Extended Kalman filter and adaptive backstepping for mean temperature control of a three‐way catalytic converter

Utz, Tilman; Fleck, Christian; Frauhammer, J.; Seiler-Thull, Daniel; Kugi, Andreas

doi:10.1002/rnc.3065

Cited by 11 publications

(4 citation statements)

References 23 publications

(27 reference statements)

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“…There are many control methods have been presented so far. For example, the sliding mode control applying in uncertain systems with known relative degree, 18 adaptive backstepping control for the mean temperature, 19 passive control of unsteady condensation shock wave, 20 active control for a flexible plate in restraining the plate vibration, 21 and fuzzy adaptive control of nozzle structure for multi-material rapid prototyping, 22 etc. Thus, finally, two hyperchaos control methods are given.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Cui

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Firstly, a novel six-dimensional (6D) hyperchaotic particle motion system is formulated. The equilibrium points and their characteristics, Poincaré sections, Lyapunov exponents, bifurcations and multi-periodic windows are studied. Secondly, we present two nonholonomic constrained systems. In order to analyze the particle motion trajectories under constraints, the explicit equations for constrained systems are given. Based on Lyapunov exponents, Poincaré maps and bifurcations, we can see that the different hyperchaotic phenomena of the particle motion can be generated by introducing nonholonomic constraints. Finally, the stability control of the 6D hyperchaotic particle motion system is realized by separately using constraint control method and linear feedback control method. Numerical simulations of the dynamical behaviors of the six-dimensional hyperchaotic particle motion system are carried out in order to illustrate the complex phenomena of the systems and verify the analysis results.

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Section: Introductionmentioning

confidence: 99%

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Cui

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…In , the EKF was employed as a new optimal back‐stepping robust adaptive control method for the military moving power station excitation system. Furthermore, in , a kind of real‐time Kalman filtering problem was discussed for systems with distributed multichannel measurements, the EKF is employed for state profile estimation in an adaptive control strategy for the mean temperature of an automotive three‐way catalytic converter, respectively. We need to employ EKF rather than the standard KF because most of practical problems that we need to solve are nonlinear problems where g (·) and f (·) are nonlinear functions with respect to θ .…”

Section: Introductionmentioning

confidence: 99%

Variants of extended Kalman filtering approaches for Bayesian tracking

Lim

Shin

Hwang

2016

Intl J Robust & Nonlinear

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Summary We provide a tutorial for a number of variants of the extended Kalman filter (EKF). In these methods, so called, sigma points are employed to tackle the nonlinearity of problems. The sigma points exactly represent the mean and the variance of the state distribution function in a dynamic state equation. The initially developed EKF variant, that is, unscented Kalman filter (UKF) (also called sigma point Kalman filter) shows enhanced performance compared with that of conventional EKF in the literature. Another variant, which is not well known, is central difference Kalman filter (CDKF) whose way to approximate the nonlinearity is based on the Sterling's polynomial interpolation formula instead of the Taylor series. Endeavor to reduce the computational load resulted in the development of square root versions of both UKF and CDKF, that is, square root unscented Kalman filter and square root central difference Kalman filter (SR‐CDKF). These SR‐versions are supposed to be numerically more stable than their original versions because the state covariance is guaranteed to be positive definite by avoiding the step of matrix decomposition. In this paper, we provide the step‐by‐step algorithms of above‐mentioned EKF variants with their pros and cons. We apply these filtering methods to a number of problems in various disciplines for performance assessment in terms of both mean squared error (MSE) and processing speed. Furthermore, we show how to optimize the filters in terms of MSE performance depending on diverse scenarios. According to simulation results, CDKF and SR‐CDKF show the best MSE performance in most scenarios; particularly, SR‐CDKF shows faster processing speed than that of CDKF. Therefore, we justify that SR‐CDKF is the most efficient and the best approach among the Kalman variants including the EKF for various nonlinear problems. The motivation of this paper targets at the contribution to the disseminative usage of the Kalman variants approaches, particularly, SR‐CDKF taking advantage of its estimating performance and high processing speed. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Because of that, there have been increasing research efforts to improve the Kalman filter in order to overcome the nonlinearities and uncertainties. The extended Kalman filter approach has been traditionally used to recursively estimate the states of a nonlinear system corrupted by noise, which has a Gaussian (normal) distribution [6][7][8][9][10][11][12]. The extended Kalman filter uses local linearization to extend the scope of the Kalman filter to the problem of state estimation of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Joint state and parameter robust estimation of stochastic nonlinear systems

Stojanović

Nedić

2015

Intl J Robust & Nonlinear

101

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SUMMARYSuccessful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez-Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non-Gaussian distributions is illustrated by intensive simulations.

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Extended Kalman filter and adaptive backstepping for mean temperature control of a three‐way catalytic converter

Cited by 11 publications

References 23 publications

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Variants of extended Kalman filtering approaches for Bayesian tracking

Joint state and parameter robust estimation of stochastic nonlinear systems

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