A Variational Approach to Nonsmooth Dynamics: Applications in Unilateral Mechanics and Electronics

Description

This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis. With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics. Front Matter ....Pages i-xv Mathematical Background (Samir Adly)....Pages 1-37 Nonsmooth Dynamics: An Overview (Samir Adly)....Pages 39-51 Stability Analysis of First-Order Nonsmooth Dynamics (Samir Adly)....Pages 53-69 Stability Analysis of Second-Order Nonsmooth Dynamics (Samir Adly)....Pages 71-102 Nonsmooth Lurie Dynamical Systems (Samir Adly)....Pages 103-126 Moreau’s Sweeping Processes (Samir Adly)....Pages 127-148 Back Matter ....Pages 149-159