1,720,998 research outputs found
AUTONOMOUS VEHICLES DRIVING TRAFFIC: THE CAUCHY PROBLEM*
Full text linkThis paper deals with the Cauchy problem for a PDE-ODE model, where a system of two conservation laws, namely the Two-Phase macroscopic model proposed in [Rinaldo M. Colombo, Francesca Marcellini, and Michel Rascle, SIAM J. Appl. Math., 70(7):2652–2666, 2010], is coupled with an ordinary differential equation describing the trajectory of an autonomous vehicle (AV), which aims to control the traffic flow. Under suitable assumptions, we prove a global-in-time existence result
Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost
No full textWe study viscosity solutions of Hamilton-Jacobi equations that arise in optimal control problems with unbounded controls and discontinuous Lagrangian. In our assumptions, the comparison principle will not hold, in general. We prove optimality principles that extend the scope of the results of [23] under very general assumptions, allowing unbounded controls. In particular, our results apply to calculus of variations problems under Tonelli type coercivity conditions. Optimality principles can be applied to obtain necessary and sufficient conditions for uniqueness in boundary value problems, and to characterize minimal and maximal solutions when uniqueness fails. We give examples of applications of our results in this direction
A Time Dependent Optimal Harvesting Problem with Measure Valued Solutions.
No full textThe paper is concerned with the optimal harvesting of a marine park, which is described by a parabolic heat equation with Neumann boundary conditions and a nonlinear source term. We consider a cost functional, which is linear with respect to the control; hence the optimal solution can belong to
the class of measure-valued control strategies. For each control function, we prove existence, uniqueness and stability estimates for solutions of the parabolic equation. Moreover, we prove the existence of an optimal solution. Finally, some numerical simulations conclude the paper
Vanishing viscosity for mixed systems with moving boundaries
No full textWe consider a system of scalar balance laws in one space dimension coupled with
a system of ordinary differential equations. The coupling acts through the (moving) boundary
condition of the balance laws and the vector fields of the ordinary differential equations. We
prove the existence of solutions for such systems passing to the limit in a vanishing viscosity
approximation
Well Posedness and Control in a NonLocal SIR Model
No full textSIR models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolution of the S and R populations. It is then natural to seek the “best” vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies
Vanishing Viscosity for Traffic on Networks
No full textWe consider the vanishing viscosity approximation of the traffic model, proposed by Lighthill, Whitham, and Richards, on a network composed by a single junction with n incoming and m outgoing roads. We prove that a solution of the parabolic approximation exists and, as the viscosity vanishes, the solution of the parabolic problem converges to a solution of the original problem
A Time Dependent Optimal Harvesting Problem with Measure Valued Solutions.
Full text linkThe paper is concerned with the optimal harvesting of a marine park, which is described by a parabolic heat equation with Neumann boundary conditions and a nonlinear source term. We consider a cost functional, which is linear with respect to the control; hence the optimal solution can belong to
the class of measure-valued control strategies. For each control function, we prove existence, uniqueness and stability estimates for solutions of the parabolic equation. Moreover, we prove the existence of an optimal solution. Finally, some numerical simulations conclude the paper
Optimal strategies for a time-dependent harvesting problem
No full textWe focus on an optimal control problem, introduced by Bressan and
Shen in~\cite{BS1} as a model for fish harvesting. We consider the
time-dependent case and we establish existence and uniqueness of an
optimal strategy, and sufficient conditions for optimality. We
also consider a related differential game that models the situation
where there are several competing fish companies and we prove
existence of Nash equilibria. From the technical viewpoint, the
most relevant point is establishing the uniqueness result. This
amounts to prove precise a-priori estimates for solutions of
suitable parabolic equations with measure-valued coefficients. All
the analysis is developed in the case when the fishing domain is
one-dimensional
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