arXiv subjects

Fabrizio Dabbene

Publications and source records attributed to Fabrizio Dabbene.

At least 55 records · Page 3Linked to original sources

arXiv2019

Identification of Switched Autoregressive and Switched Autoregressive Exogenous Systems from Large Noisy Data Sets

The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large values of noise for the both case of measurement noise in switched autoregressive models and process noise in switched autoregressive exogenous models. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise, which are compatible with the collected data. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.

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arXiv2019

AC optimal power flow in the presence of renewable sources and uncertain loads

The increasing penetration of renewable energy resources, paired with the fact that load can vary significantly, introduce a high degree of uncertainty in the behavior of modern power grids. Given that classical dispatch solutions are "rigid," their performance in such an uncertain environment is in general far from optimal. For this reason, in this paper, we consider AC optimal power flow (AC-OPF) problems in the presence of uncertain loads and (uncertain) renewable energy generators. The goal of AC-OPF design is to guarantee that controllable generation is dispatched at minimum cost, while satisfying constraints on generation and transmission for "almost all" realizations of the uncertainty. We propose an approach based on a randomized technique recently developed, named "scenario with certificates", which allows to tackle the problem without assuming any a-priori dependence of the voltages in the network on the uncertain generators/loads. The proposed solution can exploit the usually available probabilistic description of the uncertainty and variability, and provides solutions with a-priori probabilistic guarantees on the risk of violating the constraints on generation and transmission.

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arXiv2019

Algorithms for Optimal AC Power Flow in the Presence of Renewable Sources

This chapter presents recent solutions to the optimal power flow (OPF) problem in the presence of renewable energy sources (RES), {such} as solar photo-voltaic and wind generation. After introducing the original formulation of the problem, arising from the combination of economic dispatch and power flow, we provide a brief overview of the different solution methods proposed in the literature to solve it. Then, we explain the main difficulties arising from the increasing RES penetration, and the ensuing necessity of deriving robust solutions. Finally, we present the state-of-the-art techniques, with a special focus on recent methods we developed, based on the application on randomization-based methodologies.

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arXiv2019

Identification of Switched Autoregressive Systems from Large Noisy Data Sets

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise which are compatible with the collected data. System dynamics are estimated through expected values computation and by exploiting the strong law of large numbers. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.

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arXiv2018

Learning Political DNA in the Italian Senate

Motivated by the increasing interest of the control community towards social sciences and the study of opinion formation and belief systems, in this paper we address the problem of exploiting voting data for inferring the underlying affinity of individuals to competing ideology groups. In particular, we mine key voting records of the Italian Senate during the XVII legislature, in order to extract the hidden information about the closeness of senators to political parties, based on a parsimonious feature extraction method that selects the most relevant bills. Modeling the voting data as outcomes of a mixture of random variables and using sparse learning techniques, we cast the problem in a probabilistic framework and derive an information theoretic measure, which we refer to as Political Data-aNalytic Affinity (Political DNA). The advantages of this new affinity measure are discussed in the paper. The results of the numerical analysis on voting data unveil underlying relationships among political exponents of the Italian Senate.

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arXiv2018

Sample-based SMPC for tracking control of fixed-wing UAV: multi-scenario mapping

In this paper, a guidance and tracking control strategy for fixed-wing Unmanned Aerial Vehicle (UAV) autopilots is presented. The proposed control exploits recent results on sample-based stochastic Model Predictive Control, which allow coping in a computationally efficient way with both parametric uncertainty and additive random noise. Different application scenarios are discussed, and the implementability of the proposed approach are demonstrated through software-in-the-loop simulations. The capability of guaranteeing probabilistic robust satisfaction of the constraint specifications represents a key-feature of the proposed scheme, allowing real-time tracking of the designed trajectory with guarantees in terms of maximal deviation with respect to the planned one. The presented simulations show the effectiveness of the proposed control scheme.

