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This paper describes algorithms for the optimal control of multistate systems. As a test problem we use the reaction diffusion equation governing the steady-states of an enzyme system. The originality of such problems is that the state is not uniquely defined as a function of the control.
Resume Les algorithmes de résolution de problèmes d'optimisation basés sur la programmation quadratique successive sont réputés pour leur efficacité. Ils peuvent cependant être mis en difficulté dans le cas où le sous problème quadratique est, à certaines itérations, mal posé. Nous donnons un moyen de calculer la direction de descente d'une fonctionnelle pénalisée (différentiable ou non), grâce à...
In this paper we present an algorithm ASVD for the computation of the singular value decomposition (SVD). The method presented is a power method for calculating the largest triplets of the SVD of a matrix A when multiplication is "cheap". The method used bears a lot of similitude with the power method for finding the eigenvalues of a symmetric matrix M. The triplets are found one after another...
The history of optimal control processes has begun with the discovery of Pontryagin maximum principle [1]. This classical result has allowed to solve many applied problems and has become the basic means at constructing numerical methods of optimal control [2]. The given paper contains the recent results on solution of linear-quadratic extremal problems, optimization of linear dynamic systems with...
A numerically stable algorithm and a program for pole assignment of linear single-input systems are presented. The algorithm is based on orthogonal reduction of the closed-loop system matrix to upper quasitriangular form whose diagonal blocks correspond to the desired poles. The algorithm performs equally well with real and complex, distinct and multiple desired poles. The number of the necessary...
Résumé L'étude de la stabilité du mouvement des pales d'un hélicoptère en vol d'avancée, en atmosphère turbulente, conduit à l'étude de la stabilité de la solution d'une équation différentielle stochastique bilinéaire, à coefficients fonctions périodiques du temps. On indique comment des résultats récents de ARNOLD et KLIEMAN [2] se généralisent à cette situation, puis on étudie un algorithme qui...
This article addresses the Markov decision problem with long-run average reward Vu when there is a global constraint to be satisfied: Iu≤α, where Iu is also a long-run average. Using Lagrange multiplier techniques, existence of an optimal stationary policy is proven. Unlike the unconstrained theory,...
This paper is concerned with some properties of transfer functions in two variables which can be realized by classes of 2D systems characterized by pairs of state updating matrices which generate algebras with special structures. Two situations are mainly considered. The first deals with pairs of matrices which generate a solvable Lie algebra (i.e. are simultaneously triangularizable). The second...
The controllability preservation of controlled non stochastic continuous time linear system after discretization has been studied in [6] then in [10], [11], [12]. We study a similar problem : the controllability preservation of a non controlled stochastic linear system when the discretization process is run by renewal process. This study is concerned with discrete time and set necessary...
Résumé Dans cet article nous commencerons par rappeler la définition d'un système implicite et certaines de leur propriétés. Nous définirons ensuite la notion de système inverse, en prouvant l'existence et l'unicité du point de vue de la représentation externe. Dans un deuxième temps, nous montrerons comment la théorie des systèmes implicites permet d'écrire facilement le système inverse, et d'en...
In order to take into account the fact that the data generaly given for a linear system identification are truncated and subject to numerical errors, the paper considers the identification problem as an approximation one. We use a L2 norm, and suppose that the system is stable so that the truncation error may be considered small (at least theoretically). Using results of [2] we examine...
A computer-aided control system design package, called CTRL-C, provides a matrix workbench for the analysis and design of multivariable systems. CTRL-C is an interactive environment with a comprehensive set of tools for analysis, identification, design, and evaluation. A unified software system is possible for matrix analysis, engineering graphics, control system design, and digital signal...
The first commercial system of CAD in this field, SIRENA gives the user access to advanced techniques in simulation, signal analysis and model synthesis. SIRENA has been built to help all those who are involved in the conception, development and realisation of systems where the control of the dynamic evolution of the process is of prime importance. SIRENA belongs to a new generation of simulators...
This paper presents an interactive package — CASAD, for the Computer Aided Systems Analysis and Design. CASAD implements a complete methodology for CAD of linear multivariable control systems by state-space methods. The main steps of this methodology are: (1) plant modeling; (2)analysis of system properties; (3) design of robust compensators; and (4) simulation of control configurations. CASAD is...
We consider the adaptive equalization of an unknown linear time-invariant channel without observations of the input sequence, by updating the impulse response coefficients of the equalizer with the output of the channel times a memoryless nonlinear function of the equalizer output. To date, no such function is known to result in global convergence to the inverse of the channel when the input consists...
In this paper we first develop a new kind of numerical implementation of the so-called "square root filters" used for Kalman filtering. The method is based on the choice of an initial state transformation which "condensed" the model. This preliminary transformation can be done without loss of numerical precision and leads to substantial savings in computing time for the subsequent...
We consider the prediction of stationary stochastic processes with non-zero mean. When the covariance of the process is known, but the mean is not, the classical approach is to first estimate the mean from the past data, and then apply an optimal predictor to the zero-mean residuals. Bastin and Henriet [1] showed that an alternative was to use a predictor based on "variograms" rather than...
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