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

Description

Content: Intro Foreword Preface Contents 1 Mathematical Background 1.1 Convexity 1.1.1 Convex Sets 1.1.2 Projection onto a Convex Set 1.1.3 Tangent and Normal Cones 1.1.4 Constraint Qualification Conditions 1.1.5 Extended Real-Valued Functions 1.1.6 Lower Semicontinuous Functions 1.1.7 Continuity of Convex Functions 1.1.8 Differentiable Convex Functions 1.1.9 The Subdifferential of Convex Functions 1.1.10 Conjugate Functions 1.1.11 Subdifferential Calculus 1.2 Maximally Monotone Operators 1.2.1 Definitions 1.2.2 Minty's Theorem and Yosida Approximation. 1.3 Set-Valued Analysis and Measure Theory1.3.1 Semicontinuity of Set-Valued Mappings 1.3.2 Functions of Bounded Variation 1.4 Stability of Smooth Nonlinear Dynamics 1.4.1 Basic Facts About ODEs 1.4.2 Lyapunov Stability of ODEs 1.4.3 LaSalle's Invariance Principle 1.4.4 Nonlinear Control Systems 2 Nonsmooth Dynamics: An Overview 2.1 Piecewise Smooth Dynamics 2.2 Filippov's Solution Concept 2.3 Differential Inclusions 2.4 Complementarity Systems 2.5 Differential Variational Inequalities 2.6 Evolution Variational Inequalities 2.7 Projected Dynamical Systems. 2.8 Measure Differential Inclusions3 Stability Analysis of First-Order Nonsmooth Dynamics 3.1 Introduction 3.2 Well-Posedness and Stability Analysis 3.3 Invariance Principle for Nonsmooth Dynamics 3.4 Finite-Time Stability 3.5 Applications in Nonregular Electrical Circuits 4 Stability Analysis of Second-Order Nonsmooth Dynamics 4.1 Introduction 4.2 Second-Order Nonsmooth Dynamics 4.3 Nonsmooth Conservative Systems 4.3.1 Global Attractivity: C is Positive Definite 4.3.2 Local Attractivity: C is Not Positive Definite 4.4 Applications in Unilateral Mechanics. 4.5 DC-DC Buck Converter Model4.5.1 Existence of Trajectories 4.5.2 Stationary Solution 4.5.3 Asymptotic Properties of Trajectories 5 Nonsmooth Lurie Dynamical Systems 5.1 Introduction 5.2 Lurie Systems with Maximally Monotone Operators 5.2.1 Existence and Uniqueness 5.2.2 Stability Analysis 5.2.3 An Illustrative Example in Electronics 5.3 Lurie Systems with Nonmonotone Operators 5.3.1 Existence and Uniqueness 5.3.2 Stability and Invariance Theorems 5.3.3 Some Illustrative Examples in Electronics 6 Moreau's Sweeping Processes 6.1 Introduction 6.2 Some Applications. 6.2.1 The Planning Procedure6.2.2 Nonregular Electrical Circuits 6.3 The Absolutely Continuous Case 6.4 The Bounded Variation Case 6.5 Semicoercive Sweeping Process with Velocity Constraint Historical Vignettes References Index.