Related papers: Control of the Continuity Equation with a Non Loca…

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents…

Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…

Motivated by fatigue damage models, this paper addresses optimal control problems governed by a non-smooth system featuring two non-differentiable mappings. This consists of a coupling between a doubly non-smooth history-dependent evolution…

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…

This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…

We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the…

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a…

This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…

In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…

The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…

We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical…

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…

In this paper we study the approximate controllability and existence of optimal control of impulsive fractional semilinear delay differential equations with non-local conditions. We use Sadovskii's fixed point theorem, semigroup theory of…

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…