Preface
This book presents new methodologies for the design and analysis of adaptive
control systems based on the backstepping approach. Our emphasis is on dy-
namic uncertain systems with nonsmooth nonlinearities, such as backlash, dead-
zone, hysteresis and saturation, or time-varying parameters, or interactions.
The backstepping approach, a recursive Lyapunov-based scheme, was pro-
posed in the beginning of 1990s. With this method the construction of feedback
control laws and Lyapunov functions is systematic, following a step-by-step algo-
rithm. Backstepping can be used to relax the matching condition, which blocked
the traditional Lyapunov-based design. A major advantage of backstepping is
that it has the flexibility to avoid cancellations of useful nonlinearities and
achieve regulation and tracking properties. The technique was comprehensively
addressed by Krstic, Kanellakopoulos and Kokotovic in [1]. However, there is
still no monograph available to address problems such as the handling of non-
smooth nonlinearities, time varying parameters and system interactions using
this approach.
Nonsmooth nonlinearities such as dead-zone, backlash, hysteresis and satura-
tion are common in industrial control systems, such as mechanical, hydraulic,
biomedical, piezoelectric, and physical systems. Such nonlinearities are usually
poorly known and may vary with time, and they often limit system performance.
An effective control method should be able to accommodate such common prac-
tical nonsmooth nonlinearities. In practice, system parameters are changing with
time. Parameter time-variations may arise from linear approximations along dif-
ferent motions and may be due to unmodelled dynamics (for instance friction
parameters, electric resistances, inertias) and also some other factors such as
changes in environmental conditions. For such systems, the control problem is
very complicated and becomes even more difficult to deal with when time-varying
parameters are unknown. In the control of large scale systems, one usually faces
poor knowledge on plant parameters and interactions between subsystems. De-
centralized adaptive control strategy is an efficient and effective way for control-
ling these systems with large amount of uncertainties. Decentralized adaptive
