# Biblio

This paper studies the real-time implementation of distributed controllers on networked cyberphysical systems. We build on the strengths of event- and self-triggered control to synthesize a unified approach, termed team-triggered, where agents make promises to one another about their future states and are responsible for warning each other if they later decide to break them. The information provided by these promises allows individual agents to autonomously schedule information requests in the future and sets the basis for maintaining desired levels of performance at lower implementation cost. We establish provably correct guarantees for the distributed strategies that result from the proposed approach and examine their robustness against delays, packet drops, and communication noise. The results are illustrated in simulations of a multi-agent formation control problem.

This paper studies a distributed event-triggered communication and control strategy that solves the multi-agent average consensus problem. The proposed strategy does not rely on the continuous or periodic availability of information to an agent about the state of its neighbors, but instead prescribes isolated event times where both communication and controller updates occur. In addition, all parameters required for its implementation can be locally determined by the agents. We show that the resulting network executions are guaranteed to converge to the average of the initial agents' states, establish that events cannot be triggered an infinite number of times in any finite time period (i.e., absence of Zeno behavior), and characterize the exponential rate of convergence. We also provide sufficient conditions for convergence in scenarios with time-varying communication topologies. Simulations illustrate our results.

This chapter describes triggered control approaches for the coordination of networked cyber-physical systems. Given the coverage of the other chapters of this book, our focus is on self-triggered control and a novel approach we term team-triggered control.

This paper proposes a novel distributed event-triggered algorithmic solution to the multi-agent average consensus problem for networks whose communication topology is described by weight-balanced, strongly connected digraphs. The proposed event-triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors. In addition, it does not require the agents to have a priori knowledge of any global parameter to execute the algorithm. We show that, under the proposed law, events cannot be triggered an infinite number of times in any finite period (i.e., no Zeno behavior), and that the resulting network executions provably converge to the average of the initial agents' states exponentially fast. We also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching. Finally, we also propose and analyze a periodic implementation of our algorithm where the relevant triggering functions do not need to be evaluated continuously. Simulations illustrate our results and provide comparisons with other existing algorithms.

This paper introduces a novel team-triggered algorithmic solution for a distributed optimal deployment problem involving a group of mobile sensors. Distributed self-triggered algorithms relieve the requirement of synchronous periodic communication among agents by providing opportunistic criteria for when communication should occur. However, these criteria are often conservative since worst-case scenarios must always be considered to ensure the monotonic evolution of a relevant objective function. Here we introduce a team-triggered algorithm that builds on the idea of `promises' among agents, allowing them to operate with better information about their neighbors when they are not communicating, over a dynamically changing graph. We analyze the correctness of the proposed strategy and establish the same convergence guarantees as a coordination algorithm that assumes perfect information at all times. The technical approach relies on tools from set-valued stability analysis, computational geometry, and event-based systems. Simulations illustrate our 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.

it IFAC Workshop on Distributed Estimation and Control in Networked Systems}, Philadelphia, PA

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.

To appear

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 consider linear time-invariant networks with unknown interaction topology where only a subset of the nodes, termed manifest, can be directly controlled and observed. The remaining nodes are termed latent and their number is also unknown. Our goal is to identify the transfer function of the manifest subnetwork and determine whether interactions between manifest nodes are direct or mediated by latent nodes. We show that, if there are no inputs to the latent nodes, then the manifest transfer function can be approximated arbitrarily well in the $H_ınfty}$-norm sense by the transfer function of an auto-regressive model. Motivated by this result, we present a least-squares estimation method to construct the auto-regressive model from measured data. We establish that the least-squares matrix estimate converges in probability to the matrix sequence defining the desired auto-regressive model as the length of data and the model order grow. We also show that the least-squares auto-regressive method guarantees an arbitrarily small $H_ınfty$-norm error in the approximation of the manifest transfer function, exponentially decaying once the model order exceeds a certain threshold. Finally, we show that when the latent subnetwork is acyclic, the proposed method achieves perfect identification of the manifest transfer function above a specific model order as the length of the data increases. Various examples illustrate our results.

To appear

As multi-agent systems become ubiquitous, guaranteeing safety in these systems grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet safety constraints by guaranteeing forward invariance of a set. However, a single barrier function can rarely satisfy all safety aspects of a system, so there remains a need to address the degree to which multiple barrier functions may be composed through Boolean logic. Utilizing max and min operators represents one such method to accomplish Boolean composition for barrier functions. As such, the main contribution of this work extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. To validate these results, a Boolean compositional barrier function is deployed onto a team of mobile robots.

Accepted for publication

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.

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 develops methods to efficiently compute the set of disturbances on a power network that do not tip the frequency of each bus and the power flow in each transmission line beyond their respective bounds. For a linearized AC power network model, we propose a sampling method to provide superset and subset approximations with a desired accuracy of the set of feasible disturbances. We also introduce an error metric to measure the approximation gap and design an algorithm that is able to reduce its value without impacting the complexity of the resulting set approximations. Simulations on the IEEE 118-bus power network illustrate our results.

Controllability metrics based on the controllability Gramian have been widely used in linear control theory, and have recently seen renewed interests in the study of complex networks of dynamical systems. For example, the minimum eigenvalue and the trace of the Gramian are related to the worst-case and average minimum input energy, respectively, to steer the state from the origin to a target state. This paper explores similar questions that remain unanswered for bilinear control systems. In the context of complex networks, bilinear systems characterize scenarios where an actuator not only can affect the state of a node, but also can affect the strength of the interconnections among some neighboring nodes. Under the assumption that the infinity norm of the input is bounded by some function of the network dynamic matrices, we derive a lower bound on the minimum input energy to steer the state of a bilinear network from the origin to any reachable target state based on the generalized reachability Gramian of bilinear systems. We also provide a lower bound on the average minimum input energy over all target states on the unit hypersphere in the state space. Based on the reachability metrics proposed, we propose an actuator selection method that provides guaranteed minimum average input energy. Finally, we show that the optimal actuator selection can be found by maximizing a supermodular function under cardinality constraints.

In this paper, we present a fundamental limitation of disturbance attenuation in discrete-time single-input single-output (SISO) feedback systems when the controller has delayed side information about the external disturbance. Specifically, we assume that the delayed information about the disturbance is transmitted to the controller across a finite Shannon-capacity communication channel. Our main result is a lower bound on the log sensitivity integral in terms of open-loop unstable poles of the plant and the characteristics of the channel, similar to the classical Bode integral formula. A comparison with prior work that considers the effect of preview side information of the disturbance at the controller indicates that delayed side information and preview side information play different roles in disturbance attenuation. In particular, we show that for open-loop stable systems, delayed side information cannot reduce the log integral of the sensitivity function whereas it can for open-loop unstable systems, even when the disturbance is a white stochastic process.