Exact controllability of linear dynamical systems: A geometrical approach

María Isabel García-Planas

Displaying similar documents to “Exact controllability of linear dynamical systems: A geometrical approach”

Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$ -control only in the Dirichlet Boundary condition

I. Lasiecka, R. Triggiani (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder $\Omega\times\left[0,T\right]$ of $\mathbb{R}^{n+1}$ , via boundary controls acting on its lateral surface.

Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$ -control only in the Dirichlet Boundary condition

I. Lasiecka, R. Triggiani (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type

Karine Beauchard (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator $\partial_{x}^{2} + {| x |}^{2 γ} \partial_{y}^{2}$ ( $γ > 0$ ) in the rectangle $(x, y) \in (- 1, 1) \times (0, 1)$ or with the Kolmogorov-type operator $v^{γ} \partial_{x} f + \partial_{v}^{2} f$ ( $γ \in {1, 2}$ ) in the rectangle $(x, v) \in 𝕋 \times (- 1, 1)$ , under an additive control supported in an open subset $ω$ of the space domain. We prove that the Grushin-type...

Null controllability of Grushin-type operators in dimension two

Karine Beauchard, Piermarco Cannarsa, Roberto Guglielmi (2014)

Journal of the European Mathematical Society

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We study the null controllability of the parabolic equation associated with the Grushin-type operator $A = \partial_{x}^{2} + {|x|}^{2 γ} \partial_{γ}^{2}, (γ > 0)$ , in the rectangle $Ω = (- 1, 1) \times (0, 1)$ , under an additive control supported in an open subset $ω$ of $Ω$ . We prove that the equation is null controllable in any positive time for $γ < 1$ and that there is no time for which it is null controllable for $γ > 1$ . In the transition regime $γ = 1$ and when $ω$ is a strip $ω = (a, b) \times (0, 1) (0 < a, b \leq 1)$ ), a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks...

On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata Sikora (2019)

Kybernetika

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The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function $f$ . The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time $t > 0$ is presented....

Controllability of a quantum particle in a 1D variable domain

Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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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 $l : [0, T] \to ℝ_{+}^{*}$ with $T > 0$ , such that $l (0) = 1$ and $l (T) = 1$ ,...

Cone-type constrained relative controllability of semilinear fractional systems with delays

Beata Sikora, Jerzy Klamka (2017)

Kybernetika

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The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function $f$ . The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are...

Alternate checking criteria for reachable controllability of rectangular descriptor systems

Vikas Kumar Mishra, Nutan Kumar Tomar (2017)

Kybernetika

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Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions. A comprehensive study of different notions of controllability for linear descriptor systems is performed. Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than...

Bounded-input-bounded-state stabilization of switched processes and periodic asymptotic controllability

Andrea Bacciotti (2017)

Kybernetika

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The main result of this paper is a sufficient condition for the existence of periodic switching signals which render asymptotically stable at the origin a linear switched process defined by a pair of $2 \times 2$ real matrices. The interest of this result is motivated by the application to the problem of bounded-input-bounded-state (with respect to an external input) stabilization of linear switched processes.

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.