This ebook provides new methodologies for the layout and research of adaptive keep watch over platforms in response to the backstepping technique. Our emphasis is on - namic doubtful platforms with nonsmooth nonlinearities, equivalent to backlash, de- area, hysteresis and saturation, or time-varying parameters, or interactions. The backstepping technique, a recursive Lyapunov-based scheme, was once p- posed at the beginning of Nineties. With this technique the development of suggestions controllawsandLyapunovfunctions issystematic, followingastep-by-stepal- rithm. Backstepping can be utilized to chill the matching , which blocked the conventional Lyapunov-based layout. a tremendous good thing about backstepping is that it has the ?exibility to prevent cancellations of beneficial nonlinearities and accomplish legislation and monitoring homes. The approach used to be comprehensively addressed via Krstic, Kanellakopoulos and Kokotovic in . besides the fact that, there's nonetheless no monograph to be had to deal with difficulties corresponding to the dealing with of n- delicate nonlinearities, time various parameters and procedure interactions utilizing this procedure. Nonsmooth nonlinearities similar to dead-zone, backlash, hysteresis and satu- tion are universal in commercial regulate structures, reminiscent of mechanical, hydraulic, biomedical, piezoelectric, and actual structures. Such nonlinearities are typically poorlyknownandmayvarywithtime, andthey oftenlimitsystemperformance.