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Limitations on the control of Schrödinger equations

Reinhard Illner, Horst Lange, Holger Teismann (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control ( E ( t ) · x ) u is not controllable...

Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, Onesimo Hernández-Lerma (2001)

Applicationes Mathematicae

We consider a class of d -valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation x t + 1 = G ( x t , a t ) + ξ t (t = 0,1,... ), for each fixed n = 0,1,..., where the ξ t are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function G as n → ∞. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC) optimal for...

Linear adaptive structure for control of a nonlinear MIMO dynamic plant

Stanisław Bańka, Paweł Dworak, Krzysztof Jaroszewski (2013)

International Journal of Applied Mathematics and Computer Science

In the paper an adaptive linear control system structure with modal controllers for a MIMO nonlinear dynamic process is presented and various methods for synthesis of those controllers are analyzed. The problems under study are exemplified by the synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system, use is made of a set of (stable)...

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

Hatamleh, Raed (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.

Linear independence of boundary traces of eigenfunctions of elliptic and Stokes operators and applications

Roberto Triggiani (2008)

Applicationes Mathematicae

This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators. Part I: Let λ i be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let φ i j j = 1 i be the corresponding linearly independent (normalized) eigenfunctions...

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