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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)...
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.
In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.
A design technique for the stabilization of 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.
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....
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...
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...
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.
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.
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...
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...
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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