Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

This paper investigates the output feedback control for the uncertain nonlinear system with the integral input-to-state stable (iISS) cascade subsystem, which allow not only the unknown control direction but also the unknown output function. The unknown output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds of the generalized derivative need not to be known. To deal with the challenge raised by the unknown output function and the unknown control direction, we choose a special Nussbaum function with a faster growth rate to ensure the integrability for the derivative of the selected Lyapunov function. Then, 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. Moreover, via some appropriate transformations, the proposed control scheme is extended to deal with more general uncertain nonlinear cascade systems with quantized input signals. Finally, two simulation examples are given to show the effectiveness of the control scheme.