I&I Adaptive Control by DSC Approach for Parametric Strict-Feedback Systems

This paper presents a simple adaptive controller for a class of nonlinear systems based on Immersion and Invariance (I&I) approach. The I&I adaptive control theory proposed by Astolfi et.al. has many superior features compared to other conventional certainty-equivalence (CE) adaptive approaches. However, for a class of nonlinear systems which can be described in strict feedback form, the I&I adaptive controller, as well as the back-stepping (BS) controller and the adaptive back-stepping controller, has the problem of “explosion of complexity” caused by the repeated differentiations of virtual controls. That is, the complexity of the controller grows drastically as the order of the system increases. To overcome this problem, a design method of I&I adaptive control via dynamic surface control (DSC) approach is proposed for parametric strict-feedback systems.