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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...
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.
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 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...
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...
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...
Six models of antiangiogenic therapy are compared and analyzed from control-theoretic point of view. All of them consist of a model of tumor growth bounded by the capacity of a vascular network developed by the tumor in the process of angiogenesis and different models of dynamics of this network, and are based on the idea proposed by Hahnfeldt et al. Moreover, we analyse optimal control problems resulting from their use in treatment protocol design.
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension,...
The paper considers a methodology of mathematical modeling of
ecological-economic
processes at the regional level. The basis of the model is formed by equations,
which describe
two interacting blocks: economic and ecological ones. Equations of the economic
block are represented
by relations of generalized inter-branch balance, while the ecological part is
described
in terms of differential equations with deviations with respect to some given
state of natural resources.
Issues of i) information...
Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every time step...
Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every time step...
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