Publications Lists     [ all BibTeX ]  

In this paper, two methods to reduce the complexity of multi-parametric programming modelpredictive control are proposed. We show that the standard multi-parametric programming problem can be modified by approximating the quadratic programming constraints. For a certain controlsequence, only constraints on the first element is considered, while constraints on future elements are ignored or approximated to a simple saturation function. Both the number of critical regions and the computation time are proven to be reduced. Geometric interpretations is given and complexityanalysis is conducted. The result is tested on an illustrating example to show its effectiveness.

In this paper, we consider the problem of designing a distributed strategy to estimate the channel parameters for a generic Wireless Sensor-Actor Network. To this aim, we present a distributed least-square algorithm that complies with the constraint of transmitting only integer data through the wireless communication, which often characterizes Wireless Sensor-Actor Network embedded architectures. In this respect, we propose a quantized consensus strategy that mitigates the effects of the rounding operations applied to the wireless exchanged floating data. Moreover, the approach is based on a symmetric random gossip strategy, making it suitable for the actual deployment in multiagent networks. Finally, the effectiveness of the proposed algorithm and of its implementation as an open-source application is assessed and the employment of the procedure is illustrated through the application to radio-frequency localization experiments in a real world testbed.

The knowledge of the size of a network, i.e.\ of the number of nodes composing it, is important for maintenance and organization purposes. In networks where the identity of the nodes or is not unique or cannot be disclosed for privacy reasons, the size-estimation problem is particularly challenging since the exchanged messages cannot be uniquely associated with a specific node. In this work, we propose a totally distributed anonymous strategy based on statistical inference concepts. In our approach, each node starts generating a vector of independent random numbers from a known distribution. Then nodes compute a common function via some distributed consensus algorithms, and finally they compute the Maximum Likelihood (ML) estimate of the network size exploiting opportune statistical inferences. In this work we study the performance that can be obtained following this computational scheme when the consensus strategy is either the maximum or the average. In the max-consensus scenario, when data come from absolutely continuous distributions, we provide a complete characterization of the ML estimator. In particular, we show that the squared estimation error decreases as $1/M$, where $M$ is the amount of random numbers locally generated by each node, independently of the chosen probability distribution. Differently, in the average-consensus scenario, we show that if the locally generated data are independent Bernoulli trials, then the probability for the ML estimator to return a wrong answer decreases exponentially in $M$. Finally, we provide a discussion as how the numerical errors may affect the estimators performance under different scenarios.

The property of single prediction predictive control in the form of dynamic matrix control is studied within internal model control framework. The sensitivity function and integral squared error are used as performance evaluation criteria in the frequency and time domain respectively, to quantitativelyanalyze single prediction strategy, especially on controller with the prediction and control horizon P = M = 1. We present the correlation between system performance and model mismatch in this case. The performance limitation for tracking unit step signal is obtained through derivation and simulation.

The request for very accurate 3D reconstruction in several applications is leading to the development of very large motion capture systems. A good synchronization of all the cameras in the system is of fundamental importance to guarantee the effectiveness of the 3D reconstruction.
In this work, first, an approximation of the reconstruction error variance taking into account of synchronization errors is derived. Then, a Kalman filter approach is considered to estimate the cameras synchronization errors. The estimated delays can be used to compensate the synchronization error effect on the reconstruction of target positions. The results obtained in some simulations suggest that the proposed strategy allows to obtain a significant reduction of the 3D reconstruction error.

We consider the distributed unconstrained minimization of separable convex costfunctions, where the global cost is given by the sum of several local and private costs, eachassociated to a specific agent of a given communication network. We specifically address anasynchronous distributed optimization technique called Newton-Raphson consensus. Besidehaving low computational complexity, low communication requirements and being interpretableas a distributed Newton-Raphson algorithm, the technique has also the beneficial properties ofrequiring very little coordination and naturally support time-varying topologies. In this workwe analytically prove that under some assumptions it shows local convergence properties, andcorroborate this result by means of numerical simulations.

The paper considers the problem of reconstructing a probability density function from a finite set of samples independently drawn from it. We cast the problem in a Bayesian setting where the unknown density is modeled via a nonlinear transformation of a Bayesian prior placed on a Reproducing Kernel Hilbert Space. The learning of the unknown density function is then formulated as a minimum variance estimation problem. Since this requires the solution of analytically intractable integrals, we solve this problem by proposing a novel algorithm based on the Markov chain Monte Carlo framework. Simulations are used to corroborate the goodness of the new approach.

