Interval estimation for second-order delay differential equations with delayed measurements and uncertainties

International audienceThe interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Incorporating delayed and multi-rate measurements in navigation filter for autonomous space rendezvous

In the scope of space missions involving rendezvous between a chaser and a target, vision based navigation relies on the use of optical sensors coupled with image processing and computer vision algorithms to obtain a measurement of the target relative pose. These algorithms usually have high latency time, implying that the chaser navigation filter has to fuse delayed and multi-rate measurements. This article has two main contributions: it provides a detailed modelization of the relative dynamics within the estimation filter, and it proposes a comparison of two delay management techniques suitable for this application. The selected methods are the Filter Recalculation method -which always provides an optimal estimation at the expense of a high computational load- and the Larsen’s method -which provides a faster solution whose optimality lies on stronger requirements. The application of these techniques to the space rendezvous problem is discussed and formalized. Finally, the current article proposes a comparison of the methods based on a Monte-Carlo campaign, aimed at demonstrating whether the loss of performance of Larsen’s method due to its sub-optimality still enables target state robust tracking

Robust H∞ filtering for time-delay systems with probabilistic sensor faults

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, a new robust H∞ filtering problem is investigated for a class of time-varying nonlinear system with norm-bounded parameter uncertainties, bounded state delay, sector-bounded nonlinearity and probabilistic sensor gain faults. The probabilistic sensor reductions are modeled by using a random variable that obeys a specific distribution in a known interval [alpha,beta], which accounts for the following two phenomenon: 1) signal stochastic attenuation in unreliable analog channel and 2) random sensor gain reduction in severe environment. The main task is to design a robust H∞ filter such that, for all possible uncertain measurements, system parameter uncertainties, nonlinearity as well as time-varying delays, the filtering error dynamics is asymptotically mean-square stable with a prescribed H∞ performance level. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a certain linear matrix inequality (LMI). A numerical example is introduced to illustrate the effectiveness and applicability of the proposed methodology

Kalman filter estimation of human pilot-model parameters

The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Temperature and concentration control of exothermic chemical processes in continuous stirred tank reactors

Exothermic chemical reaction taking place in continuous stirred tank reactor is considered. Heat release from the chemical reaction, non-linear dynamic behavior of the process and uncertainty in parameters are the main factors motivating the use of robust control design. Viewing temperature and molar concentration as variables both accessible in real time, PI and optimal state-feedback controllers driven by temperature and concentration error signals are proposed to regulate the system over reactor’s steady-state working points by counteracting undesired disturbances. Since access to concentration value has proved beneficial for the reactor’s performance, estimation techniques are examined to compensate for the problematic nature of the concentration’s measurement. A linear reduced-order observer is first proposed to estimate the concentration value using temperature measurements. In addition, assuming concentration measurement is available with a relatively short delay via sample analysis, a linear and non-linear discrete-time predictor is constructed to estimate the concentration’s real-time value. A linear combination of the two estimation schemes (observer, predictor) is proposed resulting in a combined estimator, in which the emphasis between the two individual schemes can be controlled via a scalar parameter. The work presented in this paper was supported by the GLOW project – New weather-stable low gloss powder coatings based on bifunctional acrylic solid resins and nanoadditives – as part of the development of novel and efficient processing technologies regarding the production of new families of powder coatings, responding to industrial requirements for quality improvement at lower cost and shorter development cycles

Satellite Emission Range Inferred Earth Survey (SERIES) project

The Global Positioning System (GPS) was developed by the Department of Defense primarily for navigation use by the United States Armed Forces. The system will consist of a constellation of 18 operational Navigation Satellite Timing and Ranging (NAVSTAR) satellites by the late 1980's. During the last four years, the Satellite Emission Range Inferred Earth Surveying (SERIES) team at the Jet Propulsion Laboratory (JPL) has developed a novel receiver which is the heart of the SERIES geodetic system designed to use signals broadcast from the GPS. This receiver does not require knowledge of the exact code sequence being transmitted. In addition, when two SERIES receivers are used differentially to determine a baseline, few cm accuracies can be obtained. The initial engineering test phase has been completed for the SERIES Project. Baseline lengths, ranging from 150 meters to 171 kilometers, have been measured with 0.3 cm to 7 cm accuracies. This technology, which is sponsored by the NASA Geodynamics Program, has been developed at JPL to meet the challenge for high precision, cost-effective geodesy, and to complement the mobile Very Long Baseline Interferometry (VLBI) system for Earth surveying

Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

Copyright @ 2012 ElsevierIn this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0,1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.This work was supported in part by the National 973 Project under Grant 2009CB320600, National Natural Science Foundation of China under Grants 61028008, 61134009 and 60825303, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany