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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 of the Primitive Equations of the ocean with Lagrangian observations

Maëlle Nodet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...

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 control problems for variational inequalities with controls in coefficients and in unilateral constraints

Igor Bock, Ján Lovíšek (1987)

Aplikace matematiky

We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.

Optimal control problems on parallelizable riemannian manifolds : theory and applications

Ram V. Iyer, Raymond Holsapple, David Doman (2006)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group S E ( 3 ) , which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...

Optimal control problems on parallelizable Riemannian manifolds: theory and applications

Ram V. Iyer, Raymond Holsapple, David Doman (2005)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group SE(3), which is also a parallelizable Riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions...

Optimal control problems with upper semicontinuous Hamiltonians

Arkadiusz Misztela (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value function is...

Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics

Arturo Enrique Gil García, Vadim Azhmyakov, Michael V. Basin (2014)

Kybernetika

This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...

Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...

Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetric-like inequalities. As a byproduct...

Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...

Optimal design in small amplitude homogenization

Grégoire Allaire, Sergio Gutiérrez (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide...

Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem

Roman Šimeček (2013)

Applications of Mathematics

A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...

Optimal design of cylindrical shell with a rigid obstacle

Ján Lovíšek (1989)

Aplikace matematiky

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...

Currently displaying 561 – 580 of 686