Boundary control and observer design for an uncertain wave process by second-order sliding-mode technique

The primary concern of the present paper is the regulation of an uncertain wave process with collocated boundary sensing and Neumann-type actuation. It exhibits an unknown constant elasticity parameter and it is affected by a boundary disturbance, which is bounded in magnitude. The proposed robust synthesis is formed by the combination between linear PD-type control action and the Twisting second order sliding mode control algorithm. It is applied here to achieve the global asymptotic stabilization of an infinite dimensional system in a suitable Sobolev space. The proposed boundary control algorithm is also applied to design an observer for a wave PDE of the same type as that dealt with in the boundary controller design. The effectiveness of the developed controller scheme is supported by simulation results.