arXiv subjects

Giovanni Colombo

Publications and source records attributed to Giovanni Colombo.

At least 19 recordsLinked to original sources

arXiv2026

A SPHEREx Pipeline and Spectral Library for Ultracool Dwarfs

We present a Python spectrophotometry extraction tool tailored for fast-moving point sources detected in the SPHEREx mission, and use it to construct a set of 0.75-5.0 $\mu$m low-resolution ($\lambda/\Delta\lambda \sim 50$) spectrophotometry data products based on the SPHEREx Quick Release 2 (QR2) for a set of 6003 L0-Y1 ultracool dwarfs: 2050 known ultracool dwarfs, 3008 known photometric ultracool dwarf candidates, and 947 newly identified ultracool dwarfs. This work more than doubles the number of ultracool dwarfs with spectroscopy, from 3449 to 7402. We provide SPHEREx templates for each spectral subtype and a set of tools to assign automated spectral types. The QR2 data release generates spectrophotometry with an average signal-to-noise per spectral channel above $\sim$10 for most objects with WISE W2 magnitudes of 14.0 mag and brighter. The compiled data set is made available publicly at https://mocadb.ca, where new spectral compilations from future data releases will also be made available as they are published. These new data provide a significant increase in the number of substellar objects for which the 2.4-5.0 $\mu$m window is now accessible, making it possible to probe important molecular chemistry of key CNOS-bearing species for the coolest brown dwarfs. We flag 2668 ultracool dwarfs as candidate young brown dwarfs, 250 as candidate subdwarfs, and 865 as possibly otherwise peculiar for future investigation. The SPIFF library presented here opens the doors to efficient confirmation of candidate substellar objects and follow-up studies of population-level atmospheric properties of cold brown dwarfs.

astro-ph.SR↗

arXiv2026

Three Thousand Motion-Confirmed L and T Dwarf Candidates from the Backyard Worlds:~Planet 9 Citizen Science Project

The Backyard Worlds: Planet 9 citizen science project uses data from the Wide-field Infrared Survey Explorer to detect infrared objects with significant motion. In this work, we present the majority of the L and T dwarf candidates discovered through this effort. For each candidate, we provide proper motion measurements as well as optical, near-infrared, and mid-infrared photometry (when available), photometric spectral types and distance estimates. Three thousand and six new motion-confirmed discoveries are presented in this work, 2,357 with L-type photometric spectral types and 649 with T-type photometric spectral types. We also present an additional 80 objects as likely L or T dwarfs based on available photometry, but for which a significant motion measurement could not be obtained. We identify 28 objects in this sample as new comoving companions to higher-mass stars, and an additional 9 sources that are candidate binary systems made up of two ultracool dwarfs of L-type or later. Follow-up spectroscopic observations will be necessary to confirm spectral types and further characterize the sources discovered through this project. This work presents the largest single sample of motion-confirmed L and T dwarf discoveries to date, which would more than double the number of known L and T dwarfs, if confirmed. We wish to sincerely thank our citizen scientist collaborators for their monumental efforts that have directly impacted this project's success.

astro-ph.SR↗

arXiv2026

Exponential Turnpike Theorems for Nonlinear Deterministic Meanfield Optimal Control Problems

In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the Lagrangian setting, the problem is lifted to a Hilbert space of random variables, and we prove an exponential turnpike theorem by combining first-order optimality conditions, a second-order expansion of the lifted Hamiltonian, and an operator Riccati diagonalization argument. In the Eulerian setting, we derive intrinsic KKT conditions for the static constrained problem, and show how the Eulerian second-order hypotheses split into a horizontal part, transferred by unitary conjugation to the lifted space, and a vertical part which reduces to uniform pointwise stabilizability and detectability conditions on multiplication operators. This yields an exponential turnpike theorem in the Wasserstein space for optimal Pontryagin triples. Along the way, we %provide explicit the link between Wasserstein Hessians and their Lagrangian lifts, and provide several remarks clarifying the role of occupation measures, local Eulerian minimizers, and control constraints in our results.

math.OC↗

arXiv2025

EV-Flying: an Event-based Dataset for In-The-Wild Recognition of Flying Objects

Monitoring aerial objects is crucial for security, wildlife conservation, and environmental studies. Traditional RGB-based approaches struggle with challenges such as scale variations, motion blur, and high-speed object movements, especially for small flying entities like insects and drones. In this work, we explore the potential of event-based vision for detecting and recognizing flying objects, in particular animals that may not follow short and long-term predictable patters. Event cameras offer high temporal resolution, low latency, and robustness to motion blur, making them well-suited for this task. We introduce EV-Flying, an event-based dataset of flying objects, comprising manually annotated birds, insects and drones with spatio-temporal bounding boxes and track identities. To effectively process the asynchronous event streams, we employ a point-based approach leveraging lightweight architectures inspired by PointNet. Our study investigates the classification of flying objects using point cloud-based event representations. The proposed dataset and methodology pave the way for more efficient and reliable aerial object recognition in real-world scenarios.

