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résumé Considérons — formellement tout d’abord — un système dont l’état y = y(t;v) = y(v) est donné par la solution de 1.1 <m:math display=’block’> <m:mrow> <m:msup> <m:mi>y</m:mi> <m:mo>″</m:mo> </m:msup> <m:mo>+</m:mo><m:mi>A</m:mi><m:mi>y</m:mi><m:mo>=</m:mo><m:mn>0</m:mn><m:mtext>...
An optimization algorithm for finding a point satisfying infinitely many inequality constraints is presented. The algorithm approximates the maximum of an infinite number of inequalities at a point by performing a set of random experiments, resulting in a finite number of inequalities, over which the maximum is taken. It uses a constraint-dropping scheme, by which it eliminates points from a constraint-set...
The optimal shape design of a two dimensional body on a rigid foundation is analyzed. The problem is how to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that a certain energy integral (total potential energy, for example) will be minimized. It is assumed that the material of the body is elastic. Some remarks will be given concerning the design...
Résumé Pour minimiser une fonction sur Rn en présence de m contraintes d’égalité non linéaires, on propose un algorithme ayant les caractéristiques suivantes: chaque itération comprend deux pas de restauration des contraintes et un pas de minimisation de la fonction, les contraintes sont linéairisées une fois par itération, une matrice d’ordre n-m (approximation du hessien réduit du lagrangien) est...
A methodology is presented for the replacement of original worst case control system design specifications, which correspond to a set of intractable, semi-infinite inequalities, with a more conservative set of specifications which transcribe into tractable semi-infinite inequalities. These inequalities can either be solved directly or they can be incorporated into an optimal design semi-infinite optimization...
Engineering design problems often involve the solution of one or several constrained minimax optimization problems. It is sometimes crucial that all iterates constructed when solving such problems satisfy a given set of ‘hard’ inequality constraints, and generally desirable that the (maximum) objective function value improve at each iteration. In this paper, we propose an algorithm of the sequential...
Quasilinear problems of optimal control and nonlinear programming are investigated. The algorithms for approximate solution of the optimization problems are worked out on the base of the support [Gabasov R., Kirillova F.M. Constructive Methods of Optimization. P. II. Control Problems. Minsk, University Press, 1984] and asymptotic methods. The algorithms are applied to the solution of general nonlinear...
In this paper the algorithms for minimax optimal control problems are presented. Two linearization algorithms are first considered and then the new algorithms based upon a concept of conjugate directions are given together with convergence conditions. Using realistic example of a large dimension it is demonstrated that the linearization algorithms can be effectively applied to solve minimax dynamic...
The two-stage Feasible Directions Algorithm for Nonlinearly Constrained Optimization determines a search direction in two stages.First a descent direction is defined; by modifying it, a feasible descent direction is then obtained. We apply this idea in order to state a new feasible directions algorithm based on a well known method for Nonlinear Programming studied by WILSON, HAN and POWELL. ...
This report deals with the problem of guaranteed estimation of the state of a distri-buted system on the basis of available measurements. The disturbances in the initial dis-tribution, in the system inputs and in the available observations are assumed to be unk-nown in advance. No statistical information on these is given and it is only the restrictions on the possible realizations of these functions...
Summary We present two algorithms to compute the eigenvalues of a clam of closed loop linear hyperbolic contrai systems describing the vibrations of a linear structure made up of interconnected beams. They are based on an extension to analytic functions of the H. Kuhn’s method ta find the zeros of polynomials. These algorithms are very selective and accurate even for eigenvalues of large moduli. In...
An exposition of some of the results in continuous-time adaptive control systems in stability is given. We study instabilities that arise due to: high adaptation gain and/or large reference signals, interplay between unmodeled dynamics and output dis turbances and crosscoupling in decentralized controllers. In all cases simple worked examples are included to illustrate the phenomena. In the disturbance-free...
We consider a class of single input single output second order nonlinear systems whose coefficients are bounded and have bounded time-variation. We describe an adaptive observer/identifier for these systems and derive sufficient conditions on the system and on the inputs that guarantee global stability of this adaptive observer. We present an application to a robot manipulator with two degrees of...
Resume Nous présentons dans cet article quelques résultats de modélisation, d’identification et de commande adaptative d’un bras manipulateur souple un degré de liberté. La modélisation de ce procédé est basée sur la méthode des éléments finis, appliquée une poutre. Diverses approches, pour l’identification du procédé, ont été utilisées. Parmi elles, les méthodes paramétriques ont donné des modèles...
This paper presents an adaptive extension of the external linearization feedback control applied to manipulators. The design of the adaptation law is based on a Lyapunov stability analysis. This algorithm ensures stability of the error model, even in case of poor knowledge of the model parameters, as well as good robustness properties in presence of unmodelled bounded disturbances.
Recently an analogy between conventional linear system theory and the relatively new theory on discrete-event dynamic systems has been shown to exist. The system descrip-tion in the new theory resembles the one of the conventional theory, provided that the operations addition and multiplication are replaced by maximization and addition respectively. One also speaks of a system in the max-algebra,...
We examine a modular approach to the synthesis of supervisory controls for discrete-event systems. Discrete-event systems are modelled by automata together with a mechanism for enabling and disabling a subset of state transitions. The basic problem of interest is to ensure by appropriate supervision that the closed loop behavior of the system lies within a given legal behavior. Assuming this behavior...
Discrete-event systems, when studied from a control-theorist’s point of view, can be represented by a linear dynamic system in the so-called max-algebra, or dioïd. Some methods used in the usual linear-system theory still work in this algebra: z-transform, duality,... Problems arise when trying to reduce the state-dimension, or to define a canonical state-representation. This is due to the...
An important class of production systems are modeled by N-stage buf-fered transfer lines. The system states consists of the operational conditions of the workstations and the levels of the material in the buffers. The purpose of this paper is to study the asymptotic behaviour of the inner-state trasient density functions. We show the convergence towards a steady-state with exponential speed.
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