On Designing Distributed Prescribed Finite-Time Observers for Strict-Feedback Nonlinear Systems

This article is concerned with the problem of distributed prescribed finite-time observer design for a strictfeedback nonlinear system with external disturbance. The purpose is to reconstruct the unavailable system state based on a group of distributed observers, where each of them can only receive at most 1-D output measurement from the system. First, in the absence of disturbance, a new distributed prescribed finite-time observer featuring time-varying gains is constructed and designed under the assumption of joint observability. It is analytically proved that for any prescribed instant independent of system initial conditions and other design parameters, the obtained distributed observer can guarantee not only the asymptotic convergence to zero of the state error between each observer state and the system state at this prescribed instant but also the definite zero-state error after this prescribed instant. Second, a distributed prescribed finite-time bounded observer is delicately proposed to account for the presence of external disturbance in the system dynamics. It is shown that the state error can be bounded by an arbitrarily positive constant after a prescribed instant. Finally, a numerical example and an electromechanical system are presented to demonstrate the effectiveness of the proposed results.