Boundary control for a constrained two-link rigid–flexible manipulator with prescribed performance

In this paper, we consider a boundary control problem for a constrained two-link rigid–flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation–partial differential equation (ODE–PDE) dynamic model. Based on the coupled ODE–PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.