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Scope and generalization of the theory of linearly constrained linear regulator

Paolo Alessandro, Elena de Santis (1999)

Kybernetika

A previous paper by the same authors presented a general theory solving (finite horizon) feasibility and optimization problems for linear dynamic discrete-time systems with polyhedral constraints. We derived necessary and sufficient conditions for the existence of solutions without assuming any restrictive hypothesis. For the solvable cases we also provided the inequative feedback dynamic system, that generates by forward recursion all and nothing but the feasible (or optimal, according to the cases)...

Separation principle for nonlinear systems: a bilinear approach

Mohamed Hammami, Hamadi Jerbi (2001)

International Journal of Applied Mathematics and Computer Science

In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.

Simultaneous output-feedback stabilization for continuous systems in Banach spaces

Fouad M. AL-Sunni, Frank L. Lewis (1998)

Kybernetika

A design technique for the stabilization of M linear systems by one constant output-feedback controller is developed. The design equations are functions of the state and the control weighting matrices. An example of the stabilization of an aircraft at different operating points is given.

Single input controllability of a simplified fluid-structure interaction model

Yuning Liu, Takéo Takahashi, Marius Tucsnak (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem....

Sixty years of cybernetics: a comparison of approaches to solving the H 2 control problem

Vladimír Kučera (2008)

Kybernetika

The H2 control problem consists of stabilizing a control system while minimizing the H2 norm of its transfer function. Several solutions to this problem are available. For systems in state space form, an optimal regulator can be obtained by solving two algebraic Riccati equations. For systems described by transfer functions, either Wiener-Hopf optimization or projection results can be applied. The optimal regulator is then obtained using operations with proper stable rational matrices: inner-outer...

Smooth homogeneous asymptotically stabilizing feedback controls

H. Hermes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

If a smooth nonlinear affine control system has a controllable linear approximation, a standard technique for constructing a smooth (linear) asymptotically stabilizing feedbackcontrol is via the LQR (linear, quadratic, regulator) method. The nonlinear system may not have a controllable linear approximation, but instead may be shown to be small (or large) time locally controllable via a high order, homogeneous approximation. In this case one can attempt to construct an asymptotically stabilizing...

Stabilisation d’une poutre. Étude du taux optimal de décroissance de l’énergie élastique

Francis Conrad, Fatima-Zahra Saouri (2002)

ESAIM: Control, Optimisation and Calculus of Variations

On se propose d’étudier la stabilité d’une poutre flexible homogène, encastrée à une extrémité. À l’autre extrémité est attachée une masse ponctuelle où on applique un moment proportionnel à la vitesse de déplacement angulaire. On montre par une analyse spectrale que le taux optimal de décroissance de l’énergie est déterminé par l’abscisse spectrale du générateur infinitésimal du semi-groupe associé au problème.

Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique

Francis Conrad, Fatima-Zahra Saouri (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.

Stabilisation exponentielle d’une équation des poutres d’Euler-Bernoulli à coefficients variables

My Driss Aouragh, Naji Yebari (2009)

Annales mathématiques Blaise Pascal

Dans ce travail, nous étudions la propriété de base de Riesz et la stabilisation exponentielle pour une équation des poutres d’Euler-Bernoulli à coefficients variables sous un contrôle frontière linéaire dépendant de la position (resp. l’angle de rotation), de la vitesse et de la vitesse de rotation dans le contrôle force (resp. moment). Nous montrons qu’il existe une suite de fonctions propres généralisées qui forme une base de Riesz de l’espace d’énergie considéré, et qu’il y a stabilité exponentielle...

Stabilisation frontière de problèmes de Ventcel

Amar Heminna (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system...

Stabilisation polynomiale et analytique de l’équation des ondes sur un rectangle

Ammar Moulahi, Salsabil Nouira (2010)

Annales mathématiques Blaise Pascal

On considère l’équation des ondes sur un rectangle avec un feedback de type Dirichlet. On se place dans le cas où la condition de contrôle géométrique n’est pas satisfaite (BLR Condition), ce qui implique qu’on n’a pas stabilité exponentielle dans l’espace d’énérgie. On prouve qu’on peut trouver un sous espace de l’espace d’énergie tel qu’on a stabilité exponentielle. De plus, on montre un résultat de décroissance polynomiale pour toute donnée initiale régulière.

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