Extremum-Seeking Regulator for a Class of Nonlinear Systems With Unknown Control Direction

This study proposes a design technique that solves a robust output regulation problem for a class of nonlinear systems subject to unknown control direction. Nussbaum function techniques are commonly used tools to investigate output regulation problems for various systems subject to unknown control direction. They often lead to large overshoots when the initial estimates of the control direction are wrong. In this study, an extremum-seeking control approach is proposed to overcome the need for Nussbaum functions. The approach yields control laws that can handle the robust practical output regulation problem for a class of nonlinear systems subject to a time-varying control direction whose sign or value is unknown. The stability of the design is proven via a Lie bracket averaging technique where uniform ultimate boundedness of the closed-loop signals is guaranteed. Finally, the simulation of a chaotic control problem for the generalized Lorenz system with an unknown time-varying coefficient is provided to illustrate the validity of the theoretical results.