This book employs the powerful and popular adaptive backstepping control technology to design controllers for dynamic uncertain systems with non-smooth nonlinearities. Various cases including systems with time-varying parameters, multi-inputs and multi-outputs, backlash, dead-zone, hysteresis and saturation are considered in design and analysis. For multi-inputs and multi-outputs systems, both centralized and decentralized controls are addressed. This book not only presents recent research results including theoretical success and practical development such as the proof of system stability and the improvement of system tracking and transient performance, but also gives self-contained coverage of fundamentals on the backstepping approach illustrated with simple examples. Detail description of methodologies for the construction of adaptive laws, feedback control laws and associated Lyapunov functions is systematically provided in each case. Approaches used for the analysis of system stability and tracking and transient performances are elaborated. Two case studies are presented to show how the presented theories are applied.

• Part I Adaptive Backstepping Control Design.- Adaptive Backstepping Control.- Adaptive Control of Time-Varying Nonlinear Systems.- Multivariable Adaptive Control.- Decentralized Stabilization of Interconnected Systems.- Part II Nonsmooth Nonlinearities.- Nonsmooth Nonlinearities.- Backstepping Control of Systems with Backlash Nonlinearity.- Inverse Control of Systems with Backlash Nonlinearity.- Stabilization of Interconnected Systems with Backlash Nonlinearity.- Adaptive Control of Nonlinear Systems with Dead-Zone Nonlinearity.- Adaptive Control of Systems with Input Saturation.- Control of a Hysteretic Structural System in Base Isolation Scheme.- Control of a Piezo-Positioning Mechanism with Hysteresis.