Nonasymptotic Fractional Derivative Estimation of the Pseudo-State for a Class of Fractional-Order Partial Unknown Nonlinear Systems.

This work is devoted to the nonasymptotic and robust fractional derivative estimation of the pseudo-state for a class of fractional-order nonlinear systems with partial unknown terms in noisy environments. In particular, the estimation for the pseudo-state can be obtained by setting the fractional derivative's order to zero. For this purpose, the fractional derivative estimation of the pseudo-state is achieved by estimating both the initial values and the fractional derivatives of the output, thanks to the additive index law of fractional derivatives.

An innovative modulating functions method for pseudo-state estimation of fractional order systems.

In this paper, the objective is to estimate the pseudo-state of fractional order systems defined by the Caputo fractional derivative from discrete noisy output measurement. For this purpose, an innovative modulating functions method is proposed, which can provide non-asymptotic estimation within finite-time and is robust against corrupting noises. First, the proposed method is directly applied to the Brunovsky's observable canonical form of the considered system.

Observer design for a class of nonlinear piecewise systems. Application to an epidemic model with treatment.

Susceptible Exposed Infectious and Recovered epidemic model endowed with a treatment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease. This paper focuses on the nonlinear observer design for a class of nonlinear piecewise systems including SEIR-T models. For this purpose, two changes of coordinates are provided to transform the considered systems into an extended nonlinear observer normal form, on which a high gain observer can be applied.