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"nonlinear observers"
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A sequential LMI approach to design a BMI-based multi-objective nonlinear observer
An observer for a nonlinear system may be required to satisfy multiple performance criteria such as minimum convergence rate and disturbance rejection, in addition to asymptotic stability. In such cases, the observer can no longer be designed using a linear matrix inequality. A bilinear matrix inequality (BMI) is needed instead and involves a non-separable product of the observer gain matrices and the Lyapunov positive definite matrix. This paper develops a technique to solve a BMI for such a multi-objective observer design problem. The BMI design condition is transformed into an eigenvalue problem and a convex-concave based sequential linear matrix inequality (LMI) optimization method is used to find a feasible solution to the BMI. The developed observer design method is applied to a robust automotive slip angle estimation problem, where the L2 gain from the disturbance to the observer error is restricted be lower than 0.2 and the estimated states converges to the neighborhood of the real states within 0.3 s in the presence of uncertain vehicle dynamics.
Journal Article
Extended nonlinear observer canonical form depending on system output and auxiliary state
This paper deals with the problem of transforming a single output nonlinear system with an auxiliary dynamics into an extended nonlinear observer canonical form (ENOCF). The proposed ENOCF depends on system output and auxiliary state, and admits a kind of high-gain observer. We provide two necessary conditions and an equivalent condition for the existence of such a transformation, and then apply the results to the Rössler system as a case study.
Journal Article
Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview
Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.
Journal Article
On-line Ladle Lining Temperature Estimation by Using Bounded Jacobian Nonlinear Observer
The knowledge of transient temperature of the ladle wall is a key factor in optimizing energy consumption in steelmaking process.The transient temperature needs to be estimated.A nonlinear lumped parameter model was used to model the thermal dynamics of the ladle.Then,the bounded Jacobian nonlinear observer was utilized to estimate the temperature.With this method,the estimation model became a closed-loop model and the observer gains were obtained by solving linear matrix inequalities and simply implemented to the system.Comparison between the simulation and recorded data at a participating steel plant in Thailand showed that the nonlinear observer accurately estimated the temperature of the ladle lining.This estimated temperature was very useful in determining suitable tapping temperature for energy conservation and steel quality.
Journal Article
On the convergence of the unscented Kalman filter
A convergence analysis of the modified unscented Kalman filter (UKF), used as an observer for a class of nonlinear deterministic continuous time systems, is presented. Under certain conditions, the extended Kalman filter (EKF) is an exponential observer for non-linear systems, i.e., the dynamics of the estimation error is exponentially stable. It is shown that unlike the EKF, the UKF is not an exponentially converging observer. A modification of the UKF – the unscented Kalman observer – is proposed, which is a better candidate for an observer.
This paper is a first step towards a proof of the global convergence of the high-gain version of the UKO.
Journal Article
State of Charge Estimation for Lithium-Ion Battery Based on Nonlinear Observer: An H∞ Method
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 a positive role in the observer design. After that, a nonlinear observer design criterion is presented based on the H ∞ method, which is formulated as linear matrix inequalities (LMIs). Compared with existing nonlinear observer-based SOC estimation methods, the proposed observer design criterion does not depend on any estimates of the unknown variables. Consequently, the convergence of the proposed nonlinear observer is guaranteed for any operating conditions. Finally, both the static and dynamic experimental cases are given to show the efficiency of the proposed nonlinear observer by comparing with the classic extended Kalman filter (EKF).
Journal Article
Integration of nonlinear observer and unscented Kalman filter for pose estimation in autonomous truck–trailer and container truck
This paper introduces a new approach to state estimation called nonlinear observer-unscented Kalman filter (NLO-UKF). The proposed method is designed to improve the accuracy of state estimation in complex systems that are subject to nonlinearity and uncertainty. The key idea of the NLO-UKF is to use a nonlinear observer to correct the projected sigma points based on a measurement, and then update the mean and covariance using the UKF. The paper provides a detailed description of the NLO-UKF algorithm and demonstrates its boundedness. The use of NLO-UKF for pose estimation is presented to compare the effectiveness of the proposed method with other state estimation methods in the simulation of an autonomous truck–trailer system and experimentation with a container truck system. The NLO-UKF demonstrates improved accuracy during steady-state estimation.
Journal Article
Event-driven-observer-based fuzzy fault-tolerant control for nonlinear system with actuator fault
In this study, a novel fuzzy logic-aided event-driven-observer-based fault-tolerant control approach is investigated for a class of nonlinear systems with time-varying actuator faults and unmatched disturbances. The considered actuator faults and disturbances are unknown. To achieve the control purpose, first, the fuzzy logic theory is used to approximate the nonlinear unknown functions. Then, a novel fuzzy-aided nonlinear observer is constructed to estimate the unmeasured states, actuator faults, and unmatched disturbances. Based on the observer outputs, a novel fault-tolerant controller is designed by utilizing the backstepping technique. Furthermore, an event-triggered control scheme is presented in the control channel to reduce the transmitted data, while the fault tolerance and disturbance rejection abilities can also be guaranteed. The Zeno phenomenon avoidance performance is verified, and finally, the application to a robotic tracking control system results shows the effectiveness of the presented control scheme.
Journal Article
Adaptive neural network control for nonlinear cyber-physical systems subject to false data injection attacks with prescribed performance
Cyber-physical systems (CPSs), as emerging products of industry 4.0 , play a key role in the development of intelligent manufacturing. This paper proposes an observer-based adaptive neural network (NN) control for nonlinear strict-feedback CPSs subject to false data injection attacks. Since there may be strict constraints on the state or output signals of nonlinear cyber-physical systems (NCPSs), we propose a time-varying asymmetric barrier Lyapunov function to realize the specific output constraints of NCPSs under cyber-attacks. Besides, since false data injection attacks will corrupt the transmitted state variables, an observer is designed to obtain observations of the exact states, and NN is used to approximate the unknown nonlinearity of NCPSs. With the proposed control strategy, the constraint control problem of NCPSs subject to false data injection attacks is settled. Finally, a numerical simulation example verifies the effectiveness of the proposed controller. This article is part of the theme issue ‘Towards symbiotic autonomous systems’.
Journal Article