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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 design of the cooling plunger cavity

Petr Salač (2013)

Applications of Mathematics

An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity. The cost functional is the second power of the norm in the weighted space L r 2 of difference...

Optimal internal dissipation of a damped wave equation using a topological approach

Arnaud Münch (2009)

International Journal of Applied Mathematics and Computer Science

We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection...

Optimal placement of controls for a one-dimensional active noise control problem

Fariba Fahroo (1998)

Kybernetika

In this paper, we investigate the optimal location of secondary sources (controls) to enhance the reduction of the noise field in a one-dimensional acoustic cavity. We first formulate the active control strategy as a linear quadratic tracking (LQT) problem in a Hilbert space, and then formulate the optimization problem as minimizing an appropriate performance criterion based on the LQT cost function with respect to the location of the controls. A numerical scheme based on the Legendre–tau method...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity

Weijiu Liu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to a related open question raised by Alabau and Komornik...

Currently displaying 301 – 320 of 441