Tracking control of a flexible beam by nonlinear boundary feedback (Q1890820)

The authors consider a hybrid system of partial and ordinary differential equations which describes the motion of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. Under dissipative nonlinear boundary feedback control, the authors study the problem of tracking a preassigned uniform motion. The dynamical system can be interpreted as a system of evolution equations, defined by a maximal monotone operator in an appropriate Hilbert space. The norm in the space coincides with the energy of the system. The authors prove some results about well-posedness, asymptotic stability and uniform decay of solutions.