Catálogo de publicaciones - libros

The objective of this paper is to present the grand schemes of a model to be used in an agricultural Decision support System. We start by explaining and justifying the need for a hybrid system that uses both Multi-Agent System and Constraint Programming paradigms. Then we show our approach for Constraint Programming and Multi-Agent System mixing based on the concept of . Also, we present some concrete constraints and agents to be used in an application based on our proposed approach for modeling the problem of water use for agricultural purposes.

This work presents the principal algebraic, arithmetic and geometrical properties of the spline functions in the temporal space as well as in the frequencial space. Thanks to their good properties of regularity, of smoothness and compactness in both spaces, precise and powerful computations implying spline functions can be considered. The main algebraic property of spline functions is to have for coefficients of their functional expansion of a considered function, the whole set of partial or total derivatives up to the order k of the considered function. In this way spline function can be defined as the interpolating functions of the set of the all Taylor Mac Laurin expansion up to the degree defined at each point of discretization of the considered studying function. This fundamental property allows a much easier representation of complex systems in the linear case as well as in the nonlinear case. Then traditional differential and integral calculus lead in the spline functional spaces to new functional and invariant calculus.

In this article, we describe a method to solve differential equations involved in dynamical nonlinear problems with spline functions and their algebraic properties. spline functions generate time continuous and derivable approximations. These functions seem to be very efficient in several applied nonlinear differential problems. The computation of functions involved in nonlinear dynamical problem uses the algebraic methods known as Gröbner Bases, which are more robust, more accurate and often more efficient than the purely numerical methods. An example on solving nonlinear differential equations using these methods is presented.

One problem for efficient control of complex systems is to take into account the influence of unknown dynamics in interaction with a fixed defined one by a set of defined time varying parameters behaviour coming from coupling partially unknown dynamics. Under the assumption of robust model, nonlinear state feedback decoupling methods can be used for the control of such systems. We show in our paper, that if these parameters are slowly varying in time before the main dynamics (the exact mathematical meaning of this notion is given in the article), the classical decoupling methods remain valid with parameterized laws, but if parameters dynamic are non negligible before the main dynamic, we are in the fast varying parameters case, and we show that in this case decoupling methods operators must be changed in order to include these dynamical effects. We show also that in this case the use of classical decoupling methods, leads to non effcient control and multiple spurious effects. The computation of the static and dynamic feedback laws, in case of fast varying parameters, are given, for nonlinear decoupling methods, linearization and rejection of perturbations, as the research of the functional invariants of the output. A robust example in robotics is given, and the contribution of parameters dynamic is shown.

We present here, in the framework of resonnant behaviours, an eigenfrequency invariance properties for loaded flexural and torsional deformable bodies. We found that under a preload condition each eigenfrequency is invariant versus the load . For the mode 7 and beyond the preload conditions are less than = 1, and the seven first modes (form 0 to 6) can be easily modelled by polynomial functions of in the neighbourhood of useful . These properties open the way to new finite dimension controllers.

We present here in the framework of resonnant behaviours, eigenfrequencies invariance properties for compliant loaded flexural and torsional deformable bodies. We will see that compliant behaviours create a new order on the system which leads to a large invariance property in the ( × × ) space. As in the preceeding paper the notion of preload condition can be used and we see that compliance diminishes drastically the preload condition.