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This paper presents a tool for multi-step system identification that leverages first-order optimization and exact gradient computation. Drawing inspiration from neural network training and Automatic Differentiation (AD), the proposed method computes and analyzes the gradients with respect to the parameters to identify by propagating them through system dynamics. Thus, it defines a linear, time-varying dynamical system that models the gradient evolution. This allows to formally address the "exploding gradient" issue, by providing conditions for a reliable and efficient optimization and identification process for dynamical systems. Results indicate that the proposed method is both effective and efficient, making it a promising tool for future research and applications in nonlinear systems identification and non-convex optimization.

Many scientific problems aim to evaluate the function fo relating variables u and y measured from a physical phenomenon. An exact knowledge of fo cannot be expected, and many methods are used for deriving approximate functions fa giving small error fo-fa. It is shown that deriving functions fa having finite error is not possible using measured data only, and hypothesis, i.e., assumptions, on the function fo and on the disturbances corrupting the measurements must be introduced. Two main classes of assumptions are used in the literature. The most widely used is the Parametric Stochastic class, where fo is assumed to be a function depending on a vector p and disturbances are stochastic variables. In last decades, assumptions belonging to Set Membership class have been investigated, where fo is assumed to a smooth function with bounded smoothness parameter and disturbances are bounded variables. At first, it is shown that SM methods achieve "theoretical" properties (e.g., finding fa with known and minimal error error, if assumptions hold) for general nonlinear assumptions on function fo, while are achieved by PS methods under very restricted assumptions on fo. Then, it is proved that no method can be found for validating PS or SM assumptions, so that at best the chosen assumptions can be falsified, i.e. recognized not true. No falsification test of PS assumptions is known, for general nonlinear assumptions on fo. A falsification test of SM assumptions is proposed. Finally, the new class of Physical Set Membership assumptions is proposed, able to integrate the information provided by a function fp obtained by a PS method, with a suitably designed SM method. It is shown that PSM methods enjoy the strong results of SM methods on theoretical properties and assumption falsification, and that, making use of the information provided by fp, may be more accurate than using only SM assumptions., Comment: 11 pages, 1 figure

In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates physical principles with black-box basis functions to compensate for unmodeled dynamics, ensuring accuracy over long prediction horizons and computational efficiency. Additionally, we introduce penalty terms to enforce physical consistency and stability during training. We provide a comprehensive analysis of theoretical properties related to multi-step nonlinear system identification, establishing bounds on parameter estimation errors and conditions for gradient stability and sparsity recovery. The proposed framework demonstrates significant potential for improving model accuracy and reliability in various engineering applications, making a substantial step towards the effective use of combined off-white and sparse black models in system identification. The effectiveness of the proposed approach is demonstrated on a nonlinear system identification benchmark.

This document briefly describes the noise models and shapes used for the synthesis of the Drag-Free and Attitude Control System in the LISA space mission. LISA (Laser Interferometer Space Antenna) is one of the next large-class missions from the European Space Agency (ESA), expected to be launched in 2034. The main goal of the mission is to detect the gravitational waves, which are undulatory perturbations of the space-time fabric, extremely important to collect experimental proofs for the General Relativity Theory. In the 90s, different international collaborations of institutes laid the foundations for the first ground-based interferometers (see, e.g., LIGO and Virgo). However, ground-based interferometers have a limited bandwidth due to the Earth's environmental noises and short arm-length of few kilometers. Therefore, they cannot observe gravitational waves belonging to the portion of the spectrum below 1 Hz. This issue can be overcome by means of space-based interferometers, that can have arm-lengths up to millions of kilometers and exploit a quieter environment than the Earth's surface. The LISA system is affected by actuation, sensing and environmental disturbances and noises. Among the actuation noises we have those given by the Micro Propulsion System (MPS), the Gravitational Reference Sensor (GRS) and the Optical Assembly (OA) motor. Among the sensing noises we consider the interferometer, the Differential Wavefront Sensor (DWS) and the GRS. The environmental disturbances are given by the solar radiation pressure, the test-mass stiffness and self-gravity, and the environmental noises acting directly on the test-mass.

The aim of this paper is to present a novel physics-based framework for the identification of dynamical systems, in which the physical and structural insights are reflected directly into a backpropagation-based learning algorithm. The main result is a method to compute in closed form the gradient of a multi-step loss function, while enforcing physical properties and constraints. The derived algorithm has been exploited to identify the unknown inertia matrix of a space debris, and the results show the reliability of the method in capturing the physical adherence of the estimated parameters.

We propose a Nonlinear Model Predictive Control approach to spacecraft rendezvous in non-Keplerian Lunar orbits. The approach is based on the Pontryagin Minimum Principle and allows the accomplishment of minimum-propellant maneuvers. The relative motion between the chaser and the target is described by the nonlinear and unstable dynamics of the circular restricted three body-problem. In the proposed formulation, we design a minimum-propellant controller, which leads to a bang-bang behavior of the control signal. Under suitable assumptions, simplified dynamics is employed as prediction model, in order to reduce the complexity of the controller algorithm but, at the same time, without penalizing the controller tracking performance. The proposed approach's effectiveness is validated by a simulation example.

