Khalid Addi

A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics

The main object of this paper is to present a general mathematical theory applicable to the study of a large class of linear variational inequalities arising in electronics. Our approach uses recession tools so as to define a new class of problems that we call “semi-complementarity problems”. Then we show that the study of semi-complementarity problems can be used to prove new qualitative results applicable to the study of linear variational inequalities of the second kind.

A sensitivity analysis of a class of semi-coercive variational inequalities using recession tools

Using the recession analysis we study necessary and sufficient conditions for the existence and the stability of a finite semi-coercive variational inequality with respect to data perturbation. Some applications of the abstract results in mechanics and in electronic circuits involving devices like ideal diode and practical diode are discussed.

IMPACT DYNAMICS IN BIPED LOCOMOTION ANALYSIS: TWO MODELLING AND IMPLEMENTATION APPROACHES

Stability during the biped locomotion and especially humanoid robots walking is a big challenge in robotics modelling. This paper compares the classical and novel methodologies of modelling and algorithmic implementation of the impact/contact dynamics that occurs during a biped motion. Thus, after establishing the free biped locomotion system model, a formulation using variational inequalities theory via a Linear Complementarity Problem then an impedance model are explicitly developed. Results of the numerical simulations are compared to the experimental measurements then the both approaches are discussed.

Complementarity and Variational Inequalities in Electronics

The purpose of this chapter is to review and describe the main mathematical models applicable to the study of electrical networks involving devices like diodes whose Ampere–Volt characteristics are set-valued graphs. The mathematical models in question are related to complementarity problems, variational inequalities, and non-regular dynamical systems.