Inverse Optimal Boundary Tracking Control and Observer Design for a One-Link Rotating Flexible Arm

A new design of an inverse optimal boundary control law is first proposed to force a one-link rotating flexible arm with a tip mass subject to bounded disturbances to track a reference model. The proposed boundary control law ensures global practical exponential stability of the tracking error system and is optimal in the sense that it minimizes a cost functional that appropriately penalizes both the tracking errors and the boundary control without having to solve a Hamilton-Jacobi-Bellman equation. Based on the above boundary control development, an observer-control approach is proposed to design a new inverse optimal observer that globally practically exponentially estimates the one-link rotating flexible arm's states using only measurements at the actuated boundary.