We consider a finite-dimensional control system $\left(\Sigma \right)\dot{x}\left(t\right)=f(x\left(t\right),u\left(t\right))$, such that there exists a feedback stabilizer k that renders $\dot{x}=f(x,k\left(x\right))$ globally asymptotically stable. Moreover, for (H,p,q) with H an output map and $1\le p\le q\le \infty$, we assume that there exists a ${𝒦}_{\infty }$-function α such that $\parallel H\left(x_u\right){\parallel }_q\le {\alpha (\parallel u\parallel }_p)$, where xu is the maximal solution of ${\left(\Sigma \right)}_k\dot{x}\left(t\right)=f(x\left(t\right),k\left(x\left(t\right)\right)+u\left(t\right))$, corresponding to u and to the initial condition x(0)=0. Then, the gain function $G_{(H,p,q)}$ of (H,p,q) given by 14.5cm $$G_{(H,p,q)}\left(X\right)\stackrel{\mathrm{def}}{=}\underset{{\parallel u\parallel }_p=X}{sup}{\parallel H\left(x_u\right)\parallel }_q,$$ is well-defined. We call profile of k for (H,p,q) any ${𝒦}_{\infty }$-function which is of the same order of...

We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are...

A method is presented to compute the activity of a radioactive source. The principle of the method is based on the tuning of b, the time constant of the RC circuit of the detector with l being the rate of emission of the source, using a statistical argument.The stochastical process involved refers to the distribution of the following random voltage:Vt = ∑(0 < ti ≤ t) Yi c-b(t - ti)where the ti are Poisson dates of emission and the Yi are random or deterministic pulse heights. The case of...

We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

This work studies the null-controllability of a class of abstract parabolic equations. The main contribution in the general case consists in giving a short proof of an abstract version of a sufficient condition for null-controllability which has been proposed by Lebeau and Robbiano. We do not assume that the control operator is admissible. Moreover, we give estimates of the control cost. In the special case of the heat equation in rectangular domains, we provide an alternative way to check...

This work studies the null-controllability of a class of abstract parabolic equations. The main contribution in the general case consists in giving a short proof of an abstract version of a sufficient condition for null-controllability which has been proposed by Lebeau and Robbiano. We do not assume that the control operator is admissible. Moreover, we give estimates of the control cost. In the special case of the heat equation in rectangular domains, we provide an alternative way to check...

In this paper, the observability of fuzzy logic second order control system is studied from the aspect of fuzzy differential equations. The fuzzy observability in the weak sense is created using the concept of “likelihood” to indicate on which level and along which solution the state is most likely observable. One of the initial state range has been derived with the given input and output. The result generalizes the previous results.

This paper deals with the local (around the equilibrium) optimal decentralized control of autonomous multivariable systems of nonlinearities and couplings between subsystems which can be expressed as power series in the state-space are allowed in the formulation. They only affect for the optimal performance integrals in cubic and higher terms in the norm of the initial conditions of the dynamical differential system. The basic hypothesis which is made is that the system is centrally-stabilizable...

In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties...

The purpose of this paper is to prove the minimum variance property of a new class of 2D, recursive, finite-dimensional filters. The filtering algorithms are derived from general basic assumptions underlying the stochastic modelling of an image as a 2D gaussian random field. An appealing feature of the proposed algorithms is that the image pixels are estimated one at a time; this makes it possible to save computation time and memory requirement with respect to the filtering procedures based on strip...