Anna Scampicchio

Last Name

Scampicchio

First Name

Anna

ORCID

0000-0002-2238-6341

Organisational unit

09563 - Zeilinger, Melanie / Zeilinger, Melanie

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Publications 1 - 10 of 12

Stable and robust LQR design via scenario approach
Scampicchio, Anna; Aravkin, Aleksandr; Pillonetto, Gianluigi (2021)
Automatica
Linear Quadratic Regulator (LQR) design is one of the most classical optimal control problems, whose well-known solution is an input sequence expressed as a state-feedback. In this work, finite-horizon and discrete-time LQR is solved under stability constraints and uncertain system dynamics. The resulting feedback controller balances cost value and closed-loop stability. Robustness of the solution is modeled using the scenario approach, without requiring any probabilistic description of the uncertainty in the system matrices. The new methods are tested and compared on the Leslie growth model, where we control population size while minimizing a suitable finite-horizon cost function.
A Markov Chain Monte Carlo approach for Pseudo-Input selection in Sparse Gaussian Processes
Scampicchio, Anna; Chandrasekaran, Sanjay; Zeilinger, Melanie (2023)
IFAC-PapersOnLine ~ 22nd IFAC World Congress
The effectiveness of non-parametric methods for regression comes at the price of high computational complexity. In fact, these methods scale as O(N3), where N is the number of available data points. One possible option to address this issue consists in introducing a set of fictitious (pseudo-) inputs of size M ≪ N such that the computational effort is reduced to O(M2N). To estimate hyper-parameters and pseudo-inputs, a non-convex optimization problem needs to be solved. As opposed to the conventional gradient-based approach used in the literature, this paper proposes a stochastic scheme leveraging Markov Chain Monte Carlo methods. Numerical comparisons show that the latter returns a more efficient set of pseudo-inputs, leading to a superior performance in terms of mean squared error.
Bayesian multi-task learning using finite-dimensional models: A comparative study
Arcari, Elena; Scampicchio, Anna; Carron, Andrea; et al. (2021)
2021 60th IEEE Conference on Decision and Control (CDC)
Simultaneous estimation of related tasks has been widely studied in the statistics and machine learning literature, and its effectiveness has been proven in many contexts such as econometrics and bioinformatics. However, state-of-the-art approaches leveraging Gaussian processes are encumbered by high computational costs that hinder their applicability to model-based and adaptive control design. In this paper, we address this issue by approximating non-parametric multi-task models by means of trigonometric basis functions. We estimate the involved parameters in a Bayesian framework using several deterministic and stochastic approaches, and highlight their advantages within an extensive comparative study. Overall, the proposed setup is able to suitably leverage task relatedness to outperform single-task methods, especially when single datasets are small.
Bayesian Multi-Task Learning MPC for Robotic Mobile Manipulation
Arcari, Elena; Minniti, Maria Vittoria; Scampicchio, Anna; et al. (2023)
IEEE Robotics and Automation Letters
Mobile manipulation in robotics is challenging due to the need to solve many diverse tasks, such as opening a door or picking-and-placing an object. Typically, a basic first-principles system description of the robot is available, thus motivating the use of model-based controllers. However, the robot dynamics and its interaction with an object are affected by uncertainty, limiting the controller's performance. To tackle this problem, we propose a Bayesian multi-task learning model that uses trigonometric basis functions to identify the error in the dynamics. In this way, data from different but related tasks can be leveraged to provide a descriptive error model that can be efficiently updated online for new, unseen tasks. We combine this learning scheme with a model predictive controller, and extensively test the effectiveness of the proposed approach, including comparisons with available baseline controllers. We present simulation tests with a ball-balancing robot, and door opening hardware experiments with a quadrupedal manipulator.
An update-and-design scheme for scenario-based LQR synthesis
Scampicchio, Anna; Iannelli, Andrea (2022)
2022 American Control Conference (ACC)
This paper deals with a finite-horizon Linear Quadratic Regulator (LQR) design for unknown linear time-invariant plants. The objective is to provide a flexible approach which gives robustness guarantees on the closed-loop cost, while avoiding an overly conservative design. The proposed method consists of computing the posterior distribution of the system's matrices, and using samples from the desired credible region to solve a convex scenario-based program; the result is an open-loop solution of the robust LQR that is then expressed as state-feedback and is used to obtain a new system trajectory. By updating the system estimates as more data are gathered, the algorithm ensures controllers the same robustness guarantees while having to cope with less dispersion in the samples.