To maintain and organize distributed systems it is necessary to have a certain degree of knowledge of their status like the number of cooperating agents. The estimation of this number, usually referred as the network size, can pose challenging questions when agents' identification information cannot be disclosed, since the exchanged information cannot be associated to who originated it. In this paper we propose a totally distributed network size estimation strategy based on statistical inference concepts that can be applied under anonymity constraints. The scheme is based on the following paradigm: agents locally generate some Bernoulli trials, then distributedly compute averages of these generated data, finally locally compute the Maximum Likelihood estimate of the network size exploiting its probabilistic dependencies with the previously computed averages. In this work we study the statistical properties of this estimation strategy, and show how the probability of returning a wrong evaluation decreases exponentially in the number of locally generated trials. Finally, we discuss how practical implementation issues may affect the estimator, and show that there exists a neat phase transition between insensitivity to numerical errors and uselessness of the results.

We consider the problem of commanding the electronic power interfaces of the microgenerators in a low voltage microgrid for the task of optimal reactive power compensation. In this work, we analyze the convergence of the strategy proposed by Tenti et al. in 2012. The proof of convergence gives some additional insight on the behavior of the algorithm and allows the characterization of its rate of convergence as a function of the microgrid parameters.

In this paper we address the problem of exploitingthe distributed energy resources (DER) available in a smartmicro-grid to minimize the power distribution losses via optimalreactive power compensation. Due to their typically smallsize, the amount of reactive power provided by each micro-generator is subject to tight saturation constraints. As aconsequence, it might be impossible to achieve convergence tothe global optimum based on algorithms that rely on short-range, gossip-type communication. We therefore propose arandomized multi-hop protocol that guarantees convergence ofthe distributed optimization algorithm also when only short-range communications are possible, at the expense of someadditional communication overhead.

In this paper we focus on collaborative wireless sensor networks, where agents are randomly distributed over a region of interest and collaborate to achieve a common estimation goal. In particular, we introduce two consensus-based distributed linear estimators. The first one is designed for a Bayesian scenario, where an unknown common finite-dimensional parameter vector has to be reconstructed,  while the second one  regards the nonparametric reconstruction of an unknown function sampled at different locations by the sensors. Both of the algorithms are characterized in terms of the trade-off between estimation performance, communication, computation and memory complexity. In the finite-dimensional setting, we derive mild sufficient conditions which ensure that distributed estimator performs better than the local optimal ones in terms of estimation error variance. In the nonparametric setting, we introduce an on-line algorithm that allows the agents both to compute the function estimate with small computational, communication and data storage efforts, and to quantify its distance from the centralized estimate given by a Regularization Network, one of the most powerful regularized kernel methods. These results are obtained by deriving bounds on the estimation error that provide insights on how the uncertainty inherent in a sensor network, such as imperfect knowledge on the number of agents and the measurement models used by the sensors, can degrade the performance of the estimation process. Numerical experiments are included to support the theoretical findings.

We consider the problem of estimating the size of dynamic anonymous networks, motivated by network maintenance. The proposed algorithm is based on max-consensus information exchange protocols, and extends a previous algorithm for static anonymous networks. A regularization term is accounting for a-priori assumptions on the smoothness of the estimate, and we specifically consider quadratic regularization terms since they lead to closed-form solutions and intuitive design laws. We derive an explicit estimation scheme for a particular peer-to-peer service network, starting from its statistical model. To validate the accuracy of the algorithm, we perform numerical experiments and show how the algorithm can be implemented using finite precision arithmetics as well as small communication burdens.

In this paper we study the problem of real-time optimal distributed partitioning for perimeter patrolling in the context of multi-camera networks for surveillance. The objective is to partition a given segment into non-overlapping sub-segments, each assigned to a different camera to patrol. Each camera has both physical mobility range and limited speed, and it must patrol its assigned sub-segment by sweeping it back and forth at maximum speed. Here we first review the solution for the centralized optimal partitioning. Then we propose two different distributed control strategies to determine the extremes of the optimal patrolling areas of each camera. Both these strategies require only local communication with the neighboring cameras but adopt different communication schemes, respectively, symmetric gossip and asynchronous asymmetric broadcast. The first scheme is shown to be provably convergent to the optimal solution. Some theoretical insights are provided also for the second scheme whose effectiveness is validated through numerical simulations.

In this work we consider a multidimensional distributed optimization technique that is suitable for multiagents systems subject to limited communication connectivity. In particular, we consider a convex unconstrained additive problem, i.e. a case where the global convex unconstrained multidimensional cost function is given by the sum of local cost functions available only to the specific owning agents. We show how, by exploiting the separation of time-scales principle,the multidimensional consensus-based strategy approximates a Newton-Raphson descent algorithm. We propose two alternative optimization strategies corresponding to approximations of the main procedure. These approximations introduce tradeoffs between the required communication bandwidth and the convergence speed/accuracy of the results. We provide analytical proofs of convergence and numerical simulations supporting the intuitions developed through the paper.

