On Feedback Identification of Unknown Biochemical Characteristics in an Artificial Lake

The problem of dynamical identification of unknown characteristics (states/parameters) in a biochemical model of an artificial lake with only inflow and given observations of some states is considered. An algorithm that solves this simultaneous state and parameter estimation problem and that is stable with respect to bounded informational noises and computational errors is presented. The algorithm is based on the principle of auxiliary models with adaptive controls. Convergence of the algorithm is proven and a convergence rate is derived. The performance of the algorithm is illustrated to a typical single-species environmental example

Adaptive nonlinear parameter estimation for a proton exchange membrane fuel cell

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksParameter estimation is vital for modeling and control of fuel cell systems. However, the nonlinear parameterization is an intrinsic characteristic in the fuel cell models such that classical parameter estimation schemes developed for linearly parameterized systems cannot be applied. In this paper, an alternative framework of adaptive parameter estimation is designed to address the real-time parameter estimation for fuel cell systems. The parameter estimation can be divided into two cascaded components. First, the dynamics with the unknown parameters are estimated by a new unknown system dynamics estimator (USDE). Inspired by an invariant manifold, this USDE is designed by applying simple filter operations such that the information of the state derivative is not required. Secondly, an adaptive law driven by the function approximation error is proposed for recovering unknown model parameters. Exponential convergence of the estimated parameters to the true values can be proved under the monotonicity condition. Finally, experimental results on a practical proton exchange membrane fuel cell system are given to verify the effectiveness of the proposed schemes.Peer ReviewedPostprint (author's final draft

Local adaptive observer for linear time-varying systems with parameter-dependent state matrices

We present an adaptive observer for linear time-varying systems whose state matrix depends on unknown parameters. We first assume that the state matrix is affine in these parameters. In this case, the proposed observer generates state and parameter estimates, which exponentially converge to the plant state and the true parameter, respectively, provided a persistence of excitation condition holds and the unknown parameters lie in a neighborhood of some known nominal values. Hence, some prior knowledge on the unknown parameters is required, but not on the state. We then modify the adaptive observer and its convergence analysis to systems whose state matrix is smooth, instead of being affine, in the unknown parameters. The convergence is approximate, and no longer exponential, in this case. An example is provided to illustrate the results, for which the required distance between the unknown parameters and their nominal values is investigated numerically

Local adaptive observer for linear time-varying systems with parameter-dependent state matrices

International audienceWe present an adaptive observer for linear time-varying systems whose state matrix depends on unknown parameters. We first assume that the state matrix is affine in these parameters. In this case, the proposed observer generates state and parameter estimates, which exponentially converge to the plant state and the true parameter, respectively, provided a persistence of excitation condition holds and the unknown parameters lie in a neighborhood of some known nominal values. Hence, some prior knowledge on the unknown parameters is required, but not on the state. We then modify the adaptive observer and its convergence analysis to systems whose state matrix is smooth, instead of being affine, in the unknown parameters. The convergence is approximate, and no longer exponential, in this case. An example is provided to illustrate the results, for which the required distance between the unknown parameters and their nominal values is investigated numerically

Performance Analysis of eXogenous Kalman Filter for INS/GNSS Navigation Solutions

There are several methods of fusing data for navigation solutions using Inertial Navigation System (INS) aided by Global Navigation Satellite System (GNSS). The most used solutions are nonlinear observer (NLO) and extended Kalman filter (EKF) of various architectures. EKF based estimation methods guarantees sub-optimal solutions but not stability, on the contrary NLO based estimation guarantees stability but not optimality. These complimentary features of EKF and NLO has been combined to design an eXogenous Kalman filter (XKF) where the estimate from the NLO is used as an exogenous signal to calculate the linearized model of the EKF. The performance of the designed XKF is tested on real flight test data collected using a Slingsby T67C ultra-light aircraft. The results show that during the outage of GNSS, in some cases the divergence of position estimates using XKF is lower compared to EKF and NLO, however no clear benefit is achieved

Nonlinear Observer for Tightly Integrated Inertial Navigation Aided by Pseudo-Range Measurements

A modular nonlinear observer for inertial navigation aided by pseudo-range measurements is designed and analyzed. The attitude observer is based on a recent nonlinear complementary filter that uses magnetometer and accelerometer vector measurements to correct the quaternion attitude estimate driven by gyro measurements, including gyro bias estimation. A tightly integrated translational motion observer is driven by accelerometer measurements, employs the attitude estimates, and makes corrections using the pseudo-range and range-rate measurements. It estimates position, range bias errors, velocity and specific force in an earth-fixed Cartesian coordinate frame, where the specific force estimate is used as a reference vector for the accelerometer measurements in the attitude observer. The exponential stability of the feedback interconnection of the two observers is analyzed and found to have a semiglobal region of attraction with respect to the attitude observer initialization and local region of attraction with respect to translational motion observer initialization. The latter is due to linearization of the range measurement equations that is underlying the selection of injection gains by solving a Riccati equation. In typical applications, the pseudo-range equations admit an explicit algebraic solution that can be easily computed and used to accurately initialize the position and velocity estimates. Hence, the limited region of attraction is not seen as a practical limitation of the approach for many applications. Advantages of the proposed nonlinear observer are low computational complexity and a solid theoretical foundation

Uniting observers

International audienceWe propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviours for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: one, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behaviour. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented