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A Brauer’s theorem and related results

Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

A continuation method for motion-planning problems

Yacine Chitour (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

A continuation method for motion-planning problems

Yacine Chitour (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms

Paolo Mercorelli (2012)

Kybernetika

In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...

A new approach to the constrained controllability problem

Ali Boutoulout, Layla Ezzahri, Hamid Bourray (2014)

Applicationes Mathematicae

We consider the problem of internal regional controllability with output constraints. It consists in steering a hyperbolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by characterizing the optimal control in terms of a subdifferential associated with the minimized functional.

A null controllability data assimilation methodology applied to a large scale ocean circulation model

Galina C. García, Axel Osses, Jean Pierre Puel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

A null controllability data assimilation methodology applied to a large scale ocean circulation model*

Galina C. García, Axel Osses, Jean Pierre Puel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

A singular controllability problem with vanishing viscosity

Ioan Florin Bugariu, Sorin Micu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? The characteristic of our viscous term is that it contains the fractional power α of the Dirichlet Laplace operator. Through the parameter α we may increase or decrease the strength of the high frequencies damping which allows us to cover a large class of dissipative mechanisms. The viscous term,...

A singular perturbation problem in exact controllability of the Maxwell system

John E. Lagnese (2001)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection,...

A Singular Perturbation Problem in Exact Controllability of the Maxwell System

John E. Lagnese (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for...

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