A class of time-varying and nonlinear discrete systems with random and uncertain parameters is considered. The method of an estimation (evaluation) of the probability or the certainty index that the system is globally asymptotically stable is presented. The estimation consists in the determination of the lower and upper bounds for the probability and the certainty index via the determination of...

There are many programs for fitting nonlinear models to experimental data, and the use of this type of software is now widespread. After fitting a model or sequence of models, these programs usually calculate x2, run, sign, F and I statistics as an aid to model discrimination and parameter estimation. The distribution of such statistics from linear regression is well known, but these random var...

Innovative aspects To apply non-linear estimation techniques to represent the knowlegde acquired by a mobile sensor about the geometric structure of the spatial field that surrounds it, and to use this knowledge to design effective observation strategies to estimate a number of associated features. The results of the study will be applied to the problem of detecting a leaking source in a turbul...

In this paper we address the problem of state observation for sensorless control of nonlinear magnetic levitation systems, that is, the regulation of the position of a levitated object measuring only the voltage and current of the electrical supply. Instrumental for the development of the theory is the use of parameter estimation-based observers, which combined with the dynamic regressor extens...

This paper develops an adaptive partial differential equation (PDE) observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics...

This paper develops an adaptive PDE observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical...

This work is focused on the state of charge (SOC) estimation of a lithium-ion battery based on a nonlinear observer. First, the second-order resistor-capacitor (RC) model of the battery pack is introduced by utilizing the physical behavior of the battery. Then, for the nonlinear function of the RC model, a one-sided Lipschitz condition is proposed to ensure that the nonlinear function can play ...

The Bayesian approach provides a rather powerful framework for handling nonlinear, as well as linear, estimation problems. We can in fact pose a general solution to the nonlinear estimation problem. However, in the general case there does not exist any closed-form solution and we are forced to use approximate techniques. In this thesis we will study one such technique, the sequential Monte Carl...

Stochastic nonlinear state-space models (SSMs) are prototypical mathematical models in geoscience. Estimating unknown parameters in nonlinear SSMs is an important issue for environmental modeling. In this paper, we present two recently developed methods that are based on the sequential Monte Carlo (SMC) method for parameter estimation in nonlinear SSMs. The first method, which belongs to classi...

We discuss the problem of parameter estimation in nonlinear stochastic di€erential equations (SDEs) based on sampled time series. A central message from the theory of integrating SDEs is that there exist in general two time scales, i.e. that of integrating these equations and that of sampling. We argue that therefore, maximum likelihood estimation is computationally extremely expensive. We disc...