve consensus are established by constructing an error dynamical system and applying the Lyapunov function. Second, in order to further reduce the communication burden, an improved event triggered intermittent control (I-ETIC) strategy is presented, along with corresponding convergence analysis. Notably, the difference between the two control protocols lies in the fact that the former protocol only determines when to control or not based on the trigger conditions, while the latter, building upon this, designs new event trigger conditions for the update of the controller during the control stage. Finally, two numerical simulation examples are provided to demonstrate the effectiveness of the theoretical results

Distributed Calculation of Edge-Disjoint Spanning Trees for Robustifying Distributed Algorithms Against Man-in-the-Middle Attacks

In this paper we provide a distributed methodology to allow a network of agents, tasked to execute a distributed algorithm, to overcome Man-in-the-middle attacks that aim at steering the result of the algorithm towards inconsistent values or dangerous configurations. We want the agents to be able to restore the correct result of the algorithm in spite of the attacks. To this end, we provide a distributed algorithm to let the set of agents, interconnected by an undirected network topology, construct several $edge-disjoint spanning trees$ by assigning a label to their incident edges. The ultimate objective is to use these spanning trees to run multiple instances of the same distributed algorithm in parallel, in order to be able to detect Man-in-the- middle attacks or other faulty or malicious link behavior (e.g., when the instances yield different results) and to restore the correct result (when the majority of instances is unaffected). The proposed algorithm is lightweight and asynchronous, and is based on iterated depth-first visits on the graph. We complement the paper with a thorough analysis of the performance of the proposed algorithms. IEEE Journal Articl