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Accurate satellite pose estimation is crucial for autonomous guidance, navigation, and control (GNC) systems in in-orbit servicing (IOS) missions. This paper explores the impact of different tasks within a multi-task learning (MTL) framework for satellite pose estimation using monocular images. By integrating tasks such as direct pose estimation, keypoint prediction, object localization, and segmentation into a single network, the study aims to evaluate the reciprocal influence between tasks by testing different multi-task configurations thanks to the modularity of the convolutional neural network (CNN) used in this work. The trends of mutual bias between the analyzed tasks are found by employing different weighting strategies to further test the robustness of the findings. A synthetic dataset was developed to train and test the MTL network. Results indicate that direct pose estimation and heatmap-based pose estimation positively influence each other in general, while both the bounding box and segmentation tasks do not provide significant contributions and tend to degrade the overall estimation accuracy.

We consider multi-agent systems with cooperative interactions and study the convergence to consensus in the case of time-dependent lack of interaction. We prove a new condition ensuring consensus: we define a graph in which directed arrows correspond to connection functions that converge (in the weak sense) to some function with a positive integral on all intervals of the form $[t,+\infty)$. If the graph has a vertex reachable from all other indices, then the system converges to consensus. We show that this requirement generalizes some known sufficient conditions for convergence, such as the Persistent Excitation one. We also give a second new condition, transversal to the known ones: total connectedness of the undirected graph formed by the non-vanishing of limiting functions.

For networked systems, Persistent Excitation and Integral Scrambling Condition are conditions ensuring that communication failures between agents can occur, but a minimal level of service is ensured. We consider cooperative multi-agent systems satisfying either of such conditions. For first-order systems, we prove that consensus is attained. For second-order systems, flocking is attained under a standard condition of nonintegrability of the interaction function. In both cases and under both conditions, the original goal is reached under no additional hypotheses on the system with respect to the case of no communication failures., Comment: arXiv admin note: text overlap with arXiv:2403.07549

Modern spacecraft are increasingly relying on machine learning (ML). However, physical equipment in space is subject to various natural hazards, such as radiation, which may inhibit the correct operation of computing devices. Despite plenty of evidence showing the damage that naturally-induced faults can cause to ML-related hardware, we observe that the effects of radiation on ML models for space applications are not well-studied. This is a problem: without understanding how ML models are affected by these natural phenomena, it is uncertain "where to start from" to develop radiation-tolerant ML software. As ML researchers, we attempt to tackle this dilemma. By partnering up with space-industry practitioners specialized in ML, we perform a reflective analysis of the state of the art. We provide factual evidence that prior work did not thoroughly examine the impact of natural hazards on ML models meant for spacecraft. Then, through a "negative result", we show that some existing open-source technologies can hardly be used by researchers to study the effects of radiation for some applications of ML in satellites. As a constructive step forward, we perform simple experiments showcasing how to leverage current frameworks to assess the robustness of practical ML models for cloud detection against radiation-induced faults. Our evaluation reveals that not all faults are as devastating as claimed by some prior work. By publicly releasing our resources, we provide a foothold -- usable by researchers without access to spacecraft -- for spearheading development of space-tolerant ML models.

We consider the Follow-the-Leader (FtL) model and study which properties of the initial positioning of the vehicles ensure its convergence to the classical Lighthill-Whitham-Richards (LWR) model for traffic flow. Robustness properties of both FtL and LWR models with respect to the initial discretization schemes are investigated. Some numerical simulations are also discussed.

We prove that a first-order cooperative system of interacting agents converges to consensus if the so-called Persistence Excitation condition holds. This condition requires that the interaction function between any pair of agents satisfies an integral lower bound. The interpretation is that the interaction needs to ensure a minimal amount of service.

We consider a control system driven by a nonlocal continuity equation. Admissible controls are Lipschitz vector fields acting inside a fixed open set. We demonstrate that small perturbations of the initial measure, traced along Wasserstein geodesics, may be neutralized by admissible controls. More specifically, initial perturbations of order $\varepsilon$ can be reduced to order $\varepsilon^{1+\kappa}$, where $\kappa$ is a positive constant., Comment: 6 pages, 2 figures. arXiv admin note: text overlap with arXiv:2403.02837

We discuss stabilization around trajectories of the continuity equation with nonlocal vector fields, where the control is localized, i.e., it acts on a fixed subset of the configuration space. We first show that the correct definition of stabilization is the following: given an initial error of order $\varepsilon$, measured in Wasserstein distance, one can improve the final error to an order $\varepsilon^{1+\kappa}$ with $\kappa>0$. We then prove the main result: assuming that the trajectory crosses the subset of control action, stabilization can be achieved. The key problem lies in regularity issues: the reference trajectory needs to be absolutely continuous, while the initial state to be stabilized needs to be realized by a small Lipschitz perturbation or being in a very small neighborhood of it., Comment: 26 pages, 4 figures

Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to describe collective dynamics that are independent of any coordinate change or external influence. We particularize the results to some key examples, i.e. for the most basic low dimensional symmetries that appear in collective dynamics on manifolds.

