A branch and bound approach for minimizing the energy consumption of an electrical vehicle

National audienceIn this paper we discuss about the way to approximate the solution of an optimal control problem with a switched command. Our Method is based on a discretization technique associated with a Branch and Bound algorithm. The problem that we focus on is the minimization of the consumption of the energy of an electrical vehicle during some imposed displacements

Optimal time control to swing-up the inverted pendulum-cart in open-loop form

National audienceThis work deals with simulation on an Inverted Pendulum (IP). The control strategy of an IP is split into two main control phases: (i) swing-up control to bring back the pendulum from the downward position to the upward one, and (ii) upright stabilization control to maintain the pendulum to the upright vertical position. In the case (ii), a feedback or a neuro-fuzzy controller is used to stabilize the pendulum cart, while in the first case (i), a non-linear controller based on the energy of the pendulum is used in order to reach the desired performance with a minimum number of swings. Our contribution is to present a simulation using MatLab of time-optimal control system for swinging-up the pendulum, with a single control law in an open-loop form. From the bang-bang structure of the time-optimal control resulting from the necessary condition of the Pontryagin Maximum Principle, the solution obtained from direct discretization method is adjusted by using Newton based method

Estimation H^1 pour la solution de l'équation de Lamé avec conditions au bord mixte

In this paper we consider Lamé's system of equations on a polygonal domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L^2 norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H^1 norm of this solution. Note that the obtained bounds are not optimal .On considère dans cet article le système d'équations de Lamé posé sur un domaine polygonal avec conditions au bord mixtes de type Dirichlet-Neumann. On établit une estimation en norme L^2 explicite pour le gradient de la solution de ce problème. Ce qui permet de majorer explicitement la norme H^1 de cette solution. Noter que les majorations obtenues ne sont pas optimales

Z-equilibria in Bi-matrix Games with Uncertain Payoffs

International audienceThe concept of Z-equilibrium has been introduced by Zhukovskii (Mathematical Methods in Operations Research. Bulgarian Academy of Sciences, Sofia (1985) 103–195) for games in normal form. This concept is always Pareto optimal and individually rational for the players. Moreover, Pareto optimal Nash equilibria are Z-equilibria. We consider a bi-matrix game whose payoffs are uncertain variables. By appropriate ranking criteria of Liu uncertainty theory, we introduce some concepts of equilibrium based on Z-equilibrium for such games. We provide sufficient conditions for the existence of the introduced concepts. Moreover, using mathematical programming, we present a procedure for their computation. A numerical example is provided for illustration