Biblio

This paper studies the multi-agent average consensus problem under the requirement of differential privacy of the agents' initial states against an adversary that has access to all messages. As a fundamental limitation, we first establish that a differentially private consensus algorithm cannot guarantee convergence of the agents' states to the exact average in distribution, which in turn implies the same impossibility for other stronger notions of convergence. This result motives our design of a novel differentially private Laplacian consensus algorithm in which agents linearly perturb their state-transition and message-generating functions with exponentially decaying Laplace noise. We prove that our algorithm converges almost surely to an unbiased estimate of the average of the agents' initial states, compute the exponential mean-square rate of convergence, and formally characterize its differential privacy properties. Furthermore, we also find explicit optimal values of the design parameters that minimize the variance of the algorithm's convergence point around the exact average. Various simulations illustrate our results.

We study a class of distributed convex constrained optimization problem where a group of agents aims to minimize the sum of individual objective functions while each desires to keep its function differentially private. We prove the impossibility of achieving differential privacy using strategies based on perturbing with noise the inter-agent messages when the underlying noise-free dynamics is asymptotically stable. This justifies our algorithmic solution based on the perturbation of the individual objective functions with Laplace noise within the framework of functional differential privacy. We carefully design post-processing steps that ensure the perturbed functions regain the smoothness and convexity properties of the original functions while preserving the differentially private guarantees of the functional perturbation step. This methodology allows to use any distributed coordination algorithm to solve the optimization problem on the noisy functions. Finally, we explicitly bound the magnitude of the expected distance between the perturbed and true optimizers, and characterize the privacy-accuracy trade-off. Simulations illustrate our results.

This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the inter-transmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.

This paper studies the problem of privacy-preserving average consensus in multi-agent systems. The network objective is to compute the average of the initial agent states while keeping these values differentially private against an adversary that has access to all inter-agent messages. We establish an impossibility result that shows that exact average consensus cannot be achieved by any algorithm that preserves differential privacy. This result motives our design of a differentially private discrete-time distributed algorithm that corrupts messages with Laplacian noise and is guaranteed to achieve average consensus in expectation. We examine how to optimally select the noise parameters in order to minimize the variance of the network convergence point for a desired level of privacy.

This paper addresses the problem of event-triggered control of linear time-invariant systems over time-varying rate limited communication channels, including the possibility of channel blackouts, which are intervals of time when the communication channel is unavailable for feedback. In order to design an effective event-triggered controller that operates successfully even in the presence of blackouts, we analyze the channel data capacity, which is the total maximum number of bits that could be communicated over a given time interval. We provide an efficient real-time algorithm to estimate the channel capacity for a time-slotted model of channel evolution. Equipped with this algorithm we then propose an event-triggering scheme, which using prior knowledge of the channel information, guarantees exponential stabilization at a desired convergence rate despite intermittent channel blackouts. The contributions are the notion of channel blackouts, the effective control despite their occurrence, and the analysis and quantification of the data capacity for a class of time-varying continuous-time channels.

This paper addresses the problem of asymptotic stabilization for linear time-invariant (LTI) systems using event-triggered control under finite data rate communication - both in the sense of finite precision data at each transmission and finite average data rate. Given a prescribed rate of convergence for asymptotic stability, we introduce an event-triggered control implementation that opportunistically determines the transmission instants and the finite precision data to be transmitted at each transmission. We show that our design exponentially stabilizes the origin while guaranteeing a positive lower bound on the inter-transmission times, ensuring that the number of bits transmitted at each transmission is upper bounded, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted on a previous transmission. In our technical approach, we consider both the case of instantaneous and non-instantaneous transmissions. Several simulations illustrate the results.