Boundary control for a general class of nonlinear actuator-string systems

In this paper, we design a controller for a boundary actuated-string model which avoids: 1) use of the standard small amplitude simplifying assumption, 2) use of the constant tension assumption, and 3) neglection of the actuator dynamics. Specifically, we design a nonlinear, exact model knowledge boundary controller which asymptotically stabilizes the total energy of the actuator-string system. We then redesign the exact model knowledge boundary controller as an adaptive boundary controller which compensates for parametric uncertainty and asymptotically stabilizes the total energy of the system