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In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent ... where N¹ ≥ 4 and Ω is a C¹ bounded domain in ℝN with 0 ∈ ∂Ω. 0 < s < 2, α+β = 2* (s) = 2(N-2)/N-2,α, β > 1, λ > 0 and 1 < p < N+2/N-2 . The case when 0 belongs to the boundary of Ω is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem (*) possesses at least a positive solution. [ABSTRACT FROM AUTHOR]

This paper deals with the back up control problem of an autonomous vehicle, using heuristic and stable fuzzy control. The first approach is based on linguistic rules obtained by using intuition and common sense. Although this control law type presents many advantages, the stability analysis of this closed-loop system remains difficult. Therefore, we present a second control design based on a fuzzy model. The stability analysis and the original design technique for fuzzy control are discussed using the Lyapunov approach. Simulation and experimental results are presented to highlight the performance of the proposed methods. The main contribution of this paper consists in the real-time application of this algorithm to a specific mobile robot. [ABSTRACT FROM AUTHOR]

This paper deals with the adaptive control of a class of continuous-time nonlinear dynamic systems preceded by an unknown dead-zone. By using a new description of a dead-zone and by exploring the properties of this dead-zone model intuitively and mathematically, a robust adaptive control scheme is developed without constructing the dead-zone inverse. The new control scheme ensures global stability of the adaptive system and achieves desired tracking precision. Simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach. [Copyright &y& Elsevier]