cs.CV↗

arXiv2024

Discovery of 118 New Ultracool Dwarf Candidates Using Machine Learning Techniques

We present the discovery of 118 new ultracool dwarf candidates, discovered using a new machine learning tool, named \texttt{SMDET}, applied to time series images from the Wide-field Infrared Survey Explorer. We gathered photometric and astrometric data to estimate each candidate's spectral type, distance, and tangential velocity. This sample has a photometrically estimated spectral class distribution of 28 M dwarfs, 64 L dwarfs, and 18 T dwarfs. We also identify a T subdwarf candidate, two extreme T subdwarf candidates, and two candidate young ultracool dwarfs. Five objects did not have enough photometric data for any estimations to be made. To validate our estimated spectral types, spectra were collected for 2 objects, yielding confirmed spectral types of T5 (estimated T5) and T3 (estimated T4). Demonstrating the effectiveness of machine learning tools as a new large-scale discovery technique.

astro-ph.SR↗

arXiv2024

Optimal control of perturbed sweeping processes with applications to general robotics models

This paper primarily focuses on the practical applications of optimal control theory for perturbed sweeping processes within the realm of robotics dynamics. By describing these models as controlled sweeping processes with pointwise control and state constraints and by employing necessary optimality conditions for such systems, we formulate optimal control problems suitable to these models and develop numerical algorithms for their solving. Subsequently, we use the Python Dynamic Optimization library GEKKO to simulate solutions to the posed robotics problems in the case of any fixed number of robots under different initial conditions.

math.OC↗

arXiv2024

Thirteen New M Dwarf + T Dwarf Pairs Identified with WISE/NEOWISE

We present the discovery of 13 new widely separated T dwarf companions to M dwarf primaries, identified using WISE/NEOWISE data by the CatWISE and Backyard Worlds: Planet 9 projects. This sample represents a $\sim$60% increase in the number of known M+T systems, and allows us to probe the most extreme products of binary/planetary system formation, a discovery space made available by the CatWISE2020 catalog and the Backyard Worlds: Planet 9 effort. Highlights among the sample are WISEP J075108.79-763449.6, a previously known T9 thought to be old due to its SED, which we now find is part of a common-proper-motion pair with L 34-26 A, a well studied young M3 V star within 10 pc of the Sun; CWISE J054129.32-745021.5 B and 2MASS J05581644-4501559 B, two T8 dwarfs possibly associated with the very fast-rotating M4 V stars CWISE J054129.32-745021.5 A and 2MASS J05581644-4501559 A; and UCAC3 52-1038 B, which is among the widest late T companions to main sequence stars, with a projected separation of $\sim$7100 au. The new benchmarks presented here are prime $JWST$ targets, and can help us place strong constraints on formation and evolution theory of substellar objects as well as on atmospheric models for these cold exoplanet analogs.

astro-ph.SR↗

arXiv2023

Discrete Approximations and Optimality Conditions for Controlled Free-Time Sweeping Processes

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop a novel version of the method of discrete approximations of its own qualitative and numerical values with establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. Using advanced tools of first-order and second-order variational analysis and generalized differentiation allows us to derive new necessary conditions for optimal solutions of the discrete-time problems and then, by passing to the limit in the discretization procedure, for designated local minimizers in the original problem of sweeping optimal control. The obtained results are illustrated by a numerical example.

math.OC↗

arXiv2021

Rotational controls and uniqueness of constrained viscosity solutions of Hamilton-Jacobi PDE

The classical inward pointing condition (IPC) for a control system whose state $x$ is constrained in the closure $C:=\bar\Omega$ of an open set $\Omega$ prescribes that at each point of the boundary $x\in \partial \Omega$ the intersection between the dynamics and the interior of the tangent space of $\bar \Omega$ at $x$ is nonempty. Under this hypothesis, for every system trajectory $x(.)$ on a time-interval $[0,T]$, possibly violating the constraint, one can construct a new system trajectory $\hat x(.)$ that satisfies the constraint and whose distance from $x(.)$ is bounded by a quantity proportional to the maximal deviation $d:=\mathrm{dist}(\Omega,x([0,T]))$. When (IPC) is violated, the construction of such a constrained trajectory is not possible in general. However, for a control system of the form $\dot{x}=f_1(x)u_1+f_2(x)u_2$, we prove in this paper that a "higher order" inward pointing condition involving Lie brackets of the dynamics' vector fields allows for a novel construction of a constrained trajectory $\hat x(.)$ whose distance from the reference trajectory $x(.)$ is bounded by a quantity proportional to $\sqrt{d}$. Our method requires a further assumption of non-positiveness of a sort of curvature and is based on the implementation of a suitable "rotating" control strategy. As an application, we establish the continuity up to the boundary of the value function $V$ of a classical optimal control problem, a continuity that allows to regard $V$ as the unique constrained viscosity solution of the corresponding Bellman equation.

