Global output feedback control for uncertain nonlinear cascade systems with non-smooth output functions

The paper investigates the output feedback control for nonlinear systems with non-smooth unknown output functions. The output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds for which may not to be known. The considered system includes more other uncertainties, for example, the integral input-to-state stable (iISS) cascade subsystem, the unknown control direction, the unmeasured states and the external disturbance. To overcome the effects caused by the external disturbance, we first treat the disturbance as an extended state, and a state observer is designed to estimate both the unavailable system states and the external disturbance. In addition, to deal with the challenge raised by the unknown control direction and the non-smooth output function, we choose a special Nussbaum function with a fast growth rate to ensure the integrability for the derivative of the selected Lyapunov function. After that, a dynamic output feedback controller is designed to drive the system states to the origin while keeping the boundedness for all other closed-loop signals. Finally, a simulation example is given to show the effectiveness of the control scheme.