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arXiv2018

Randomized opinion dynamics over networks: influence estimation from partial observations

In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which $n$ individual communicate in a gossip way. At each step, a random subset of the social actors is active and interacts with randomly chosen neighbors. The opinions evolve according to a Friedkin and Johnsen mechanism, in which the individuals updates their belief to a convex combination of their current belief, the belief of the agents they interact with, and their initial belief, or prejudice. Leveraging recent results of estimation of vector autoregressive processes, we reconstruct the social network topology and the strength of the interconnections starting from \textit{partial observations} of the interactions, thus removing one of the main drawbacks of finite horizon techniques. The effectiveness of the proposed method is shown on randomly generation networks.

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arXiv2018

An Offline-Sampling SMPC Framework with Application to Automated Space Maneuvers

In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need of real-time implementability of guidance and control strategies for automated rendezvous and proximity operations between spacecraft. The paper presents considers the validation of the proposed control algorithm on an experimental testbed, showing how it may indeed be implemented in a realistic framework. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided, and under mild assumptions, asymptotic stability in probability of the origin can be established. The offline sampling approach in the control design phase is shown to reduce the computational cost, which usually constitutes the main limit for the adoption of Stochastic Model Predictive Control schemes, especially for low-cost on-board hardware. These characteristics are demonstrated both through simulations and by means of experimental results.

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arXiv2016

Randomized and robust methods for uncertain systems using R-RoMulOC, with applications to DEMETER satellite benchmark

R-RoMulOC is a freely distributed toolbox which aims at making easily available to the users different optimization-based methods for dealing with uncertain systems. It implements both deterministic LMI-based results, that provide guaranteed performances for all values of the uncertainties, and probabilistic randomization-based approaches, that guarantee performances for all values of the uncertainties except for a subset with arbitrary small probability measure. The paper is devoted to the description of these two approaches for analysis and control design when applied to a satellite benchmark proposed by CNES, the French Space Agency. The paper also describes the modeling of the DEMETER satellite and its integration into the R-RoMulOC toolbox as a challenging test example. Design of state-feedback controllers and closed-loop performance analysis are carried out with the randomized and robust methods available in the R-RoMulOC toolbox.

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arXiv2016

Sampling methods for multistage robust convex optimization problems

In this paper, probabilistic guarantees for constraint sampling of multistage robust convex optimization problems are derived. The dynamic nature of these problems is tackled via the so-called scenario-with-certificates approach. This allows to avoid the conservative use of explicit parametrizations through decision rules, and provides a significant reduction of the sample complexity to satisfy a given level of reliability. An explicit bound on the probability of violation is also given. Numerical results dealing with a multistage inventory management problem show the efficacy of the proposed approach.

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arXiv2016

Robust linear static anti-windup with probabilistic certificates

In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed static anti-windup analysis and robust performance synthesis correspond to several optimization goals, ranging from minimization of the nonlinear input/output gain to maximization of the stability region or maximization of the domain of attraction. We also introduce a novel paradigm accounting for uncertainties in the energy of the disturbance inputs. Due to the special structure of linear static anti-windup design, wherein the design variables are decoupled from the Lyapunov certificates, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is of independent interest for similar robust synthesis problems involving parameter-dependent Lyapunov functions. We demonstrate that the scenario with certificates robust design formulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions and to remove restrictive assumptions about convexity with respect to the uncertain parameters. Subsequently, to reduce the computational cost, we present a sequential randomized algorithm for iteratively solving this problem. The obtained results are illustrated by numerical examples.

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arXiv2016

Stochastic MPC with Offline Uncertainty Sampling

For discrete-time linear systems subject to parametric uncertainty described by random variables, we develop a sampling-based Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline sampling approach in the design phase instead of online scenario generation. The paper highlights the structural difference between online and offline sampling and provides rigorous bounds on the number of samples needed to guarantee chance constraint satisfaction. The approach does not only significantly speed up the online computation, but furthermore allows to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Under mild assumptions, asymptotic stability of the origin can be established.

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arXiv2016

Constraint-Tightening and Stability in Stochastic Model Predictive Control

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence of a solution and feasibility of a suitable, a priori known candidate solution. Subsequently, a Stochastic Model Predictive Control algorithm which unifies previous results is derived, leaving the designer the option to balance an increased feasible region against guaranteed bounds on the asymptotic average performance and convergence time. Besides typical performance bounds, under mild assumptions, we prove asymptotic stability in probability of the minimal robust positively invariant set obtained by the unconstrained LQ-optimal controller. A numerical example, demonstrating the efficacy of the proposed approach in comparison with classical, recursively feasible Stochastic MPC and Robust MPC, is provided.

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arXiv2015

Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.

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arXiv2015

Simple Approximations of Semialgebraic Sets and their Applications to Control

Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes (non-convex, and even non-connected), which renders very difficult their manipulation. It is therefore of considerable importance to find simple-enough approximations of these sets, able to capture their main characteristics while maintaining a low level of complexity. For these reasons, in the past years several convex approximations, based for instance on hyperrect-angles, polytopes, or ellipsoids have been proposed. In this work, we move a step further, and propose possibly non-convex approximations , based on a small volume polynomial superlevel set of a single positive polynomial of given degree. We show how these sets can be easily approximated by minimizing the L1 norm of the polynomial over the semialgebraic set, subject to positivity constraints. Intuitively, this corresponds to the trace minimization heuristic commonly encounter in minimum volume ellipsoid problems. From a computational viewpoint, we design a hierarchy of linear matrix inequality problems to generate these approximations, and we provide theoretically rigorous convergence results, in the sense that the hierarchy of outer approximations converges in volume (or, equivalently, almost everywhere and almost uniformly) to the original set. Two main applications of the proposed approach are considered. The first one aims at reconstruction/approximation of sets from a finite number of samples. In the second one, we show how the concept of polynomial superlevel set can be used to generate samples uniformly distributed on a given semialgebraic set. The efficiency of the proposed approach is demonstrated by different numerical examples.

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arXiv2015

Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering

The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a nonlinear function.We introduce minimum-volume approximations which have the characteristic of guaranteeing a low probability of violation, i.e.,we admit for a probability that some points in the image set are not contained in the approximating set,but this probability is kept below a pre-specified threshold.In the second part of the paper, this idea is then exploited to develop a new family of randomized prediction-corrector filters.These filters represent a natural extension and rapprochement of Gaussian and set-valued filters,and bear similarities with modern tools such as particle filters.

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arXiv2014

An Improved Constraint-Tightening Approach for Stochastic MPC

The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing recursive feasibility and low computational complexity, is addressed. We propose a novel, less restrictive scheme which is based on considering stability and recursive feasibility separately. Through an explicit first step constraint we guarantee recursive feasibility. In particular we guarantee the existence of a feasible input trajectory at each time instant, but we only require that the input sequence computed at time $k$ remains feasible at time $k+1$ for most disturbances but not necessarily for all, which suffices for stability. To overcome the computational complexity of probabilistic constraints, we propose an offline constraint-tightening procedure, which can be efficiently solved via a sampling approach to the desired accuracy. The online computational complexity of the resulting Model Predictive Control (MPC) algorithm is similar to that of a nominal MPC with terminal region. A numerical example, which provides a comparison with classical, recursively feasible Stochastic MPC and Robust MPC, shows the efficacy of the proposed approach.

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arXiv2014

Scenario optimization with certificates and applications to anti-windup design

In this paper, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is motivated by the observation that in many control problems only some of the optimization variables are used in the design phase, while the other variables play the role of certificates. Examples are all those control problems that can be reformulated in terms of linear matrix inequalities involving parameter-dependent Lyapunov functions. These control problems include static anti-windup compensator design for uncertain linear systems with input saturation, where the goal is the minimization of the nonlinear gain from an exogenous input to a performance output. The main contribution of this paper is to show that randomization is a useful tool, specifically for anti-windup design, to make the overall approach less conservative compared to its robust counterpart. In particular, we demonstrate that the scenario with certificates reformulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions. Finally, to further reduce the computational cost of this one-shot approach, we present a sequential randomized algorithm for iteratively solving this problem.

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