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An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov...

An application of the Fourier transform to optimization of continuous 2-D systems

Vitali Dymkou, Michael Dymkov (2003)

International Journal of Applied Mathematics and Computer Science

This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.

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...

An SQP trust region method for solving the discrete-time linear quadratic control problem

El-Sayed M.E. Mostafa (2012)

International Journal of Applied Mathematics and Computer Science

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution...

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...

Approximation of control problems involving ordinary and impulsive controls

Fabio Camilli, Maurizio Falcone (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative u ˙ . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of u ˙ . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation....

Aubry sets and the differentiability of the minimal average action in codimension one

Ugo Bessi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Let ℒ (x,u,∇u) be a Lagrangian periodic of period 1 in x1,...,xn,u. We shall study the non self intersecting functions u: Rn → R minimizing ℒ ; non self intersecting means that, if u(x0 + k) + j = u(x0) for some x0∈Rn and (k , j) ∈Zn × Z, then u(x) = u(x + k) + j ∀ x. Moser has shown that each of these functions is at finite distance from a plane u = ρ · x and thus has an average slope ρ; moreover, Senn has proven that it is possible to define the average action of u, which is usually called β ( ρ ) since...

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