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

Nussbaum function techniques are commonly used to investigate output regulation problems for various systems subject to unknown control direction. However, their implementation often leads to large overshoots when the initial estimates of the control direction are wrong, which yields systems with poor transient performance. This study proposes an extremum-seeking control approach to overcome the need for Nussbaum-type functions. The approach yields control laws that can handle the robust practical output regulation problem for a class of nonlinear systems subject to an unknown time-varying control direction. The stability of the design is proven using a Lie bracket averaging technique. It is shown that uniform ultimate boundedness of the closed-loop signals is guaranteed. Finally, a simulation study is performed involving a chaotic control problem for the generalized Lorenz system with an unknown time-varying coefficient to illustrate the validity of the theoretical results.