arXiv subjects

Teodoro Alamo

Publications and source records attributed to Teodoro Alamo.

32 records · Page 2Linked to original sources

arXiv2021

Probabilistic interval predictor based on dissimilarity functions

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.

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arXiv2021

Implementation of model predictive control for tracking in embedded systems using a sparse extended ADMM algorithm

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard MPC formulations, such as an increased domain of attraction and guaranteed recursive feasibility even in the event of a sudden reference change. However, this comes at the expense of the addition of a small amount of decision variables to the MPC's optimization problem that complicates the structure of its matrices. We propose a sparse optimization algorithm, based on an extension of the alternating direction method of multipliers, that exploits the structure of this particular MPC formulation. We describe the controller formulation and detail how its structure is exploited by means of the aforementioned optimization algorithm. We show closed-loop simulations comparing the proposed solver against other solvers and approaches from the literature.

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arXiv2021

Probabilistic performance validation of deep learning-based robust NMPC controllers

Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low-cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We propose a probabilistic validation technique based on finite families, combined with the idea of generalized maximum and constraint backoff to enable statistically valid conclusions related to general performance indicators. The potential of the proposed approach is demonstrated with simulation results of an uncertain nonlinear system.

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arXiv2021

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.

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arXiv2021

Data-Driven Methods for Present and Future Pandemics: Monitoring, Modelling and Managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

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arXiv2021

Real-time implementation of MPC for tracking in embedded systems: Application to a two-wheeled inverted pendulum

This article presents the real-time implementation of the model predictive control for tracking formulation to control a two-wheeled inverted pendulum robot. This formulation offers several advantages over standard MPC formulations at the expense of the addition of a small number of decision variables, which complicates the inner structure of the matrices of the optimization problem. We implement a sparse solver, based on an extension of the alternating direction method of multipliers, in the system's embedded hardware. The results indicate that the solver is suitable for controlling a real system with sample times in the range of milliseconds using current, readily-available hardware.

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arXiv2021

Harmonic based model predictive control for set-point tracking

This paper presents a novel model predictive control (MPC) formulation for set-point tracking. Stabilizing predictive controllers based on terminal ingredients may exhibit stability and feasibility issues in the event of a reference change for small to moderate prediction horizons. In the MPC for tracking formulation, these issues are solved by the addition of an artificial equilibrium point as a new decision variable, providing a significantly enlarged domain of attraction and guaranteeing recursive feasibility for any reference change. However, it may suffer from performance issues if the prediction horizon is not large enough. This paper presents an extension of this formulation where a harmonic artificial reference is used in place of the equilibrium point. The proposed formulation achieves even greater domains of attraction and can significantly outperform other MPC formulations when the prediction horizon is small. We prove the asymptotic stability and recursive feasibility of the proposed controller, as well as provide guidelines for the design of its main ingredients. Finally, we highlight its advantages with a case study of a ball and plate system.

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arXiv2021

Chance constrained sets approximation: A probabilistic scaling approach -- EXTENDED VERSION

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then allows to rescale these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problem in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.

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arXiv2020

Data-Driven Methods to Monitor, Model, Forecast and Control Covid-19 Pandemic: Leveraging Data Science, Epidemiology and Control Theory

This document analyzes the role of data-driven methodologies in Covid-19 pandemic. We provide a SWOT analysis and a roadmap that goes from the access to data sources to the final decision-making step. We aim to review the available methodologies while anticipating the difficulties and challenges in the development of data-driven strategies to combat the Covid-19 pandemic. A 3M-analysis is presented: Monitoring, Modelling and Making decisions. The focus is on the potential of well-known datadriven schemes to address different challenges raised by the pandemic: i) monitoring and forecasting the spread of the epidemic; (ii) assessing the effectiveness of government decisions; (iii) making timely decisions. Each step of the roadmap is detailed through a review of consolidated theoretical results and their potential application in the Covid-19 context. When possible, we provide examples of their applications on past or present epidemics. We do not provide an exhaustive enumeration of methodologies, algorithms and applications. We do try to serve as a bridge between different disciplines required to provide a holistic approach to the epidemic: data science, epidemiology, controltheory, etc. That is, we highlight effective data-driven methodologies that have been shown to be successful in other contexts and that have potential application in the different steps of the proposed roadmap. To make this document more functional and adapted to the specifics of each discipline, we encourage researchers and practitioners to provide feedback. We will update this document regularly.

