This book addresses the asymptotic regulation of dynamical systems, focusing on the output regulation problem relevant in control theory. It stems from a four-year research project at Eindhoven University, aiming to bridge gaps between controlled synchronization and output regulation, enhancing solutions from local to global contexts in nonlinear systems.
This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on important open problems with contributions that represent the state of the art in nonlinear control.
Stability of motion is a key theme in mechanical system dynamics. This monograph systematically explores mechanical systems with unilateral constraints, such as contact, impact, and friction, which lead to non-smooth dynamical models. It begins with a discussion of the mathematical foundations of non-smooth analysis, measure and integration theory, and an introduction to non-smooth dynamical systems. Unilateral constraints are modeled using set-valued force laws from non-smooth mechanics, resulting in dynamical models that exhibit impulsive phenomena. The framework of measure differential inclusions is employed to formalize these models. The text presents stability results for these inclusions, which are then applied to nonlinear mechanical systems with unilateral constraints. The study concludes with an examination of convergence properties for a specific class of measure differential inclusions, highlighting a stability property relevant to systems with time-varying inputs, essential for controlling mechanical systems with unilateral constraints. This work not only offers a comprehensive stability theory for such mechanical systems but also serves as a tutorial on their modeling within the measure differential inclusions framework, appealing to engineers, scientists, and students in non-smooth mechanics and dynamics.