Parameter estimation and compensation in systems with nonlinearly parameterized perturbations

State and parameter estimation for linear systems with nonlinearly parameterized perturbations

“…In this paper, we consider observer design for systems that can be described by a linear part with a nonlinear, time-varying perturbation that is parameterized by a vector of unknown, constant parameters. Our design extends the results of [1], [2], where parameter identification for systems with full state measurement was considered.…”

“…where Ä is the ratio of the largest to the smallest eigenvalue of 1 . Above, we have used the property [9,…”

Fast Sampling of Evolving Systems with Periodic Trajectories

“…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).…”

Backlash estimation for industrial drive-train systems

“…The approach followed in this paper is based on a method for parameter estimation in nonlinearly parametrized systems presented in Grip et al [2010]. The basic idea relates to estimating a perturbation of the system dynamics that depends on the unknown parameter and then finding an adaptive law for estimating the parameter itself.…”

“…The estimator design is inspired by the method proposed in Grip et al [2010] for the estimation of unknown parameters. For the rest of the analysis we consider that the unknown parameter δ lies in a compact set D ⊂ R, withδ = 0 and we define the backlash angle estimation error asδ = δ −δ .…”