Geometric triangulation is at the basis of the estimation of the 3D position of a target from a set of camera measurements. The problem of optimal estimation (minimizing the L2 norm) of the target position from multi-view perspective projective measurements is typically a hard problem to solve. In literature there are different types of algorithms for this purpose, based for example on the exhaustive check of all the local minima of a proper eigenvalue problem [2], or branch- and-bound techniques [3]. However, such methods typically become unfeasible for real time applications when the number of cameras and targets become large, calling for the definition of approximate procedures to solve the reconstruction problem.
In the first part of this paper, linear (fast) algorithms, computing an approximate solution to such problems, are described and compared in simulation. Then, in the second part, a Gaussian approximation to the measurement error is used to express the reconstruction error’s standard deviation as a function of the position of the reconstructed point. An upper bound, valid over all the target domain, to this expression is obtained for a case of interest. Such upper bound allows to compute a number of cameras sufficient to obtain a user defined level of position estimation accuracy.

We consider the convergence rates of two peculiar2 convex optimization strategies in the context of multi agent3 systems, namely the Newton-Raphson consensus optimization4 and a distributed Gradient-Descent opportunely derived from5 the first. To allow analytical derivations, the convergence6 analyses are performed under the simplificative assumption of7 quadratic local cost functions. In this framework we derive8 sufficient conditions which guarantee the convergence of the9 algorithms. From these conditions we then obtain closed form10 expressions that can be used to tune the parameters for11 maximizing the rate of convergence. Despite these formulae12 have been derived under quadratic local cost functions13 assumptions, they can be used as rules-of-thumb for tuning14 the parameters of the algorithms in general situations.

We considered the problem of minimizing reactive power flows in a smart microgrid. First we modeled this problem as a linearly constrained quadratic optimization, in which the decision variables are the amount of reactive power that compensators inject into the network. Then, we designed a distributed algorithm in which agents are clustered into overlapping subsets, according to a given communication graph that allows them to coordinate and to exchange information. At each time, one subset is triggered, and agents belonging to it update their states in order to minimize the reactive power flows on the grid. We showed that, by sensing the network at their points of connection, agents can perform this minimization with just the data that they can gather from the other agents belonging to the subset. We characterized convergence of this algorithm in term of conditions on the subsets and on the randomized triggering sequence. Moreover, we studied the rate of convergence, obtaining also a convenient upper bound. We finally analyzed the rate of convergence for some specic topologies of the grid and for some choices of the agents communication topologies.

We consider the scenario of a low voltage microgrid populated by a number of distributed microgenerators. We focus on the problem of obtaining a dynamic model that describes the input-output relation between complex power commands sent to the microgenerator inverters and the voltage measurements across the network. Such a model is intended as a necessary tool in the design of distributed and centralized control algorithms for the provision of ancillary services in the power distribution grid. Because this model is to be used for the design of such algorithms, we look for an analytical derivation instead of a simulative tool. The proposed model is linear and explicitly contains the network parameters and topology. Simulation shows how the proposed model approximates well the behavior of the original nonlinear system.

We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems.

We also show how this model provides the tools for a distributed approach, in which agents have a partial knowledge of the problem parameters and state, and can only perform local measurements.

Then, we design a randomized, gossip-like optimization algorithm, providing conditions for convergence together with an analytical characterization of the convergence speed. The analysis shows that the best performance can be achieved when we command cooperation among agents that are neighbors in the smart microgrid topology. Numerical simulations are included to validate the proposed model and to confirm the analytical results about the performance of the proposed algorithm.

In this work we study the problem of unconstrained distributed optimization in the context of multi-agents systems subject to limited communication connectivity. In particular we focus on the minimization of a sum of convex cost functions, where each component of the global function is available only to a specific agent and can thus be seen as a private local cost. The agents need to cooperate to compute the minimizer of the sum of all costs. We propose a consensus-like strategy to estimate a Newton-Raphson descending update for the local estimates of the global minimizer at each agent. In particular, the algorithm is based on the separation of time-scales principle and it is proved to converge to the global minimizer if a specific parameter that tunes the rate of convergence is chosen sufficiently small. We also provide numerical simulations and compare them with alternative distributed optimization strategies like the Alternating Direction Method of Multipliers and the Distributed Subgradient Method.