The problem of identifying models of post-disaster reconstruction is an issue that has been dealt with in depth in a number of works, mostly dedicated to individual cases or to the comparison of models. There are also a number of works that have attempted a systematisation on an historiographic basis. To date, however, there is no overall work aimed at constructing a quantitative method for evaluating and comparing reconstruction experiences. This article proposes to establish a scientific method for the systematic classification of post-disaster reconstructions, based on data analysis. The method consists of four phases: the redrawing of cases with a precise replicable technique; the choice of indicators; the measurement of urban development; the classification of cases. The method is applied to cases that are comparable with each other in terms of type of event and period: we have chosen post-World War II reconstructions in Europe given the larger availability of documentation. The paper leads both to the consolidation of the model as effective and replicable and to the construction of the application, which revises the qualitative classification of most of the addressed cases.

We study the possibility of defining a distance on the whole space of measures, with the property that the distance between two measures having the same mass is the Wasserstein distance, up to a scaling factor. We prove that, under very weak and natural conditions, if the base space is unbounded, then the scaling factor must be constant, independently of the mass. Moreover, no such distance can exist, if we include the zero measure. Instead, we provide examples with non-constant scaling factors for the case of bounded base spaces.

We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on a vanishing viscosity method: we prove the convergence of the same problem where a diffusion term is added, with a small viscosity parameter. By using stochastic optimal control, we first show the existence of a sequence of optimal controls for the problem with diffusion. We then build the optimizer of the original problem by letting the viscosity parameter go to zero.

Recent advances in text-to-speech (TTS) synthesis, such as Tacotron and WaveRNN, have made it possible to construct a fully neural network based TTS system, by coupling the two components together. Such a system is conceptually simple as it only takes grapheme or phoneme input, uses Mel-spectrogram as an intermediate feature, and directly generates speech samples. The system achieves quality equal or close to natural speech. However, the high computational cost of the system and issues with robustness have limited their usage in real-world speech synthesis applications and products. In this paper, we present key modeling improvements and optimization strategies that enable deploying these models, not only on GPU servers, but also on mobile devices. The proposed system can generate high-quality 24 kHz speech at 5x faster than real time on server and 3x faster than real time on mobile devices., Comment: 7 pages 2 figures, accepted to ASRU 2021

The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e. its Lebesgue measure is zero). We also provide several counterexample showing that the hypotheses of our theorem are close to sharp., Comment: 12 pages, 1 figure

Social dynamics models may present discontinuities in the right-hand side of the dynamics for multiple reasons, including topology changes and quantization. Several concepts of generalized solutions for discontinuous equations are available in the literature and are useful to analyze these models. In this chapter, we study Caratheodory and Krasovsky generalized solutions for discontinuous models of opinion dynamics with state dependent interactions. We consider two definitions of "bounded confidence" interactions, which we respectively call metric and topological: in the former, individuals interact if their opinions are closer than a threshold; in the latter, individuals interact with a fixed number of nearest neighbors. We compare the dynamics produced by the two kinds of interactions, in terms of existence, uniqueness and asymptotic behavior of different types of solutions.

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number goes to infinity. While solutions of the discrete problem always exist in a unique and explicit form, the behavior of their macroscopic counterparts is very sensitive to the magnitude of the time horizon and penalization parameter. When one minimizes the final variance, there always exists a Lipschitz-in-space optimal controls for the infinite dimensional problem, which can be obtained as a suitable extension of the optimal controls for the finite-dimensional problems. The same holds true for variance maximizations whenever the time horizon is sufficiently small. On the contrary, for large final times (or equivalently for small penalizations of the control cost), it can be proven that there does not exist Lipschitz-regular optimal controls for the macroscopic problem., Comment: 6 pages (double columns), 4 figures

We consider a mean-field control problem with linear dynamics and quadratic control. We apply the vanishing viscosity method: we add a (regularizing) heat diffusion with a small viscosity coefficient and let such coefficient go to zero. The main result is that, in this case, the limit optimal control is exactly the optimal control of the original problem.

Self-organization and control around flocks and mills is studied for second-order swarming systems involving self-propulsion and potential terms. It is shown that through the action of constrained control, is it possible to control any initial configuration to a flock or a mill. The proof builds on an appropriate combination of several arguments: LaSalle invariance principle and Lyapunov-like decreasing functionals, control linearization techniques, and quasi-static deformations. A stability analysis of the second-order system guides the design of feedback laws for the stabilization to flock and mills, which are also assessed computationally.

