Dissipative Adaptive Control for Strict Feedback Form Systems

This paper presents a tracking algorithm for the adaptive control of nonlinear dynamic systems represented in strict feedback form with parametric uncertainty. The construction of the stabilizing algorithm is given using Passivity-based arguments that result in an adaptive Passivity-based controller (APBC). The construction of the controller results in a chain of interconnected subsystems with the outputs and inputs of adjacent subsystems sharing a strictly passive relationship. The stability of the overall system is shown via Passivity arguments combined with an adaptive algorithm. This is in contrast with other approaches that utilize Lyapunov-based controller designs. This paper also shows a comparison with a controller designed via adaptive backstepping with tuning functions, the most popular method for controlling systems of this form. The adaptive backstepping controller (ABC) has many additional coupling terms that make its design and implementation more complex and may also result in unwanted transients. On the other hand, the APBC has a convenient decoupling property that provides a diagnostic tool for detection of non-parametric model error.