Finite time estimation for time-varying systems with delay in the measurements

Abstract

We build finite time observers for time-varying nonlinear systems with delays in the outputs, using a dynamic extension that computes fundamental matrices. Our observers achieve finite time convergence when no disturbances are present. When disturbances are present, we provide approximate values for the solutions, which lead to an upper bound on the approximation error after a suitable finite time. We illustrate our work in a class of systems arising in the study of vibrating membranes, where time-varying coefficients can be used to represent intermittent measurements.

New Fixed Time and Fast Converging Reduced Order Observers

“…Instead, the observer we propose here uses discrete variables and the observability Gramian and the solutions of the observer are continuous. It is also very different from those of [1], [4], [9], [12], and [16], which are based on observers with delays. By not using the delays that occur in earlier observer designs, we obtain simpler reduced order controllers that still enjoy the required fixed time or arbitrarily fast convergence of the observation error to zero.…”

A parametric design method of observer‐based state feedback controller for quasi‐linear systems

“…Combing the coefficients of s of Equation (20) with Equation ( 21), we can obtain the following relations…”

“…When estimating a state which is near the operating point and not necessarily in a stable manifold, such an observer will not have sufficient observation performance. Subsequently, some other observer research methods have also been developed, such as nonlinear observers through output injection [14,15], state-dependent Riccati equation observers [16][17][18], finite-time observers [19][20][21][22], adaptive observers [23,24], observer-based predictive controller [25][26][27]. It can be seen that there is no general research method for observers of nonlinear systems.…”

Fixed-time Observer Design for LTI Systems by Time-varying Coordinate Transformation

“…Moreover, the implementation of the delay operators required by [12] and [13] poses additional challenges in the continuous-time framework. Further alternatives to sliding mode observers are provided by Fliess's algebraic state reconstruction method (see [14]- [16]), or the integral-based modulating functions (see [17]- [20]), that exploit integral operators over compact domains able to annihilate the effect of initial conditions. Modulation function methods also found application to signal differentiation [21] and state estimation for fractional order systems [22].…”