Nussbaum gain adaptive backstepping control of nonlinear strict-feedback systems with unmodeled dynamics and unknown dead zone

Abstract

This paper investigates an adaptive state feedback control problem for a class of single-input and single-output nonlinear systems with strict-feedback form. A novel adaptive control strategy is developed for nonlinear systems with unmodeled dynamics, unknown control directions, dynamic disturbances and unknown dead zone. To stabilize this category of systems, a dynamic signal is introduced to dominate the unmodeled dynamics. Nussbaum gain technique is used to overcome the unknown control directions problem. Nonlinear damping terms are framed to counteract the dynamic disturbances, and the assistant signal is constructed to compensate the influence of symmetric dead zone. The adaptive control approach ensures all signals in the closed-loop system to be bounded. Finally, a numerical example is used to verify the effectiveness of the theoretical results.