Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters

Abstract

We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non-uniform convergence and is subjected to persistency of excitation conditions. In the absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes. In this respect, the proposed method constitutes a generalization of the conventional canonical adaptive observer design.

Adaptive high gain observer for uniformly observable systems with nonlinear parametrization

“…Adaptive versions of high gain observers have been proposed in [4] and [7]. Though most results on adaptive (nonlinear) observer design deal with linear parametrization, some results dealing with nonlinear parameterizations are available in the literature [13], [11], [20], [10], [7], [23], [22].…”

State estimation for MISO non–linear systems in controller canonical form

“…Chen et al (2011) and Bouraoui et al (2015) addressed the problem of uncertainty of non-linear models. One way of overcoming the problem of parametric uncertainty is to use adaptive observers (Tyukina et al, 2013;Alma and Darouach, 2014;Farza et al, 2014), in the particular case where the measurements are only available at discrete instants and have disturbances. Another approach (Mazenc and Dinh, 2014;Thabet et al, 2014) consists in defining interval observers.…”

Fast Sampling of Evolving Systems with Periodic Trajectories

“…Answers to these questions are provided in the next section. We begin with the following property of linear systems regarding input detectability (cf [25])…”

“…This is a standard inverse problem, and many methods for finding solutions to this problem have been developed to date (sensitivity functions [20], splines [6], interval analysis [15], adaptive observers [19], [5], [9], [12], [24], [25], [8] and particle filters and Bayesian inference methods [1]). Despite these methods are based on different mathematical frameworks, they share a common feature: one is generally required to repeatedly find numerical solutions of nonlinear ordinary differential equations (ODEs) over given intervals of time (solve the direct problem).…”