\epsilon-regularity for systems involving non-local, antisymmetric operators

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations

Artificial co-drivers as a universal enabling technology for future intelligent vehicles and transportation systems

This position paper introduces the concept of artificial “co-drivers” as an enabling technology for future intelligent transportation systems. In Sections I and II, the design principles of co-drivers are introduced and framed within general human–robot interactions. Several contributing theories and technologies are reviewed, specifically those relating to relevant cognitive architectures, human-like sensory-motor strategies, and the emulation theory of cognition. In Sections III and IV, we present the co-driver developed for the EU project interactIVe as an example instantiation of this notion, demonstrating how it conforms to the given guidelines. We also present substantive experimental results and clarify the limitations and performance of the current implementation. In Sections IV and V, we analyze the impact of the co-driver technology. In particular, we identify a range of application fields, showing how it constitutes a universal enabling technology for both smart vehicles and cooperative systems, and naturally sets out a program for future research

Agent architecture for adaptive behaviours in autonomous driving

Evolution has endowed animals with outstanding adaptive behaviours which are grounded in the organization of their sensorimotor system. This paper uses inspiration from these principles of organization in the design of an artificial agent for autonomous driving. After distilling the relevant principles from biology, their functional role in the implementation of an artificial system are explained. The resulting Agent, developed in an EU H2020 Research and Innovation Action, is used to concretely demonstrate the emergence of adaptive behaviour with a significant level of autonomy. Guidelines to adapt the same principled organization of the sensorimotor system to other agents for driving are also obtained. The demonstration of the system abilities is given with example scenarios and open access simulation tools. Prospective developments concerning learning via mental imagery are finally discussed

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Artificial co-drivers as a universal enabling technology for future intelligent vehicles and transportation systems

This position paper introduces the concept of artificial “co-drivers” as an enabling technology for future intelligent transportation systems. In Sections I and II, the design principles of co-drivers are introduced and framed within general human–robot interactions. Several contributing theories and technologies are reviewed, specifically those relating to relevant cognitive architectures, human-like sensory-motor strategies, and the emulation theory of cognition. In Sections III and IV, we present the co-driver developed for the EU project interactIVe as an example instantiation of this notion, demonstrating how it conforms to the given guidelines. We also present substantive experimental results and clarify the limitations and performance of the current implementation. In Sections IV and V, we analyze the impact of the co-driver technology. In particular, we identify a range of application fields, showing how it constitutes a universal enabling technology for both smart vehicles and cooperative systems, and naturally sets out a program for future research

Will intelligent vehicles evolve into human-peer robots?

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Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

Global results on reset-induced periodic trajectories of planar systems

We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the balance between the energy dissipated during flows and the energy restored by resets, at jumps. The stability of the periodic orbit is studied with hybrid Lyapunov tools. The satisfaction of the so-called hybrid basic conditions ensures the robustness of the asymptotic stability. Extensions of the approach to more general mechanical systems are discussed.Work supported in part by ANR under project LimICoS, contract number 12 BS03 005 01, by the iCODE institute, research project of the Idex ParisSaclay, and by the University of Trento, grant OptHySYS.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by IEEE

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014