arXiv subjects

Francesco Bullo

Publications and source records attributed to Francesco Bullo.

At least 145 records · Page 8Linked to original sources

arXiv2013

Mixed Human-Robot Team Surveillance

We study the mixed human-robot team design in a system theoretic setting using the context of a surveillance mission. The three key coupled components of a mixed team design are (i) policies for the human operator, (ii) policies to account for erroneous human decisions, and (iii) policies to control the automaton. In this paper, we survey elements of human decision-making, including evidence aggregation, situational awareness, fatigue, and memory effects. We bring together the models for these elements in human decision-making to develop a single coherent model for human decision-making in a two-alternative choice task. We utilize the developed model to design efficient attention allocation policies for the human operator. We propose an anomaly detection algorithm that utilizes potentially erroneous decision by the operator to ascertain an anomalous region among the set of regions surveilled. Finally, we propose a stochastic vehicle routing policy that surveils an anomalous region with high probability. Our mixed team design relies on the certainty-equivalent receding-horizon control framework.

math.OC↗

arXiv2013

Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids

Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it maintains the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes.

math.OC↗

arXiv2013

Consensus Networks over Finite Fields

This work studies consensus strategies for networks of agents with limited memory, computation, and communication capabilities. We assume that agents can process only values from a finite alphabet, and we adopt the framework of finite fields, where the alphabet consists of the integers {0,...,p-1}, for some prime number p, and operations are performed modulo p. Thus, we define a new class of consensus dynamics, which can be exploited in certain applications such as pose estimation in capacity and memory constrained sensor networks. For consensus networks over finite fields, we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. We show that consensus networks over finite fields converge in finite time, a feature that can be hardly achieved over the field of real numbers. For the design of finite-field consensus networks, we propose a general design method, with high computational complexity, and a network composition rule to generate large consensus networks from smaller components. Finally, we discuss the application of finite-field consensus networks to distributed averaging and pose estimation in sensor networks.

eess.SY↗

arXiv2012

Stochastic Surveillance Strategies for Spatial Quickest Detection

We design persistent surveillance strategies for the quickest detection of anomalies taking place in an environment of interest. From a set of predefined regions in the environment, a team of autonomous vehicles collects noisy observations, which a control center processes. The overall objective is to minimize detection delay while maintaining the false alarm rate below a desired threshold. We present joint (i) anomaly detection algorithms for the control center and (ii) vehicle routing policies. For the control center, we propose parallel cumulative sum (CUSUM) algorithms (one for each region) to detect anomalies from noisy observations. For the vehicles, we propose a stochastic routing policy, in which the regions to be visited are chosen according to a probability vector. We study stationary routing policy (the probability vector is constant) as well as adaptive routing policies (the probability vector varies in time as a function of the likelihood of regional anomalies). In the context of stationary policies, we design a performance metric and minimize it to design an efficient stationary routing policy. Our adaptive policy improves upon the stationary counterpart by adaptively increasing the selection probability of regions with high likelihood of anomaly. Finally, we show the effectiveness of the proposed algorithms through numerical simulations and a persistent surveillance experiment.

cs.RO↗

arXiv2012

Exploring Synchronization in Complex Oscillator Networks

The emergence of synchronization in a network of coupled oscillators is a pervasive topic in various scientific disciplines ranging from biology, physics, and chemistry to social networks and engineering applications. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among the oscillators. These two ingredients give rise to a rich dynamic behavior that keeps on fascinating the scientific community. In this article, we present a tutorial introduction to coupled oscillator networks, we review the vast literature on theory and applications, and we present a collection of different synchronization notions, conditions, and analysis approaches. We focus on the canonical phase oscillator models occurring in countless real-world synchronization phenomena, and present their rich phenomenology. We review a set of applications relevant to control scientists. We explore different approaches to phase and frequency synchronization, and we present a collection of synchronization conditions and performance estimates. For all results we present self-contained proofs that illustrate a sample of different analysis methods in a tutorial style.

math.OC↗

arXiv2012

Synchronization in Complex Oscillator Networks and Smart Grids

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among them. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here we present a novel, concise, and closed-form condition for synchronization of the fully nonlinear, non-equilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters, or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters, they are statistically correct for almost all networks, and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks such as electric power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex networks scenarios and in smart grid applications.

