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Controllability of a simplified model of fluid-structure interaction

S. Ervedoza, M. Vanninathan (2014)

ESAIM: Control, Optimisation and Calculus of Variations

This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, RAM: Res. Appl. Math. John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially...

Controllability of a slowly rotating Timoshenko beam

Martin Gugat (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an odd...

Controllability of a slowly rotating Timoshenko beam

Martin Gugat (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Consider a Timoshenko beam that is clamped to an axis perpendicular to the axis of the beam. We study the problem to move the beam from a given initial state to a position of rest, where the movement is controlled by the angular acceleration of the axis to which the beam is clamped. We show that this problem of controllability is solvable if the time of rotation is long enough and a certain parameter that describes the material of the beam is a rational number that has an even numerator and an...

Controllability of analytic functions for a wave equation coupled with a beam.

Brice Allibert, Sorin Micu (1999)

Revista Matemática Iberoamericana

We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model, microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time, related to the amount of analyticity of the...

Controllability of evolution equations and inclusions driven by vector measures

N.U. Ahmed (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on...

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Abada Nadjat, Benchohra Mouffak, Hammouche Hadda, Ouahab Abdelghani (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.

Controllability of invariant control systems at uniform time

Víctor Ayala, José Ayala-Hoffmann, Ivan de Azevedo Tribuzy (2009)

Kybernetika

Let G be a compact and connected semisimple Lie group and Σ an invariant control systems on G . Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time s Σ such that the system turns out controllable at uniform time s Σ . Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if A = ⋂ t > 0 A ( t , e ) denotes the reachable set from arbitrary...

Controllability of linear impulsive matrix Lyapunov differential systems with delays in the control function

Vijayakumar S. Muni, Raju K. George (2018)

Kybernetika

In this paper, we establish the controllability conditions for a finite-dimensional dynamical control system modelled by a linear impulsive matrix Lyapunov ordinary differential equations having multiple constant time-delays in control for certain classes of admissible control functions. We characterize the controllability property of the system in terms of matrix rank conditions and are easy to verify. The obtained results are applicable for both autonomous (time-invariant) and non-autonomous (time-variant)...

Controllability of linear impulsive systems – an eigenvalue approach

Vijayakumar S. Muni, Raju K. George (2020)

Kybernetika

This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation...

Controllability of nilpotent systems

Victor Bravo (1995)

Banach Center Publications

In this paper we study the controllability property of invariant control systems on Lie groups. In [1], the authors state: ``If there exists a real function strictly increasing on the positive trajectories, then the system cannot be controllable". To develop this idea, the authors define the concept of symplectic vector via the co-adjoint representation. We are interested in finding algebraic conditions to determine the existence of symplectic vectors in nilpotent Lie algebras. In particular, we...

Controllability of nonlinear discrete systems

Jerzy Klamka (2002)

International Journal of Applied Mathematics and Computer Science

Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear...

Controllability of nonlinear implicit fractional integrodifferential systems

Krishnan Balachandran, Shanmugam Divya (2014)

International Journal of Applied Mathematics and Computer Science

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

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