Prescribed-Time Sliding Mode Observer for Nonlinear Triangular Systems

This paper deals with the problem of prescribed-time sliding mode observer design for a class of triangular nonlinear systems. The contribution of the paper is twofold. First, we propose a new prescribed-time observer based on Super-Twisting-Algorithm (STA), for a triangular two-dimensional system. Such an STA algorithm is based on the use of two power terms, instead of only one as with the standard STA. Then we exploit this algorithm to develop a novel step-by-step arbitrary order sliding mode observer for a general class of triangular systems. An application to vehicle motion estimation in a platoon is provided to show the validity and efficiency of the proposed step-by-step sliding mode observer. For this case study, we use a third-order longitudinal kinematic linear vehicle model.