Adaptive Boundary Control for a Flexible Manipulator with State Constraints Using a Barrier Lyapunov Function

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.