The purpose of this work is to give a contribution to the understanding of the COVID-19 contagion in Italy. To this end, we developed a modified Susceptible-Infected-Recovered-Deceased (SIRD) model ...for the contagion, and we used official data of the pandemic for identifying the parameters of this model. Our approach features two main non-standard aspects. The first one is that model parameters can be time-varying, allowing us to capture possible changes of the epidemic behavior, due for example to containment measures enforced by authorities or modifications of the epidemic characteristics and to the effect of advanced antiviral treatments. The time-varying parameters are written as linear combinations of basis functions and are then inferred from data using sparse identification techniques. The second non-standard aspect resides in the fact that we consider as model parameters also the initial number of susceptible individuals, as well as the proportionality factor relating the detected number of positives with the actual (and unknown) number of infected individuals. Identifying the model parameters amounts to a non-convex identification problem that we solve by means of a nested approach, consisting in a one-dimensional grid search in the outer loop, with a Lasso optimization problem in the inner step.
This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive ...disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to nonconvex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this work is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a priori assigned probability p , while the system's state reaches the target set either asymptotically, or in finite time with probability at least p . The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.
We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation ...function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem.
This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex ...constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.
In this article, we propose an efficient multiclass classification scheme based on sparse centroids classifiers. The proposed strategy exhibits linear complexity with respect to both the number of ...classes and the cardinality of the feature space. The classifier we introduce is based on binary space partitioning, performed by a decision tree where the assignation law at each node is defined via a sparse centroid classifier. We apply the presented strategy to the time series classification problem, showing by experimental evidence that it achieves performance comparable to that of state-of-the-art methods, but with a significantly lower classification time. The proposed technique can be an effective option in resource-constrained environments where the classification time and the computational cost are critical or, in scenarios, where real-time classification is necessary.
An algorithm is proposed to determine output feedback policies that solve finite-horizon linear-quadratic (LQ) optimal control problems without requiring knowledge of the system dynamical matrices. ...To reach this goal, the <inline-formula> <tex-math notation="LaTeX">Q </tex-math></inline-formula>-factors arising from finite-horizon LQ problems are first characterized in the state feedback case. It is then shown how they can be parameterized as functions of the input-output vectors. A procedure is then proposed for estimating these functions from input/output data and using these estimates for computing the optimal control via the measured inputs and outputs.
A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic ...nature and that the system’s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios’) are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example.
The COVID‐19 pandemic has led to the unprecedented challenge of devising massive vaccination rollouts, toward slowing down and eventually extinguishing the diffusion of the virus. The two‐dose ...vaccination procedure, speed requirements, and the scarcity of doses, suitable spaces, and personnel, make the optimal design of such rollouts a complex problem. Mathematical modeling, which has already proved to be determinant in the early phases of the pandemic, can again be a powerful tool to assist public health authorities in optimally planning the vaccination rollout. Here, we propose a novel epidemic model tailored to COVID‐19, which includes the effect of nonpharmaceutical interventions and a concurrent two‐dose vaccination campaign. Then, we leverage nonlinear model predictive control to devise optimal scheduling of first and second doses, accounting both for the healthcare needs and for the socio‐economic costs associated with the epidemics. We calibrate our model to the 2021 COVID‐19 vaccination campaign in Italy. Specifically, once identified the epidemic parameters from officially reported data, we numerically assess the effectiveness of the obtained optimal vaccination rollouts for the two most used vaccines. Determining the optimal vaccination strategy is nontrivial, as it depends on the efficacy and duration of the first‐dose partial immunization, whereby the prioritization of first doses and the delay of second doses may be effective for vaccines with sufficiently strong first‐dose immunization. Our model and optimization approach provide a flexible tool that can be adopted to help devise the current COVID‐19 vaccination campaign, and increase preparedness for future epidemics.
A novel approach based on probability and randomization has emerged to synergize with the standard deterministic methods for control of systems with uncertainty. The main objective of this paper is ...to provide a broad perspective on this area of research known as “probabilistic robust control”, and to address in a systematic manner recent advances. The focal point is on design methods, based on the interplay between uncertainty randomization and convex optimization, and on the illustration of specific control applications.
Sparse ℓ1- and ℓ2-Center Classifiers Calafiore, Giuseppe C.; Fracastoro, Giulia
IEEE transaction on neural networks and learning systems,
2022-March, 20220301, Letnik:
33, Številka:
3
Journal Article
In this article, we discuss two novel sparse versions of the classical nearest-centroid classifier. The proposed sparse classifiers are based on <inline-formula> <tex-math notation="LaTeX">\ell _{1} ...</tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\ell _{2} </tex-math></inline-formula> distance criteria, respectively, and perform simultaneous feature selection and classification, by detecting the features that are most relevant for the classification purpose. We formally prove that the training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) at a linear computational cost. Especially, the proposed sparse classifiers are trained in <inline-formula> <tex-math notation="LaTeX">O(mn)+O(m\log k) </tex-math></inline-formula> operations, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the number of samples, <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> is the total number of features, and <inline-formula> <tex-math notation="LaTeX">k \leq m </tex-math></inline-formula> is the number of features to be retained in the classifier. Furthermore, the complexity of testing and classifying a new sample is simply <inline-formula> <tex-math notation="LaTeX">O(k) </tex-math></inline-formula> for both methods. The proposed models can be employed either as stand-alone sparse classifiers or fast feature-selection techniques for prefiltering the features to be later fed to other types of classifiers (e.g., SVMs). The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection and classification techniques while having a substantially lower computational cost.
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