Backstepping for nonsmooth systems
The paper presents a smooth version of the backstepping stabilization method. More precisely, the authors consider the system \[ \begin{cases} \dot\eta= f(\eta)+ g(\eta)\xi\\\;\xi=u \end{cases} \] under the assumption that the first subsystem is stabilized by a possibly discontinuous feedback \(\xi=\varphi (\eta)\) (the solutions of the closed-loop system are intended in Filippov's sense). Making use of the Clarke generalized directional derivative, they provide an explicit expression for a stabilizer \(u=\psi (\eta,\xi)\) of the overall system. As illustrative examples, they discuss the case of a mobile robot and the case of the electronic throttle control.
Clarke generalized directional derivative
scientific article; zbMATH DE number 1956150
scientific article