We analyze the problem of data sets reduction

for support vector classification. The work is also motivated

by distributed problems, where sensors collect binary mea-

surements at different locations moving inside an environment

that needs to be divided into a collection of regions labeled in

two different ways. The scope is to let each agent retain and

exchange only those measurements that are mostly informative

for the collective reconstruction of the decision boundary. For

the case of separable classes, we provide the exact conditions

and an efficient algorithm to determine if an element in the

training set can become a support vector when new data arrive.

The analysis is then extended to the non-separable case deriving

a sufficient discardability condition and a general data selection

scheme for classification. Numerical experiments relative to the

distributed problem show that the proposed procedure allows

the agents to exchange a small amount of the collected data to

obtain a highly predictive decision boundary.

In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading ofthe Radio Strength Signal Indicator (RSSI) due to uncalibrated sensors. Then we show how the computation of the optimal wireless channels parameters, which are the solution of a global least-square optimization problem, can be obtained with a consensus-based algorithm. The proposed algorithms are general algorithms for sensor calibration and distributed least-square parameter identification,and do not require any knowledge on the global topology of the network nor the total number of nodes. Finally, we apply these algorithms to experimental data collected from an indoor wireless sensor network.

We consider a distributed system of N agents, on which we define a quadratic optimization problem subject to a linear equality constraint. We assume that the nodes can estimate the gradient of the cost function by measuring the steady state response of the system. Even if the cost function cannot be decoupled into individual terms for the agents, and the linear constraint involves the whole system state, we are able to design a distributed, gradient-driven, algorithm, for the solution of the optimization problem. This algorithm belongs to the class of quasi-Newton methods and requires minimal knowledge of the system to behave fairly well. We proved finite time convergence of the algorithm in its centralized version, and we designed its distributed implementation in the case in which a communication graph is given. In this latter case, the tool of average consensus results to be fundamental for the distribution of the algorithm. As a testbed for the proposed method, we consider the problem of optimal distributed reactive power compensation in smart microgrids.

The distributed estimation of the number of active sensors in a network can be important for estimation and organization purposes. We propose a design methodology based on the following paradigm: some locally randomly generated values are exchanged among the various sensors and thus modified by known consensus-based strategies. Statistical analysis of the a-consensus values allows estimation of the number of participant sensors. The main features of this approach are: algorithms are completely distributed, since they do not require leader election steps; sensors are not requested to transmit authenticative information (for example identificative numbers or similar data), and thus the strategy can be implemented whenever privacy problems arise. After a rigorous formulation of the paradigma we analyze some practical examples, fully characterize them from a statistical point of view, and finally we provide some general theoretical results and asymptotic analyses.

Wind energy is a random, uncontrollable, and highly variable source of energy, which will lead to serious challenges to grid integration at deep penetration levels. It is clear that the current extra-market approach to supporting wind integration (ex: California's Participating Intermittent Renewable Program (PIRP)) will not scale with an increase in installed wind capacity. At these deep penetration levels, forecasting, storage, demand response, and novel market mechanisms all become necessary ingredients to realize the promise of wind energy. In this paper, we examine the interplay between energy storage and market strategies to address the difficulties of wind integration. We attempt to answer the basic question: when faced with uncertainty in future market prices and wind power, how should a scheduling coordinator for a wind power plant exploit the ability to store energy so as to maximize revenue when scheduling wind power in a sequence of nested markets (day-ahead, hour-ahead, and real-time)? The problem is framed as a nonstandard chance-constrained model predictive control (MPC) problem. In formalizing the problem, we develop idealized models for electricity markets, wind energy revenue, energy storage, and the physical wind process. As chance constraints are, in general, nonlinear and difficult to handle in optimization problems, we suggest several stochastic models for wind that lead to tractable computations. This approach provides a contrast to scenario-based techniques for dealing with uncertainty in stochastic optimization problems.

In this paper a distributed clock synchronization algorithm is proposed. The algorithm requires gossip asynchronous communication between the nodes of the network, and because of its proportional-integral (PI) structure it is able to compensate both initial offsets and different clock speeds. Convergence of the algorithm is proved and analysed with respect to the controller parameter, while scalability issues are addressed by simulations.

In this paper we analyze the problem of estimating a function from different noisy data sets collected by spatially distributed sensors and subject to unknown temporal shifts. We propose a novel approach based on non-parametric Gaussian regression and reproducing kernel Hilbert space theory that exploit compact and accurate representations of function estimates. As a first result, suitable minimization of inner products in reproducing kernel Hilbert spaces is used to obtain a novel time delay estimation technique when attention is restricted only to two signals. Then, we derive both a centralized and a distributed estimator to simultaneously identify the unknown function and delays for a generic number of networked sensors subject to a restricted communication graph. Numerical simulations are used to test the effectiveness of the proposed approaches.