Observer based nonlinear robust control for a flexible wing with unknown time-varying output constraints

This paper addresses the robust output regulation and even output constraints of a flexible wing system, where an exosystem is supposed to generate the unknown time-varying output constraints, output disturbances, distributed disturbances, boundary disturbances and references. Besides the signals of displacements and velocities, high-order boundary signals are used to guarantee the exponential convergence of the tracking errors. At first, two exosystem observers are designed based on the PDE observer of the wing system in order to give the approximation of the unknown references and output constraints. Then, two observer based output feedback controls are proposed based on state feedback controls and the PDE-ODE coupled observer. For the closed-loop system, the tracking errors are proved to be convergent toward zero, and further regulated to be restrained by two unknown time-varying and positive trajectories. Numerical simulation shows the effectiveness of the proposed robust controls.