Finite-Time Resilient Formation Control with Bounded Inputs

In this paper we consider the problem of a multi-agent system achieving a formation in the presence of misbehaving or adversarial agents. We introduce a novel continuous time resilient controller to guarantee that normally behaving agents can converge to a formation with respect to a set of leaders. The controller employs a norm-based filtering mechanism, and unlike most prior algorithms, also incorporates input bounds. In addition, the controller is shown to guarantee convergence in finite time. A sufficient condition for the controller to guarantee convergence is shown to be a graph theoretical structure which we denote as Resilient Directed Acyclic Graph (RDAG). Further, we employ our filtering mechanism on a discrete time system which is shown to have exponential convergence. Our results are demonstrated through simulations

Resilient Distributed Optimization Algorithms for Resource Allocation

Distributed algorithms provide flexibility over centralized algorithms for resource allocation problems, e.g., cyber-physical systems. However, the distributed nature of these algorithms often makes the systems susceptible to man-in-the-middle attacks, especially when messages are transmitted between price-taking agents and a central coordinator. We propose a resilient strategy for distributed algorithms under the framework of primal-dual distributed optimization. We formulate a robust optimization model that accounts for Byzantine attacks on the communication channels between agents and coordinator. We propose a resilient primal-dual algorithm using state-of-the-art robust statistics methods. The proposed algorithm is shown to converge to a neighborhood of the robust optimization model, where the neighborhood's radius is proportional to the fraction of attacked channels.Comment: 15 pages, 1 figure, accepted to CDC 201

Genuinely Distributed Byzantine Machine Learning

Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a Byzantine behavior. Several approaches have been proposed recently to tolerate Byzantine workers. Yet all require trusting a central parameter server. We initiate in this paper the study of the ``general'' Byzantine-resilient distributed machine learning problem where no individual component is trusted. We show that this problem can be solved in an asynchronous system, despite the presence of $\frac{1}{3}$ Byzantine parameter servers and $\frac{1}{3}$ Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which solves the general Byzantine-resilient distributed machine learning problem by relying on three major schemes. The first, Scatter/Gather, is a communication scheme whose goal is to bound the maximum drift among models on correct servers. The second, Distributed Median Contraction (DMC), leverages the geometric properties of the median in high dimensional spaces to bring parameters within the correct servers back close to each other, ensuring learning convergence. The third, Minimum-Diameter Averaging (MDA), is a statistically-robust gradient aggregation rule whose goal is to tolerate Byzantine workers. MDA requires loose bound on the variance of non-Byzantine gradient estimates, compared to existing alternatives (e.g., Krum). Interestingly, ByzSGD ensures Byzantine resilience without adding communication rounds (on a normal path), compared to vanilla non-Byzantine alternatives. ByzSGD requires, however, a larger number of messages which, we show, can be reduced if we assume synchrony.Comment: This is a merge of arXiv:1905.03853 and arXiv:1911.07537; arXiv:1911.07537 will be retracte

Optimal Topology Design for Disturbance Minimization in Power Grids

The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a unified framework based on $H_2$ norm is presented to analyze the robustness to ambient fluctuations. Such objectives include loss reduction, weighted consensus of phase angle deviations, oscillations in nodal frequency, and other graphical metrics. The framework is then used to study the problem of optimal topology design for robust control goals of different grids. For radial grids, the problem is shown as equivalent to the hard "optimum communication spanning tree" problem in graph theory and a combinatorial topology construction is presented with bounded approximation gap. Extended to loopy (meshed) grids, a greedy topology design algorithm is discussed. The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids. Overall, this paper analyzes topology design algorithms on a broad class of control problems in power grid by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201