Backstepping is a widely applicable control technique based on Lyapunov theory that under rather mild assumptions leads to families of control laws for a large class of nonlinear systems. Focusing on systems of ordinary differential equations, we introduce the basic concept (integrator backstepping), generalize it, among others, to systems in strict feedback form and pure feedback form, which all enjoy an inherent controllability property, captured in the system structure. The course ends with extending the setting to the adaptive backstepping case, resorting to the certainty equivalence principle and Barbalat's lemma. The course is furnished by a series of exercises to let the students gather experience on tailored examples.
Dr. Johann Reger received his diploma degree (Dipl.-Ing.) in Mechanical Engineering in 1999 and his doctorate (Dr.-Ing.) in Control Engineering in 2004, both from the University of Erlangen-Nuremberg in Germany. He has held several postdoc positions, among others, with the Mechatronics Department at CINVESTAV-IPN in Mexico-City, the EECS Control Laboratory at the University of Michigan in Ann Arbor, and the Control Systems Group at TU Berlin. Since 2008 he is a full professor and head of the Control Engineering Group at the Computer Science and Automation Faculty, TU Ilmenau, in Germany. There he also serves as vice-dean and director of the Institute for Automation and Systems Engineering. His current research foci are on adaptive and robust control, variable structure and sliding mode control, state and parameter estimation. Application areas include robotics, mechatronics, automotive, and water systems.