Hardening cyber physical assets is both crucial and labor-intensive. Recently, Machine Learning (ML) in general and Reinforcement Learning RL) more specifically has shown great promise to automate tasks that otherwise would require significant human insight/intelligence. The development of autonomous RL agents requires a suitable training environment that allows us to quickly evaluate various alternatives, in particular how to arrange training scenarios that pit attackers and defenders against each other. CyberBattleSim is a training environment that supports the training of red agents, i.e., attackers. We added the capability to train blue agents, i.e., defenders. The paper describes our changes and reports on the results we obtained when training blue agents, either in isolation or jointly with red agents. Our results show that training a blue agent does lead to stronger defenses against attacks. In particular, training a blue agent jointly with a red agent increases the blue agent's capability to thwart sophisticated red agents., Comment: To appear in Proceedings of the 2022 International Conference on Computational Science and Computational Intelligence

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von K\'arm\'an flow, Rayleigh-B\'enard convection and a zero-pressure-gradient turbulent boundary layer over a flat plate. The results for the von K\'arm\'an flow compare well with previous experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh-B\'enard convection agree with those obtained for K\'arm\'an flow, while results for the logarithmic layer within the boundary layer differ slightly, and we provide a potential explanation. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories.

Accurate design of labelled oligo probes for the detection of miRNA biomarkers by Surface Enhanced Raman Scattering (SERS) may improve the exploitation of the plasmonic enhancement. This work, thus, critically investigates the role of probe labelling configuration on the performance of SERS based bioassays for miRNA quantitation. To this aim, highly efficient SERS substrates based on Ag-decorated porous silicon/PDMS membranes are functionalized according to two different bioassays relying on a one-step or two-step hybridization of the target miRNA with oligonucleotide probes. The detection configuration is varied, exploring the impact of the position of the Raman reporter along the oligo sequence and of the reporter identity on bioassay sensitivity. In the high miRNA concentration regime(100-10 nM), a significantly increased SERS intensity is detected when the reporters are located closer to the plasmonic surface compared to farther probe labelling positions. Counterintuitively, a levelling-off of the SERS intensity from the two configuration is instead recorded at low miRNA concentration. Such effect is explained by an increased contribution of Raman hot spot to the whole SERS signal, as confirmed by simulations of the electric near field for a simplified model of the Ag nanostructures. The beneficial effect of reducing the reporter-to-surface distance is however partially retained for the two-step hybridization assay thanks to the less sterically hindered environment in which the second hybridization occurs. The study thus demonstrates that the limit of detection of the assay can be lowered by tuning the probe labelling position, but sheds at the same time light on the complexity of the bionanointerfaces in SERS and on the multiple factors affecting bioassay sensitivity.

We present a numerically efficient Nonlinear Model Predictive Control (NMPC) approach, called Set Membership based NMPC (SM-NMPC). In particular, a Set Membership method is used to derive from data an approximation and tight bounds on the optimal NMPC control law. These quantities are used to reduce the dimensionality and volume of the search domain of the NMPC optimization problem, allowing a significant shortening of the computation time. The proposed SM-NMPC strategy is tested in simulation, considering realistic autonomous vehicle scenarios, like parallel parking and lane keeping maneuvers., Comment: We need more time to consolidate some results

In Networked Control Systems (NCS), the absence of physical communication links in the loop leads to relevant issues, such as measurement delays and asynchronous execution of the control commands. These issues may lead to unwanted control behaviours. This ArXiv paper is intended to give additional results to the work presented in "Embedded Model Control of Networked Control Systems: an Experimental Case-study". The last one presents an original approach, based on the Embedded Model Control, to deal with experimental scenarios characterized by asynchronous control timing. The effectiveness of the proposed approach is demonstrated with a differential-drive robot, first with high-fidelity simulations and finally with several experimental tests. Specifically, the present work aims to study the stability analysis of the EMC experimental setup and to give further experimental results, to complement those presented in the main paper, "Embedded Model Control of Networked Control Systems: an Experimental Case-study"., Comment: 8 pages, 8 figures, supplementary article to the main paper "Embedded Model Control of Networked Control Systems: an Experimental Case-study"

A Pontryagin-based approach to solve a class of constrained Nonlinear Model Predictive Control problems is proposed which employs the method of barrier functions for dealing with the state constraints. Unlike the existing works in literature the proposed method is able to cope with nonlinear input and state constraints without any significant modification of the optimization algorithm. A stability analysis of the closed-loop system is carried out by using the L-2 norm of the predicted state tracking error as a Lyapunov function. Theoretical results are tested and confirmed by numerical simulations on the Lotka-Volterra prey/predator system., Comment: 11 pages, 5 figures