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Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

George Avalos, Irena Lasiecka (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function ℰ min ( T ) , as terminal time T ↓ 0 . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator 𝒜 , as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate...

Optimal control of a rotating body beam

Weijiu Liu (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical...

Optimal Control of a Rotating Body Beam

Weijiu Liu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose ...

Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

Hengyan Li, Shuguan Ji (2011)

Open Mathematics

This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore,...

Optimal control of systems determined by strongly nonlinear operator valued measures

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure...

Optimal design problems for a dynamic viscoelastic plate. I. Short memory material

Igor Bock (1995)

Applications of Mathematics

We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.

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 LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Ilyasse Aksikas, Joseph J. Winkin, Denis Dochain (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential...

Optimization problems for structural acoustic models with thermoelasticity and smart materials

Irena Lasiecka (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...

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