Error Analysis of Regularized Trigonometric Linear Regression With Unbounded Sampling: A Statistical Learning Viewpoint
Scampicchio, Anna; Arcari, Elena; Zeilinger, Melanie N. (2023)
IEEE Control Systems Letters
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques based on sparse spectrum Gaussian processes, we focus on models given by regularized trigonometric linear regression. This letter provides an analysis of the performance of such an estimation set-up within the statistical learning framework. In particular, we derive a novel bound for the sample error in finite-dimensional spaces, accounting for noise with potentially unbounded support. Next, we study the approximation error and discuss the bias-variance trade-off as a function of the regularization parameter by combining the two bounds.
On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics
Compagnoni, Enea Monzio; Scampicchio, Anna; Biggio, Luca; et al. (2023)
2023 International Joint Conference on Neural Networks (IJCNN)
Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory and leverages the so-called Signature Transform. This algorithm enjoys strong theoretical guarantees but is hard to scale to high-dimensional data. In this paper, we study a recently derived random projection variant called Randomized Signature, obtained using the Johnson-Lindenstrauss Lemma. We provide an in-depth experimental evaluation of the effectiveness of the Randomized Signature approach, in an attempt to showcase the advantages of this reservoir to the community. Specifically, we find that this method is preferable to the truncated Signature approach and alternative deep learning techniques in terms of model complexity, training time, accuracy, robustness, and data hungriness.
Sample Complexity and Minimax Properties of Exponentially Stable Regularized Estimators
Pillonetto, Gianluigi; Scampicchio, Anna (2022)
IEEE Transactions on Automatic Control
Recent studies have shown how regularization may play an important role in linear system identification. An effective approach consists of searching for the impulse response in a high-dimensional space, e.g., a reproducing kernel Hilbert space (RKHS). Complexity is then controlled using a regularizer, e.g., the RKHS norm, able to encode smoothness and stability information. Examples are RKHSs induced by the so-called stable spline or tuned-correlated kernels, which contain a parameter that regulates impulse response exponential decay. In this article, we derive nonasymptotic upper bounds on the ℓ 2 error of these regularized schemes and study their optimality in order (in the minimax sense). Under white noise inputs and Gaussian measurement noises, we obtain conditions which ensure the optimal convergence rate for all the class of stable spline estimators and several generalizations. Theoretical findings are then illustrated via a numerical experiment.
Active Learning-Based Model Predictive Coverage Control
Rickenbach, Rahel; Köhler, Johannes; Scampicchio, Anna; et al. (2024)
IEEE Transactions on Automatic Control
The problem of coverage control, i.e., of coordinating multiple agents to optimally cover an area, arises in various applications. However, coverage applications face two major challenges: 1) dealing with nonlinear dynamics while respecting system and safety critical constraints and 2) performing the task in an initially unknown environment. We solve the coverage problem by using a hierarchical framework, in which references are calculated at a central server and passed to the agents' local model predictive control (MPC) tracking schemes. Furthermore, to ensure that the environment is actively explored by the agents a probabilistic exploration-exploitation tradeoff is deployed. In addition, we derive a control framework that avoids the hierarchical structure by integrating the reference optimization in the MPC formulation. Active learning is then performed drawing inspiration from Upper Confidence Bound (UCB) approaches. For all developed control architectures, we guarantee closed-loop constraint satisfaction and convergence to an optimal configuration. Furthermore, all methods are tested and compared on hardware using a miniature car platform.
Inverse Optimal Control as an Errors-in-Variables Problem
Rickenbach, Rahel; Scampicchio, Anna; Zeilinger, Melanie N. (2024)
Proceedings of Machine Learning Research ~ Proceedings of the 6th Annual Learning for Dynamics & Control Conference
Inverse optimal control (IOC) is about estimating an unknown objective of interest given its optimal control sequence. However, truly optimal demonstrations are often difficult to obtain, e.g., due to human errors or inaccurate measurements. This paper presents an IOC framework for objective estimation from multiple sub-optimal demonstrations in constrained environments. It builds upon the Karush-Kuhn-Tucker optimality conditions, and addresses the Errors-In-Variables problem that emerges from the use of sub-optimal data. The approach presented is applied to various systems in simulation, and consistency guarantees are provided for linear systems with zero mean additive noise, polytopic constraints, and objectives with quadratic features.

Publications 1 - 10 of 12

Anna Scampicchio

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