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A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

Jean-Paul Daniel (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...

A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure

Andrei Dmitruk, Ivan Samylovskiy (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.

An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

Andreas Rauh, Luise Senkel, Harald Aschemann, Vasily V. Saurin, Georgy V. Kostin (2016)

International Journal of Applied Mathematics and Computer Science

In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance,...

An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System

N. C. Apreutesei (2010)

Mathematical Modelling of Natural Phenomena

An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular...

Application of the optimal control theory to the wastewater elimination problem.

Lino José Alvarez-Vázquez, Alfredo Bermúdez, Aurea Martínez, Carmen Rodríguez, Miguel Ernesto Vázquez-Méndez (2002)

RACSAM

The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the ría of Arousa (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained...

Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance

Łukasz Delong (2012)

Applicationes Mathematicae

We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target...

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