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Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control…
This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…
We present a theoretical study of the optimal control of a qubit interacting with a structured environment. We consider a model system in which the bath is a bosonic reservoir at zero temperature and the qubit frequency is the only control…
In this paper we consider three different synchronization problems consisting in designing a nonlinear feedback unidirectional coupling term for two (possibly chaotic) dynamical systems in order to drive the trajectories of one of them, the…
We present here a new approach of the partial control method, which is a useful control technique applied to transient chaotic dynamics affected by a bounded noise. Usually we want to avoid the escape of these chaotic transients outside a…
The collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied when the natural frequency distribution does not possess an even symmetry with respect to the average natural frequency…
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the solution -- and the so-called singular limit. First, the existence…
We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal.…
We explore rectification phenomena in a system where two-dimensional random walkers interact with a funnel-shaped ratchet under two distinct classes of reflection rules. The two classes include the angle of reflection exceeding the angle of…
In this paper, we consider a class of optimal control problems for a one-dimensional time-discrete constrained quasilinear diffusion state-systems of singular Allen--Cahn types and its regularized approximating problems. We note that the…
Shared resources synchronization is a well studied problem, in both shared memory environment or distributed memory environment. Many synchronization mechanisms are proposed, with their own way to reach certain consistency level. This…
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…
This paper presents a controller design framework aiming to balance control performance and actuation rate. Control performance is evaluated by an infinite-horizon average cost, and the number of control actions is penalized via…
The present paper addresses the problem of existence of an (output) feedback law to the purposes of asymptotically steering to zero a given controlled variable, while keeping all state variables bounded, for any initial conditions in a…
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving…
The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are…