Ruggero Carli

Distributed Kalman filtering based on consensus strategies

In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and on the estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain for scalar systems. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we show that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some relevant scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

Communication constraints in the average consensus problem

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.

Quantized Coordination Algorithms for Rendezvous and Deployment

In this paper we study motion coordination problems for groups of robots that exchange information through a rate-constrained communication network. For one-dimensional rendezvous and deployment problems with communication path graphs, we propose an integrated control and communication scheme combining a logarithmic coder/decoder with linear coordination algorithms. We show that the closed-loop performance is comparable to that achievable in the quantization-free model: the time complexity is, asymptotically on the size of the network, unchanged, and the exponential convergence factor degrades smoothly as the quantization accuracy becomes coarser.

Optimal Synchronization for Networks of Noisy Double Integrators

In this technical note, we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are nonidentical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds are nonidentical and are subject to variations. This synchronization protocol is formally studied in its synchronous implementation. In particular, we provide a completely distributed strategy that guarantees convergence for any undirected connected communication graph and we also propose an optimal design strategy when the underlaying communication graph is known. Moreover, this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations including also randomized implementation of the proposed algorithm are presented.

Distributed Kalman filtering using consensus strategies

In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of message exchange per sampling time is small. Moreover, we prove that under certain conditions the optimal consensus matrix should be doubly stochastic. We also provide some numerical examples to clarify some of the analytical results.

A PI Consensus Controller for Networked Clocks Synchronization

Abstract In this paper we propose a novel distributed clock synchronization protocol for networks of clocks which have different initial offsets and internal clock speeds. The algorithm is based on an PI-like consensus protocol where the proportional (P) part compensates the different clock speeds while the integral part (I) eliminates the different clock offsets. This synchronization protocol is formally studied in its synchronous implementation and we provide both convergence guarantees as well optimal design using standard optimization tools when the underlaying communication graph is known. We also show how this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations are presented.

Distributed Reactive Power Feedback Control for Voltage Regulation and Loss Minimization

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed strategy, microgenerators are smart agents that can measure their phasorial voltage, share these data with the other agents on a cyber layer, and adjust the amount of reactive power injected into the grid, according to a feedback control law that descends from duality-based methods applied to the optimal reactive power flow problem. Convergence to the configuration of minimum losses and feasible voltages is proved analytically for both a synchronous and an asynchronous version of the algorithm, where agents update their state independently one from the other. Simulations are provided in order to illustrate the performance and the robustness of the algorithm, and the innovative feedback nature of such strategy is discussed.

Network Clock Synchronization Based on the Second-Order Linear Consensus Algorithm

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the linear consensus algorithm which is able to synchronize a family of identical double integrators. Since in reality the various clocks may have different drifts, the algorithm needs to be designed in such a way that it works correctly also in case of heterogeneous double integrators. We start by reviewing an unrealistic synchronous implementation of the clock synchronization algorithm, that has been recently proposed in the context of noisy double integrators. The main contribution of this paper is to propose a realistic pseudo-synchronous implementation of this algorithm. This pseudo-synchronous algorithm is shown to be a perturbation of the synchronous one and so, through arguments related to the center manifold theorem, it is proved to be locally convergent under the assumption of absence of process noise, measurement noise and propagation delays. However, through numerical simulations, the performance of this algorithm is evaluated also in the case the communication delays are not negligible, the clock drifts are time-varying and the communication channels are unreliable. Moreover, again through numerical simulations, the strategy we propose in this paper is compared with other fully distributed strategies recently proposed in the literature. While being slightly slower to reach the asymptotic synchronization, our strategy seems to significantly outperform the other strategies in terms of robustness to process and measurement noises and time-varying clock drifts.

Communication constraints in coordinated consensus problems

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems. Particular examples are systems comprised of multiple agents. When it comes to coordinately control a group of autonomous mobile agents in order to achieve a common task, communications constraints impose limits on the achievable control performance. Starting from an emerging problem, studied in the robotics and control communities, called consensus or state agreement problem, we characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the agreement. In particular we show that communication networks that exhibit particular symmetries yield slow convergence, if the amount of information exchanged does not scale with the number of agents. On the other hand, if we allow exchange of logarithmic quantized data, the control performance significantly improves with little growth of the required communication effort

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 operate safely and reliably a power grid. 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 voltage 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 the 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 network measurements.