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A bang-bang principle for the conditional expectation vector measure
No full textWe prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of the set of selections of its extreme points part. As a by-product, we obtain straightforwardly a purification principle
Times Are Changing and so Is Safety
No full textInternational audienceAbstract Reflecting about the challenges ahead and the evolution of safety raises a multitude of questions about the future but also about safety. This introductory chapter first nuances the notion of safety as if it were a homogeneous whole. It starts with an overview of the macro-safety model that underpins safety in high-risk industries, or more precisely, of the way industries are expected by society, and thus regulators, to ensure the safety of their operations. Following this safety “as demonstrated” view, it zooms in closer to the field and underlines some discrepancies between this “control” perspective and the actual practices contributing to the safety of high-risk industries, including non-proceduralised ones. It then explores some of the major evolution trends for 2040 and the uncertainties attached to them and reflects upon their possible effects on safety models in the future. With this global picture in mind illustrating the complexity of the topic addressed by the book, the last section provides an overview of the content of the book and its various constitutive chapters
Twenty years of EUROPT, the EURO working group on Continuous Optimization
No full textInternational audienceEUROPT, the Continuous Optimization working group of EURO, celebrated its 20 years of activity in 2020. We trace the history of this working group by presenting the major milestones that have led to its current structure and organization and its major trademarks, such as the annual EUROPT workshop and the EUROPT Fellow recognition
Algorithme de Floyd modifié pour le calcul du nombre de chemins alternatifs
No full textInternational audienceLa robustesse est une caractéristique essentielle à tous réseaux de transport, elle garantie la qualité du service même en cas de perturbation.L'une des approches permettant de quantifier cette robustesse est basée sur le nombre de chemins alternatifs. Cependant, les algorithmes de la littérature réalisant cette tâche sont de complexité quartique.Dans ce papier, nous proposons une nouvelle approche permettant de calculer des chemins alternatifs basée sur l'algorithme de Floyd dont la complexité est cubiqu
Learned Multiagent Real-Time Guidance with Applications to Quadrotor Runway Inspection
No full textInternational audienceAircraft runways are periodically inspected for debris and damage. Instead of having pilots coordinate the motion of the quadrotors manually or hand-crafting the desired quadrotor behavior into a guidance law, this paper reports the use of deep reinforcement learning to learn a closed-loop multiagent real-time guidance strategy for quadrotors to autonomously perform such inspections. This yields a significant reduction in engineering effort while enabling highly-flexible real-time performance. The runway is discretized into a number of rectangular tiles, which must all be visited for the runway to be considered inspected. The guidance system reported here calculates a desired acceleration in real time for the quadrotor(s) to track in order to complete the task. This paper first develops the guidance technique, trains it in simulation, and evaluates it experimentally using an indoor quadrotor laboratory. This process is then repeated for an outdoor setting on a real runway, where the proposed guidance strategy is compared to a handcrafted strategy and applied to a multiquadrotor scenario where the quadrotors must learn to coordinate their behavior and be resilient to the failure of one quadrotor mid-experiment. Multiagent, fault-tolerant, learned behavior is successfully demonstrated through outdoor quadrotor flights. Additional simulations and experiments demonstrate the technique is viable in a swarm with additional quadrotors, on a variety of runway shapes and with increased discretization of the runway. This work shows how modern learning-based techniques can: 1) reduce the engineering effort required to design complex guidance systems and 2) be implemented on real hardware in a representative outdoor environment
Computer Vision, Imaging and Computer Graphics Theory and Applications
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A Geometric Approach to Study Aircraft Trajectories: the benefits of OpenSky Network ADS-B data
No full textInternational audienceTo date, the statistical analysis of aircraft trajectories has been under-exploited in the Airspace Traffic Management (ATM) literature. One reason is the need for advanced methods to tackle the high sampling irregularity and temporal correlation that both characterize a trajectory. Differential geometry provides a relevant framework to study trajectories. Modeling trajectories as parametrized curves, shape analysis allows to answer operational questions. This work presents a geodesic distance that rigorously defines and quantifies shape differences between aircraft trajectories. The key idea is to compare how the shape of a given trajectory changes from one popular data set (the Eurocontrol R&D data archive) to another one (OpenSky Network ADS-B data). Distances as well as geodesic paths are computed for a sample of flights departing from Toulouse-Blagnac (LFBO) and landing at Paris-Orly (LFPO) in 2019. Its use for clustering purposes is illustrated and discussed
Impact of Explicit Memory on Dynamic Conflict Resolution
No full textInternational audienceDue to uncertainties in weather conditions, trajectory prediction and constant flight evolution, controlling traffic in a sector is a dynamic problem. Furthermore, when the traffic increases, Air traffic control can become a complex dynamic optimization problem difficult to handle by human operators. In the context of offering air traffic controllers intelligent decision support tools adapted to the dynamic nature of traffic, we compare two options to address this issue. Previous work has already used an evolutionary algorithm to solve conflicts at given time steps. In this paper, we compare two different approaches using this evolutionary algorithm. The first one periodically calls an automatic solver, and the second one uses a memory method to guide successive resolutions. In order to choose the more adapted, we test them on different scenarios of continuous traffic. The memory approach can handle higher densities by maneuvering fewer aircraft and inducing lower delays. It is also more stable over time as early planned maneuvers are more likely to comply to effective maneuvers
Reachability Set Analysis of Closed-Loop Nonlinear Systems with Neural Network Controllers
No full textInternational audienceA forward reachability analysis method for the safety verification of nonlinear systems controlled by neural networks is presented. The proposed method relies on abstracting the activation functions in the neural networks (NN) by quadratic constraints (QCs) resorting to local sector bounds. To tackle the system nonlinearity, the nonlinear model is embedded into a linear parameter varying (LPV) representation. An outer-approximation of the forward reachable set of the closed-loop system is obtained using semidefinite programming. A numerical example clearly demonstrates the applicability of the proposed method. Comparison with some available methods reveals that the provided approach may potentially lead to less conservative results