math.OC↗

arXiv2012

Distributed Random Convex Programming via Constraints Consensus

This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas, especially in the context of decision under uncertainty, see [2],[3]. We here consider a setup in which instances of the random constraints (the scenario) are not held by a single centralized processing unit, but are distributed among different nodes of a network. Each node "sees" only a small subset of the constraints, and may communicate with neighbors. The objective is to make all nodes converge to the same solution as the centralized RCP problem. To this end, we develop two distributed algorithms that are variants of the constraints consensus algorithm [4],[5]: the active constraints consensus (ACC) algorithm, and the vertex constraints consensus (VCC) algorithm. We show that the ACC algorithm computes the overall optimal solution in finite time, and with almost surely bounded communication at each iteration. The VCC algorithm is instead tailored for the special case in which the constraint functions are convex also w.r.t. the uncertain parameters, and it computes the solution in a number of iterations bounded by the diameter of the communication graph. We further devise a variant of the VCC algorithm, namely quantized vertex constraints consensus (qVCC), to cope with the case in which communication bandwidth among processors is bounded. We discuss several applications of the proposed distributed techniques, including estimation, classification, and random model predictive control, and we present a numerical analysis of the performance of the proposed methods. As a complementary numerical result, we show that the parallel computation of the scenario solution using ACC algorithm significantly outperforms its centralized equivalent.

math.OC↗

arXiv2012

Eulerian Opinion Dynamics with Bounded Confidence and Exogenous Input

The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with non-Bayesian "rule of thumb" methods. This paper focuses on an Eulerian bounded-confidence model of opinion dynamics with a potential time-varying input. First, we prove some properties of this system's dynamics with time-varying input. Second, we derive a simple sufficient condition for opinion consensus, and prove the convergence of the population's distribution with no input to a sum of Dirac Delta functions. Finally, we define an input's attraction range, and for a normally distributed input and uniformly distributed initial population, we conjecture that the length of attraction range is an increasing affine function of population's confidence bound and input's variance.

math.DS↗

arXiv2012

Attack Detection and Identification in Cyber-Physical Systems -- Part I: Models and Fundamental Limitations

Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malignant attacks, and specific analysis tools as well as monitoring mechanisms need to be developed to enforce system security and reliability. This paper proposes a unified framework to analyze the resilience of cyber-physical systems against attacks cast by an omniscient adversary. We model cyber-physical systems as linear descriptor systems, and attacks as exogenous unknown inputs. Despite its simplicity, our model captures various real-world cyber-physical systems, and it includes and generalizes many prototypical attacks, including stealth, (dynamic) false-data injection and replay attacks. First, we characterize fundamental limitations of static, dynamic, and active monitors for attack detection and identification. Second, we provide constructive algebraic conditions to cast undetectable and unidentifiable attacks. Third, by using the system interconnection structure, we describe graph-theoretic conditions for the existence of undetectable and unidentifiable attacks. Finally, we validate our findings through some illustrative examples with different cyber-physical systems, such as a municipal water supply network and two electrical power grids.

math.OC↗

arXiv2012

Attack Detection and Identification in Cyber-Physical Systems -- Part II: Centralized and Distributed Monitor Design

Cyber-physical systems integrate computation, communication, and physical capabilities to interact with the physical world and humans. Besides failures of components, cyber-physical systems are prone to malicious attacks so that specific analysis tools and monitoring mechanisms need to be developed to enforce system security and reliability. This paper builds upon the results presented in our companion paper [1] and proposes centralized and distributed monitors for attack detection and identification. First, we design optimal centralized attack detection and identification monitors. Optimality refers to the ability of detecting (respectively identifying) every detectable (respectively identifiable) attack. Second, we design an optimal distributed attack detection filter based upon a waveform relaxation technique. Third, we show that the attack identification problem is computationally hard, and we design a sub-optimal distributed attack identification procedure with performance guarantees. Finally, we illustrate the robustness of our monitors to system noise and unmodeled dynamics through a simulation study.

math.OC↗

arXiv2011

Discrete Partitioning and Coverage Control for Gossiping Robots

We propose distributed algorithms to automatically deploy a team of mobile robots to partition and provide coverage of a non-convex environment. To handle arbitrary non-convex environments, we represent them as graphs. Our partitioning and coverage algorithm requires only short-range, unreliable pairwise "gossip" communication. The algorithm has two components: (1) a motion protocol to ensure that neighboring robots communicate at least sporadically, and (2) a pairwise partitioning rule to update territory ownership when two robots communicate. By studying an appropriate dynamical system on the space of partitions of the graph vertices, we prove that territory ownership converges to a pairwise-optimal partition in finite time. This new equilibrium set represents improved performance over common Lloyd-type algorithms. Additionally, we detail how our algorithm scales well for large teams in large environments and how the computation can run in anytime with limited resources. Finally, we report on large-scale simulations in complex environments and hardware experiments using the Player/Stage robot control system.

