Design of prescribed-time adaptive observers for uncertain nonlinear systems with unmodeled dynamics

This paper addresses the design of a prescribed-time adaptive extended observer (PTAEO) for an uncertain nonlinear systems with unmodeled dynamics. First, a prescribed-time adaptive observer (PTAO) is developed to estimate the state variables of linear systems with external disturbances and unknown parameters. Second, building upon the PTAO, a PTAEO is proposed for nonlinear systems affected by unmodeled dynamics. Both observer systems guarantee convergence to a bounded region for arbitrary initial conditions, and reach this region within the prescribed time. Finally, the effectiveness of the proposed observation scheme is illustrated through a numerical simulation example.