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Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows

Max D. Gunzburger, O. Yu. Imanuvilov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, i.e., a boundary value problem from...

Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions

Karl Kunisch, Marcus Wagner (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider optimal control problems for the bidomain equations of cardiac electrophysiology together with two-variable ionic models, e.g. the Rogers–McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions. The proof is based on a stability estimate for the primal equations and an existence theorem for weak solutions of the adjoint system.

Optimal control problem and maximum principle for fractional order cooperative systems

G. M. Bahaa (2019)

Kybernetika

In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...

Optimal design of cylindrical shells

Peter Nestler, Werner H. Schmidt (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...

Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion

Yuncheng You (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...

Optimal measures for the fundamental gap of Schrödinger operators

Nicolas Varchon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the potential which minimizes the fundamental gap of the Schrödinger operator under the total mass constraint. We consider the relaxed potential and prove a regularity result for the optimal one, we also give a description of it. A consequence of this result is the existence of an optimal potential under L1 constraints.

Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2016)

Journal of the European Mathematical Society

We consider the wave and Schrödinger equations on a bounded open connected subset Ω of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset ω of Ω during a time interval [ 0 , T ] with T > 0 . It is well known that, if the pair ( ω , T ) satisfies the Geometric Control Condition ( ω being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...

Optimal snapshot location for computing POD basis functions

Karl Kunisch, Stefan Volkwein (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The construction of reduced order models for dynamical systems using proper orthogonal decomposition (POD) is based on the information contained in so-called snapshots. These provide the spatial distribution of the dynamical system at discrete time instances. This work is devoted to optimizing the choice of these time instances in such a manner that the error between the POD-solution and the trajectory of the dynamical system is minimized. First and second order optimality systems are given. Numerical...

Optimality conditions for nonconvex variational problems relaxed in terms of Young measures

Tomáš Roubíček (1998)

Kybernetika

The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler–Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler–Lagrange equation with one part from the Weierstrass condition.

Optimality conditions for semilinear parabolic equations with controls in leading term

Hongwei Lou (2011)

ESAIM: Control, Optimisation and Calculus of Variations

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

Optimality conditions for semilinear parabolic equations with controls in leading term*

Hongwei Lou (2011)

ESAIM: Control, Optimisation and Calculus of Variations

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

Optimization and identification of nonlinear uncertain systems

Jong Yeoul Park, Yong Han Kang, Il Hyo Jung (2003)

Czechoslovak Mathematical Journal

In this paper we consider the optimal control of both operators and parameters for uncertain systems. For the optimal control and identification problem, we show existence of an optimal solution and present necessary conditions of optimality.

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