cs.RO↗

arXiv2011

On cooperative patrolling: optimal trajectories, complexity analysis, and approximation algorithms

The subject of this work is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties, and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region, and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory, and we propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.

math.CO↗

arXiv2011

Distributed Estimation via Iterative Projections with Application to Power Network Monitoring

This work presents a distributed method for control centers to monitor the operating condition of a power network, i.e., to estimate the network state, and to ultimately determine the occurrence of threatening situations. State estimation has been recognized to be a fundamental task for network control centers to ensure correct and safe functionalities of power grids. We consider (static) state estimation problems, in which the state vector consists of the voltage magnitude and angle at all network buses. We consider the state to be linearly related to network measurements, which include power flows, current injections, and voltages phasors at some buses. We admit the presence of several cooperating control centers, and we design two distributed methods for them to compute the minimum variance estimate of the state given the network measurements. The two distributed methods rely on different modes of cooperation among control centers: in the first method an incremental mode of cooperation is used, whereas, in the second method, a diffusive interaction is implemented. Our procedures, which require each control center to know only the measurements and structure of a subpart of the whole network, are computationally efficient and scalable with respect to the network dimension, provided that the number of control centers also increases with the network cardinality. Additionally, a finite-memory approximation of our diffusive algorithm is proposed, and its accuracy is characterized. Finally, our estimation methods are exploited to develop a distributed algorithm to detect corrupted data among the network measurements.

math.OC↗

arXiv2011

Synchronization and Transient Stability in Power Networks and Non-Uniform Kuramoto Oscillators

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model. Here, non-uniform Kuramoto oscillators are characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying system parameters and initial conditions.

math.OC↗

arXiv2011

On the Critical Coupling for Kuramoto Oscillators

The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features four contributions. First, we characterize and distinguish the different notions of synchronization used throughout the literature and formally introduce the concept of phase cohesiveness as an analysis tool and performance index for synchronization. Second, we review the vast literature providing necessary, sufficient, implicit, and explicit estimates of the critical coupling strength for finite and infinite-dimensional, and for first and second-order Kuramoto models. Third, we present the first explicit necessary and sufficient condition on the critical coupling to achieve synchronization in the finite-dimensional Kuramoto model for an arbitrary distribution of the natural frequencies. The multiplicative gap in the synchronization condition yields a practical stability result determining the admissible initial and the guaranteed ultimate phase cohesiveness as well as the guaranteed asymptotic magnitude of the order parameter. Fourth and finally, we extend our analysis to multi-rate Kuramoto models consisting of second-order Kuramoto oscillators with inertia and viscous damping together with first-order Kuramoto oscillators with multiple time constants. We prove that the multi-rate Kuramoto model is locally topologically conjugate to a first-order Kuramoto model with scaled natural frequencies, and we present necessary and sufficient conditions for almost global phase synchronization and local frequency synchronization. Interestingly, these conditions do not depend on the inertiae which contradicts prior observations on the role of inertiae in synchronization of second-order Kuramoto models.

math.DS↗

arXiv2011

Consensus Computation in Unreliable Networks: A System Theoretic Approach

This work addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure.

math.OC↗

arXiv2011

Flow Cytometry Based State Aggregation of a Stochastic Model of Protein Expression

In this article, we introduce the new approach "fluorescence grid based aggregation (FGBA)" to justify a dynamical model of protein expression using experimental fluorescence histograms. In this approach, first, we describe the dynamics of the gene-protein system by a chemical master equation (CME), while the protein production rates are unknown. Then, we aggregate the states of the CME into unknown group sizes. We show that these unknown values can be replaced by the data from the experimental fluorescence histograms. Consequently, final probability distributions correspond to the experimental fluorescence histograms.

math.PR↗

arXiv2011

On Opinion Dynamics in Heterogeneous Networks

This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion; and each agent updates its opinion by averaging all other opinions that are within some given confidence range. The confidence ranges are distinct for each agent. This heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. We conjecture that any trajectory of this model eventually converges to a steady state under fixed topology. To establish this conjecture, we derive two novel sufficient conditions: both conditions guarantee convergence and constant topology for infinite time, while one condition also guarantees monotonicity of the convergence. In the evolution under fixed topology for infinite time, we define leader groups that determine the followers' rate and direction of convergence.

math-ph↗