Christoforos N. Hadjicostis

Distributed Function Calculation via Linear Iterative Strategies in the Presence of Malicious Agents

Given a network of interconnected nodes, each with its own value (such as a measurement, position, vote, or other data), we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of the node values, despite the actions of malicious nodes in the network. Our scheme assumes a broadcast model of communication (where all nodes transmit the same value to all of their neighbors) and utilizes a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We consider a node to be malicious or faulty if, instead of following the predefined linear strategy, it updates its value arbitrarily at each time-step (perhaps conspiring with other malicious nodes in the process). We show that the topology of the network completely characterizes the resilience of linear iterative strategies to this kind of malicious behavior. First, when the network contains 2f or fewer vertex-disjoint paths from some node xj to another node xi , we provide an explicit strategy for f malicious nodes to follow in order to prevent node xi from receiving any information about xjs value. Next, if node xi has at least 2f+1 vertex-disjoint paths from every other (non-neighboring) node, we show that xi is guaranteed to be able to calculate any arbitrary function of all node values when the number of malicious nodes is f or less. Furthermore, we show that this function can be calculated after running the linear iteration for a finite number of time-steps (upper bounded by the number of nodes in the network) with almost any set of weights (i.e., for all weights except for a set of measure zero).

Feedback control utilizing packet dropping network links

The increasing availability of network connectivity has prompted the study of computer-based control methodologies that are implemented centrally or distributively using existing network infrastructure as the communications backbone. Recent work has looked at the stability of networked control systems (i.e., control systems in which feedback loops are closed through networks) and focused on performance guarantees under networked. induced delays and varying data packet rates. In this work, we extend these ideas in a probabilistic setting by modeling a packet dropping network as an erasure channel and by developing bounded variance stabilization schemes.

Distributed function calculation and consensus using linear iterative strategies

Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that this approach can be viewed as a linear dynamical system, with dynamics that are given by the weight matrix of the linear iteration, and with outputs for each node that are captured by the set of values that are available to that node at each time-step. In connected networks with time-invariant topologies, we use observability theory to show that after running the linear iteration for a finite number of time-steps with almost any choice of weight matrix, each node obtains enough information to calculate any arbitrary function of the initial node values. The problem of distributed consensus via linear iterations, where all nodes in the network calculate the same function, is treated as a special case of our approach. In particular, our scheme allows nodes in connected networks with time-invariant topologies to reach consensus on any arbitrary function of the initial node values in a finite number of steps for almost any choice of weight matrix.

A Two-Stage Distributed Architecture for Voltage Control in Power Distribution Systems

In this paper, we propose an architecture for voltage regulation in distribution networks that relies on controlling reactive power injections provided by distributed energy resources (DERs). A local controller on each bus of the network monitors the bus voltage and, whenever there is a voltage violation, it uses locally available information to estimate the amount of reactive power that needs to be injected into the bus in order to correct the violation. If the DERs connected to the bus can collectively provide the reactive power estimated by the local controller, they are instructed to do so. Otherwise, the local controller initiates a request for additional reactive power support from other controllers at neighboring buses through a distributed algorithm that relies on a local exchange of information among neighboring controllers. We show that the proposed architecture helps prevent voltage violations and shapes the voltage profile in radial distribution networks, even in the presence of considerable penetration of variable generation and loads. We present several case studies involving 8-, 13-, and 123-bus distribution systems to illustrate the operation of the architecture.

Finite-Time Distributed Consensus in Graphs with Time-Invariant Topologies

We present a method for achieving consensus in distributed systems in a finite number of time-steps. Our scheme involves a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. If D denotes the degree of the minimal polynomial of the weight matrix associated with the linear iteration, we show that each node can immediately calculate the consensus value as a linear combination of its own past values over at most D time-steps. We also show that each node can determine the coefficients for this linear combination in a decentralized manner. The proposed scheme has the potential to significantly reduce the time and communication required to reach consensus in distributed systems.

Failure Identification in Smart Grids Based on Petri Net Modeling

This paper presents a method to identify and localize failures in smart grids. The method is based on a carefully designed Petri net (PN) that captures the modeling details of the protection system of the distribution network and allows the detection/identification of failures in data transmission and faults in the distribution network by means of simple matrix operations. The design of the PN model is carried out by carefully composing multiple PN models for single protection systems: Such an approach allows the identification of the faults despite possible strong penetration of distributed generation. In order to verify the method, two case studies are discussed. The results highlight that the proposed method can remove a lot of the complexity of the associated data analysis despite the possible presence of malfunctioning protection systems and misinformation due to communication and other errors.

Decentralized optimal dispatch of distributed energy resources

In this paper, we address the problem of optimally dispatching a set of distributed energy resources (DERs) without relying on a centralized decision maker. We consider a scenario where each DER can provide a certain resource (e.g., active or reactive power) at some cost (namely, quadratic in the amount of resource), with the additional constraint that the amount of resource that each DER provides is upper and lower bounded by its capacity limits. We propose a low-complexity iterative algorithm for DER optimal dispatch that relies, at each iteration, on simple computations using local information acquired through exchange of information with neighboring DERs. We show convergence of the proposed algorithm to the (unique) optimal solution of the DER dispatch problem. We also describe a wireless testbed we developed for testing the performance of the algorithms.

Algebraic approaches for fault identification in discrete-event systems

In this note, we develop algebraic approaches for fault identification in discrete-event systems that are described by Petri nets. We consider faults in both Petri net transitions and places, and assume that system events are not directly observable but that the system state is periodically observable. The particular methodology we explore incorporates redundancy into a given Petri net in a way that enables fault detection and identification to be performed efficiently using algebraic decoding techniques. The guiding principle in adding redundancy is to keep the number of additional Petri net places small while retaining enough information to be able to systematically detect and identify faults when the system state becomes available. The end result is a redundant Petri net embedding that uses 2k additional places and enables the simultaneous identification of 2k-1 transition faults and k place faults (that may occur at various instants during the operation of the Petri net). The proposed identification scheme has worst-case complexity of O(k(m+n)) operations where m and n are respectively the number of transitions and places in the given Petri net.

Coordination and Control of Distributed Energy Resources for Provision of Ancillary Services

This paper discusses the utilization of distributed energy resources on the distribution side of the power grid to provide a number of ancillary services. While the individual capability of these resources to provide grid support might be very small, their presence in large numbers in many distribution networks implies that, under proper control, they can collectively become an asset for providing ancillary services. An example is the power electronics interface of a photovoltaic array mounted in a residential building roof. While its primary function is to control active power flow, when properly controlled, it can also be used to provide reactive power. This paper develops and analyzes distributed control strategies to enable the utilization of these distributed resources for provision of grid support services. We provide a careful analysis of the applicability capabilities and limitations of each of these strategies. Several simulation examples are provided to illustrate the proposed approaches.

Notions of security and opacity in discrete event systems

In this paper, we follow a state-based approach to extend the notion of opacity in computer security to discrete event systems. A system is (S, P)-opaque if the evolution of its true state through a set of secret states S remains opaque to an observer who is observing activity in the system through the projection map P. In other words, based on observations through the mapping P, the observer is never certain that the current state of the system is within the set of secret states S. We also introduce the stronger notion of (S,P, K)-opacity which requires opacity to remain true for K observations following the departure of the systems state from the set S. We show that the state-based definition of opacity enables the use of observer constructions for verification purposes. In particular, the verification of (S,P, K)-opacity is accomplished via an observer with K-delay which is constructed to capture state estimates with K-delay. These are the estimates of the state of the system K observations ago and are consistent with all observations (including the last K observations). We also analyze the properties and complexity of the observer with K- delay.