Nonsmooth Mechanics

Bernard Brogliato (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

This book is devoted to the study of a class of nonsmooth dynamical systems of the general form: $$ \begin{align} &\dot{x}(t)=g(x(t),u)\\ &f(x,t)\geq 0 \end{align} $$ where $x(t)\in \mathbb{R}^n$ is the system’s state vector, $u \in\mathbb{R}^{n_u}$ is the vector of inputs, and the function $f$ represents a set of $m_u$ unilateral constraints which are imposed on the system.

Mots clés: restitution coefficients; Darboux-Keller shock dynamics; linear complementarity systems; Moreau's sweeping process; measure differential inclusions; hybrid dynamical systems; trajectory tracking; Lyapunov stability; variational principles; impact mechanics; complementarity conditions; complementarity systems; Unilateral constraints; multiple impacts

Domaines: Mécanique des solides [physics.class-ph]; Automatique / Robotique; Optimisation et contrôle [math.OC]

Bernard Brogliato. Nonsmooth Mechanics: Models, Dynamics and Control. Springer International Publishing Switzerland; Communications and Control Engineering, 2016, 978-3-319-28662-4. ⟨10.1007/978-3-319-28664-8⟩. ⟨hal-01236953⟩