arXiv subjects

Valentina Breschi

Publications and source records attributed to Valentina Breschi.

45 records · Page 3Linked to original sources

arXiv2023

Model predictive control with dynamic move blocking

Model Predictive Control (MPC) has proven to be a powerful tool for the control of systems with constraints. Nonetheless, in many applications, a major challenge arises, that is finding the optimal solution within a single sampling instant to apply a receding-horizon policy. In such cases, many suboptimal solutions have been proposed, among which the possibility of "blocking" some moves a-priori. In this paper, we propose a dynamic approach to move blocking, to exploit the solution already available at the previous iteration, and we show not only that such an approach preserves asymptotic stability, but also that the decrease of performance with respect to the ideal solution can be theoretically bounded.

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arXiv2023

META-SMGO-$Δ$: similarity as a prior in black-box optimization

When solving global optimization problems in practice, one often ends up repeatedly solving problems that are similar to each others. By providing a rigorous definition of similarity, in this work we propose to incorporate the META-learning rationale into SMGO-$Δ$, a global optimization approach recently proposed in the literature, to exploit priors obtained from similar past experience to efficiently solve new (similar) problems. Through a benchmark numerical example we show the practical benefits of our META-extension of the baseline algorithm, while providing theoretical bounds on its performance.

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arXiv2022

Data-driven predictive control in a stochastic setting: a unified framework

Data-driven predictive control (DDPC) has been recently proposed as an effective alternative to traditional model-predictive control (MPC) for its unique features of being time-efficient and unbiased with respect to the oracle solution. Nonetheless, it has also been observed that noise may strongly jeopardize the final closed-loop performance since it affects both the data-based system representation and the control update computed from the online measurements. Recent studies have shown that regularization is potentially a successful tool to counteract the effect of noise. At the same time, regularization requires the tuning of a set of penalty terms, whose choice might be practically difficult without closed-loop experiments. In this paper, by means of subspace identification tools, we pursue a three-fold goal: $(i)$ we set up a unified framework for the existing regularized data-driven predictive control schemes for stochastic systems; $(ii)$ we introduce $γ$-DDPC, an efficient two-stage scheme that splits the optimization problem into two parts: fitting the initial conditions and optimizing the future performance, while guaranteeing constraint satisfaction; $(iii)$ we discuss the role of regularization for data-driven predictive control, providing new insight on $when$ and $how$ it should be applied. A benchmark numerical case study finally illustrates the performance of $γ$-DDPC, showing how controller design can be simplified in terms of tuning effort and computational complexity when benefiting from the insights coming from the subspace identification realm.

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arXiv2022

Data-driven design of explicit predictive controllers using model-based priors

In this paper, we propose a data-driven approach to derive explicit predictive control laws, without requiring any intermediate identification step. The keystone of the presented strategy is the exploitation of available priors on the control law, coming from model-based analysis. Specifically, by leveraging on the knowledge that the optimal predictive controller is expressed as a piecewise affine (PWA) law, we directly optimize the parameters of such an analytical controller from data, instead of running an on-line optimization problem. As the proposed method allows us to automatically retrieve also a model of the closed-loop system, we show that we can apply model-based techniques to perform a stability check prior to the controller deployment. The effectiveness of the proposed strategy is assessed on two benchmark simulation examples, through which we also discuss the use of regularization and its combination with averaging techniques to handle the presence of noise.

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arXiv2021

On the design of regularized explicit predictive controllers from input-output data

On the wave of recent advances in data-driven predictive control, we present an explicit predictive controller that can be constructed from a batch of input/output data only. The proposed explicit law is build upon a regularized implicit data-driven predictive control problem, so as to guarantee the uniqueness of the explicit predictive controller. As a side benefit, the use of regularization is shown to improve the capability of the explicit law in coping with noise on the data. The effectiveness of the retrieved explicit law and the repercussions of regularization on noise handling are analyzed on two benchmark simulation case studies, showing the potential of the proposed regularized explicit controller.

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arXiv2021

Direct data-driven model-reference control with Lyapunov stability guarantees

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block, which are shaped from data to reproduce the desired behavior in closed-loop. By focusing on the case where the reference model and the plant share the same order, we propose an optimal design procedure with Lyapunov stability guarantees, tailored to handle state measurements with additive noise. Two simulation examples are finally illustrated to show the potential of the proposed strategy as compared to the state of the art approaches.

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arXiv2021

Learning explicit predictive controllers: theory and applications

In this paper, we deal with data-driven predictive control of linear time-invariant (LTI) systems. Specifically, we show for the first time how explicit predictive laws can be learnt directly from data, without needing to identify the system to control. To this aim, we resort to the Willems' fundamental lemma and we derive the explicit formulas by suitably elaborating the constrained optimization problem under investigation. The resulting optimal controller turns out to be a piecewise affine system coinciding with the solution of the original model-based problem in case of noiseless data. Such an equivalence is proven to hold asymptotically also in presence of measurement noise, thus making the proposed method a computationally efficient (but model-free) alternative to the state of the art predictive controls. The above statements are further supported by numerical simulations on three benchmark examples.

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arXiv2020

Shrinkage Strategies for Structure Selection and Identification of Piecewise Affine Models

We propose two optimization-based heuristics for structure selection and identification of PieceWise Affine (PWA) models with exogenous inputs. The first method determines the number of affine sub-models assuming known model order of the sub-models, while the second approach estimates the model order for a given number of affine sub-models. Both approaches rely on the use of regularization-based shrinking strategies, that are exploited within a coordinate-descent algorithm. This allows us to estimate the structure of the PWA models along with its model parameters. Starting from an over-parameterized model, the key idea is to alternate between an identification step and structure refinement, based on the sparse estimates of the model parameters. The performance of the presented strategies is assessed over two benchmark examples.

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arXiv2017

Cloud-aided collaborative estimation by ADMM-RLS algorithms for connected vehicle prognostics

As the connectivity of consumer devices is rapidly growing and cloud computing technologies are becoming more widespread, cloud-aided techniques for parameter estimation can be designed to exploit the theoretically unlimited storage memory and computational power of the cloud, while relying on information provided by multiple sources. With the ultimate goal of developing monitoring and diagnostic strategies, this report focuses on the design of a Recursive Least-Squares (RLS) based estimator for identification over a group of devices connected to the cloud. The proposed approach, that relies on Node-to-Cloud-to-Node (N2C2N) transmissions, is designed so that: (i) estimates of the unknown parameters are computed locally and (ii) the local estimates are refined on the cloud. The proposed approach requires minimal changes to local (pre-existing) RLS estimators.

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