Integrator backstepping with the nonlinear PI method: An integral equation approach

In this paper we extend the nonlinear PI method within an integrator backstepping framework. The main idea of our approach is a novel selection of the virtual control laws through suitable nonlinear integral equations. Using the proposed methodology a new robust regulation control scheme is developed for time-varying strict feedback nonlinear systems with unknown control directions. A simulation study demonstrates the validity of our theoretical results.