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Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support

Luis Alberto Fernández, Alexander Yuri Khapalov (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.

Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti, Jean-Claude Vivalda (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...

Controllability theorem for nonlinear dynamical systems

Michał Kisielewicz (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.

Controllable graphs

D. Cvetković, P. Rowlinson, Z. Stanić, M. G. Yoon (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Controllablity of a quantum particle in a 1D variable domain

Karine Beauchard (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function ϕ of the particle and the control is the length l(t) of the potential well. We prove the following controllability result : given φ 0 close enough to an eigenstate corresponding to the length l = 1 and φ f close enough to another eigenstate corresponding to the length l=1, there exists a continuous function l : [ 0 , T ] → ℝ + * with T > 0, such that l(0)...

Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Grigory M. Sklyar, Grzegorz Szkibiel (2013)

International Journal of Applied Mathematics and Computer Science

Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally...

Derivation of effective transfer function models by input, output variables selection

Nicos Karcanias, Konstantinos G. Vafiadis (2002)

Kybernetika

Transfer function models used for early stages of design are large dimension models containing all possible physical inputs, outputs. Such models may be badly conditioned and possibly degenerate. The problem considered here is the selection of maximal cardinality subsets of the physical input, output sets, such as the resulting model is nondegenerate and satisfies additional properties such as controllability and observability and avoids the existence of high order infinite zeros. This problem is...

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In the constrained...

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In...

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