math.OC↗

arXiv2021

Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger $W^{1,2}$ convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.

math.DS↗

arXiv2020

Optimization of Fully Controlled Sweeping Processes

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets and additive perturbations. By using the first-order and mainly second-order tools of variational analysis and generalized differentiation, we develop a well-posed method of discrete approximations, obtain optimality conditions for solutions to discrete-time control systems, and then establish by passing to the limit verifiable necessary optimality conditions for local minimizers of the original controlled sweeping process that are expressed entirely in terms of its given data. The efficiency of the obtained necessary optimality conditions for the sweeping dynamics is illustrated by solving three nontrivial examples of their own interest.

math.OC↗

arXiv2020

On the optimal control of rate-independent soft crawlers

Existence of optimal solutions and necessary optimality conditions for a controlled version of Moreau's sweeping process are derived. The control is a measurable ingredient of the dynamics and the constraint set is a polyhedron. The novelty consists in considering time periodic trajectories, adding the requirement that the control have zero average, and considering an integral functional that lacks weak semicontinuity. A model coming from the locomotion of a soft-robotic crawler, that motivated our setting, is analysed in detail. In obtaining necessary conditions, an improvement of the method of discrete approximations is used.

math.OC↗

arXiv2020

Optimization and Discrete Approximation of Sweeping Processes with Controlled Moving Sets and Perturbations

This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive discrete approximation procedure that allows us to strongly approximate any feasible trajectory of the controlled sweeping process by feasible discrete trajectories and also establish a $W^{1,2}$-strong convergence of optimal trajectories for discretized control problems to a given local minimizer of the original continuous-time sweeping control problem of the Bolza type. Employing advanced tools of first-order and second-order variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete optimal solutions under fairly general assumptions formulated entirely in terms of the given data. The obtained results give us efficient suboptimality ("almost optimality") conditions for the original sweeping control problem that are illustrated by a nontrivial numerical example.

math.OC↗

arXiv2018

Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and completely calculate optimal solutions in particular situations.

math.OC↗

arXiv2018

Optimization of a perturbed sweeping process by constrained discontinuous controls

This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which addresses unbounded discontinuous differential inclusions with intrinsic state constraints, is truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems with constrained measurable controls, we develop a refined method of discrete approximations with establishing its well-posedness and strong convergence. This approach, married to advanced tools of first-order and second-order variational analysis and generalized differentiations, allows us to derive adequate collections of necessary optimality conditions for local minimizers, first in discrete-time problems and then in the original continuous-time controlled sweeping process by passing to the limit. The new results include an appropriate maximum condition and significantly extend the previous ones obtained under essentially more restrictive assumptions. We compare them with other versions of the maximum principle for controlled sweeping processes that have been recently established for global minimizers in problems with smooth sweeping sets by using different techniques. The obtained necessary optimality conditions are illustrated by several examples.

math.OC↗

arXiv2016

A Maximum Principle for the controlled Sweeping Process

We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin's Maximum Principle type. The results are also discussed through an example. We combine techniques from M. Sene, L. Thibault, Journal of Nonlinear and Convex Analysis 15 (2014) and from M. Brokate and P. Krejci, Discrete and continuous dynamical systems series B. Volume 18 (2013), 331-348, which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set $C(t)$, but do not require its strict convexity. Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of $C(t)$ is touched. The state space is finite dimensional.

math.OC↗

arXiv2015

Optimal control of the sweeping process over polyhedral controlled sets

The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong $W^{1,2}$-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.

math.OC↗

arXiv2012

Non-Lipschitz points and the SBV regularity of the minimum time function

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal linear control systems with constant coefficients in $\mathbb{R}^N$. We characterize points around which $T$ is not Lipschitz as those which can be reached from the origin by an optimal trajectory (of the reversed dynamics) with vanishing minimized Hamiltonian. Linearity permits an explicit representation of such set, that we call $\mathcal{S}$. Furthermore, we show that $\mathcal{S}$ is $\mathcal{H}^{N-1}$-rectifiable with positive $\mathcal{H}^{N-1}$-measure. Second, we consider a class of control-affine \textit{planar} nonlinear systems satisfying a second order controllability condition: we characterize the set $\mathcal{S}$ in a neighborhood of the origin in a similar way and prove the $\mathcal{H}^1$-rectifiability of $\mathcal{S}$ and that $\mathcal{H}^1(\mathcal{S})>0$. In both cases, $T$ is known to have epigraph with positive reach, hence to be a locally $BV$ function (see \cite{CMW,GK}). Since the Cantor part of $DT$ must be concentrated in $\mathcal{S}$, our analysis yields that $T$ is $SBV$, i.e., the Cantor part of $DT$ vanishes. Our results imply also that $T$ is locally of class $\mathcal{C}^{1,1}$ outside a $\mathcal{H}^{N-1}$-rectifiable set. With small changes, our results are valid also in the case of multiple control input.

math.OC↗