A design method for distributed luenberger observers

The paper addresses the problem of designing distributed observers for discrete linear time-invariant (LTI) systems with distributed sensor nodes subjected to bounded measurement noise. A solution is proposed in terms of a distributed LTI Luenberger observer, thus departing from common linear time-varying solutions rooted in consensus-based distributed estimation techniques, and dispensing with the need for the exchange of covariance matrices. It is shown, under the conditions of collective observability, strong connectivity of the sensor communication network, and invertibility of the state transition matrix, that the resulting observer yields ultimate boundedness of the estimation error. A design example is given where the asymptotic performance of the proposed observer is shown to be similar to that obtained using a time-varying distributed Kalman filtering approach

An adaptive disturbance rejection control scheme for voltage regulation in DC micro-grids

© 2019 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 works.Uncertain generation by renewable sources and load variations have resulted in adding energy storage systems in the grid to maintain grid parameters (voltage, frequency) within prescribed limits. The disturbances being non-deterministic in nature, the voltage regulation control by the storage systems relies mostly on dual loop architecture with an outer voltage and inner current loop. Improvement in controller dynamics can be achieved through feed forward of disturbance profile but at expense of additional sensors and communication in the grid. This work explores the application of an adaptive disturbance rejection control scheme for disturbance estimation (without using additional sensors) employing an extended state and proportional integral observer (PI+ESO). The proposed observer aim to achieve robust disturbance estimation under grid parameter uncertainty. The effectiveness of the proposed scheme over the conventional one will be put forward through H8 and H2 norm analysis of the system. The design and simulation results of the proposed scheme will be presented in this work.Peer ReviewedPostprint (author's final draft

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart

Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that propagate and create shocks. We propose a new approach based on the kinetic description of the conservation law. A kinetic equation is a first order partial differential equation in which the advection velocity is a free variable. In certain cases, it is possible to prove that the nonlinear conservation law is equivalent to a linear kinetic equation. Hence, data assimilation is carried out at the kinetic level, using a Luenberger observer also known as the nudging strategy in data assimilation. Assimilation then resumes to the handling of a BGK type equation. The advantage of this framework is that we deal with a single "linear" equation instead of a nonlinear system and it is easy to recover the macroscopic variables. The study is divided into several steps and essentially based on functional analysis techniques. First we prove the convergence of the model towards the data in case of complete observations in space and time. Second, we analyze the case of partial and noisy observations. To conclude, we validate our method with numerical results on Burgers equation and emphasize the advantages of this method with the more complex Saint-Venant system

Exponentially convergent data assimilation algorithm for Navier-Stokes equations

The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in R2. This state equation is subject to uncertain but bounded noise in the input (Kolmogorov forcing) and initial conditions, and its output is incomplete and contains bounded noise. The algorithm designs a time-dependent gain such that the estimation error converges to zero exponentially. The sufficient condition for the existence of the gain are formulated in the form of algebraic Riccati equations. To demonstrate the results we apply the proposed algorithm to the reconstruction a chaotic fluid flow from incomplete and noisy data

Sensorless torque/force control

Motion control systems represent a main subsystem for majority of processing systems that can be found in the industrial sector. These systems are concerned with the actuation of all devices in the manufacturing process such as machines, robots, conveyor systems and pick and place mechanisms such that they satisfy certain motion requirements, e.g., the pre specified reference trajectories are followed along with delivering the proper force or torque to the point of interest at which the process occurs. In general, the aim of force/torque control is to impose the desired force on the environment even if the environment has dynamical motion