Bounded-confidence models in social dynamics describe multi-agent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations with discontinuous right-hand side: this is a direct consequence of restricting interactions to a bounded region with non-vanishing strength at the boundary. Various works in the literature analyzed properties of solutions, such as barycenter invariance and clustering. On the other side, the problem of giving a precise definition of solution, from an analytical point of view, was often overlooked. However, a rich literature proposing different concepts of solution to discontinuous differential equations is available. Using several concepts of solution, we show how existence is granted under general assumptions, while uniqueness may fail even in dimension one, but holds for almost every initial conditions. Consequently, various properties of solutions depend on the used definition and initial conditions.

We introduce the optimal transportation interpretation of the Kantorovich norm on thespace of signed Radon measures with finite mass, based on a generalized Wasserstein distancefor measures with different masses.With the formulation and the new topological properties we obtain for this norm, we proveexistence and uniqueness for solutions to non-local transport equations with source terms, whenthe initial condition is a signed measure.

In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of mean-field approximations for infinite-dimensional multi-agent optimal control problems, along with a careful extension of an existence result of locally optimal Lipschitz feedbacks. The latter is based on the reformulation of a coercivity estimate in the language of Wasserstein calculus, which is used to obtain uniform Lipschitz bounds along sequences of approximations by empirical measures.

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions for the leader-follower dynamics, under suitable assumptions. We then establish, for an appropriate choice of the initial datum, the equivalence of the system with a PDE-ODE system, that consists of a continuity equation over the state space and an ODE for the transition from leader to follower or vice versa. We further introduce a stochastic process approximating the PDE, together with a jump process that models the switch between the two populations. Using a propagation of chaos argument, we show that the particle system generated by these two processes converges in probability to a solution of the PDE-ODE system. Finally, several numerical simulations of social interactions dynamics modeled by our system are discussed.

We prove the existence of a universal gap for minimum time controllability of finite dimensional quantum systems, except for some basic representations of spin groups. This is equivalent to the existence of a gap in the diameter of orbit spaces of the corresponding compact connected Lie group unitary actions on the Hermitian spheres.

In this paper, we extend and complete the classification of the generic singularities of the 3D-contact sub-Riemmanian conjugate locus in a neighbourhood of the origin., Comment: 7 pages, 2 figures

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no interaction between the agents. We give a characterization of the minimal time both for microscopic and macroscopic descriptions of a crowd. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control region to feed the desired final configuration. The construction of the control is explicit, providing a numerical algorithm for computing it. We finally give some numerical simulations.

We introduce a new formulation for differential equation describing dynamics of measures on an Euclidean space, that we call Measure Differential Equations with sources. They mix two different phenomena: on one side, a transport-type term, in which a vector field is replaced by a Probability Vector Field, that is a probability distribution on the tangent bundle; on the other side, a source term. Such new formulation allows to write in a unified way both classical transport and diffusion with finite speed, together with creation of mass. The main result of this article shows that, by introducing a suitable Wasserstein-like functional, one can ensure existence of solutions to Measure Differential Equations with sources under Lipschitz conditions. We also prove a uniqueness result under the following additional hypothesis: the measure dynamics needs to be compatible with dynamics of measures that are sums of Dirac masses.

We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using the formalism of subdifferential calculus in Wasserstein spaces. We show that the geometric approach based on needle variations and on the evolution of the covector (here replaced by the evolution of a mesure on the dual space) can be translated into this formalism., Comment: 31 pages, 1 figure

We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized on a fixed control set. We prove that, for each initial and final configuration, one can steer approximately one to another with Lipschitz controls when the uncontrolled dynamics allows to cross the control set. We also show that the exact controllability only holds for controls with less regularity, for which one may lose uniqueness of the associated solution., Comment: arXiv admin note: text overlap with arXiv:1702.07272

Cooperative systems are systems in which the forces among agents are non-repulsive. The free evolution of such systems can tend to the formation of patterns, such as consensus or clustering, depending on the properties and intensity of the interaction forces between agents. The kinetic cooperative systems are obtained as the mean field limits of these systems when the number of agents goes to infinity. These limit dynamics are described by transport partial differential equations involving non-local terms. In this article, we design a simple and robust control strategy steering any kinetic cooperative system to approximate alignment. The computation of the control at each instant will only require knowledge of the size of the support of the crowd in the phase space and of the Lipschitz constant of the interaction forces. Besides, the control we apply to our system is sparse, in the sense that it acts only on a small portion of the total population at each time. It also presents the features of being obtained through a constructive procedure and to be independent on the number of agents, making it convenient for applications., Comment: 6 pages, 1 figure

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We characterize the minimal time for a discrete crowd model, both for exact and approximate controllability. This leads to an algorithm that computes the control and the minimal time. We finally present a numerical simulation.

We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove that, for each initial and final configuration, one can steer one to another with such class of controls only if the uncontrolled dynamics allows to cross the control set $\omega$. We also prove a minimal time result for such systems. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in $\omega$ to feed the desired final configuration.