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arXiv2020

Computationally efficient stochastic MPC: a probabilistic scaling approach

In recent years, the increasing interest in Stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. To design candidate simple approximating sets, which approximate the shape of the probabilistic set, we introduce two possibilities: i) fixed-complexity polytopes, and ii) $\ell_p$-norm based sets. Once the candidate approximating set is obtained, it is scaled around its center so to enforce the expected probabilistic guarantees. The resulting scaled set is then exploited to enforce constraints in the classical SMPC framework. The computational gain obtained with the proposed approach with respect to the scenario one is demonstrated via simulations, where the objective is the control of a fixed-wing UAV performing a monitoring mission over a sloped vineyard.

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arXiv2020

Open Data Resources for Fighting COVID-19

We provide an insight into the open data resources pertinent to the study of the spread of Covid-19 pandemic and its control. We identify the variables required to analyze fundamental aspects like seasonal behaviour, regional mortality rates, and effectiveness of government measures. Open data resources, along with data-driven methodologies, provide many opportunities to improve the response of the different administrations to the virus. We describe the present limitations and difficulties encountered in most of the open-data resources. To facilitate the access to the main open-data portals and resources, we identify the most relevant institutions, at a world scale, providing Covid-19 information and/or auxiliary variables (demographics, mobility, etc.). We also describe several open resources to access Covid-19 data-sets at a country-wide level (i.e. China, Italy, Spain, France, Germany, U.S., etc.). In an attempt to facilitate the rapid response to the study of the seasonal behaviour of Covid-19, we enumerate the main open resources in terms of weather and climate variables. CONCO-Team: The authors of this paper belong to the CONtrol COvid-19 Team, which is composed of different researches from universities of Spain, Italy, France, Germany, United Kingdom and Argentina. The main goal of CONCO-Team is to develop data-driven methods for the better understanding and control of the pandemic.

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arXiv2020

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given.

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arXiv2020

A probabilistic validation approach for penalty function design in Stochastic Model Predictive Control

In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We revisit the rather classical approach based on penalty functions, with the aim of designing a control scheme that meets some given probabilistic specifications. The main difference with previous approaches is that we do not recur to the notion of probabilistic recursive feasibility, and hence we do not consider separately the unfeasible case. In particular, two probabilistic design problems are envisioned. The first randomization problem aims to design \textit{offline} the constraint set tightening, following an approach inherited from tube-based MPC. For the second probabilistic scheme, a specific probabilistic validation approach is exploited for tuning the penalty parameter, to be selected \textit{offline} among a finite-family of possible values. The simple algorithm here proposed allows designing a \textit{single} controller, always guaranteeing feasibility of the online optimization problem. The proposed method is shown to be more computationally tractable than previous schemes. This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence. The efficacy of the proposed approach is demonstrated with a numerical example.

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arXiv2019

Restart FISTA with Global Linear Convergence

Fast Iterative Shrinking-Threshold Algorithm (FISTA) is a popular fast gradient descent method (FGM) in the field of large scale convex optimization problems. However, it can exhibit undesirable periodic oscillatory behaviour in some applications that slows its convergence. Restart schemes seek to improve the convergence of FGM algorithms by suppressing the oscillatory behaviour. Recently, a restart scheme for FGM has been proposed that provides linear convergence for non strongly convex optimization problems that satisfy a quadratic functional growth condition. However, the proposed algorithm requires prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. In this paper we present a restart scheme for FISTA algorithm, with global linear convergence, for non strongly convex optimization problems that satisfy the quadratic growth condition without requiring the aforementioned values. We present some numerical simulations that suggest that the proposed approach outperforms other restart FISTA schemes.

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