Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

For nonlinear stochastic systems, controlling low‐order moment indexes, such as mean and variance, may not effectively achieve actual control requirements since they do not reflect the complete statistical characteristics of random variables. Instead, the probability density function (PDF), which provides complete characterization of statistical properties, can be used to control each order moment more efficiently. Existing PDF shape control methods are mainly suited for nonlinear systems with polynomial forms, which leads to limitations in their applications. In this article, we propose a PDF shape control method using the Fokker–Planck–Kolmogorov (FPK) equation for nonlinear stochastic systems with arbitrary expression. In the proposed method, the exact stationary solution of the FPK equation is derived first. If the nonlinear function of the stochastic system is not polynomial, it is first converted into a polynomial form using the approximation method. The controller is then devised for PDF shape control, and the parameters of the controller are optimized to obtain the optimal controller. We conducted simulation experiments to validate the effectiveness of the proposed method. The results show that the proposed method can effectively control the PDF shape of the state response for nonlinear stochastic systems, regardless of whether the target PDF is unimodal, symmetric bimodal, or asymmetric bimodal. Compared with the Fourier transform method, the control effect of the proposed method is much better. The results suggest that the proposed method provides a scientific basis for wider applications of the PDF shape control method.

Section: Introductionmentioning

confidence: 99%

Developing an innovative method to control the probability density function shape of the state response for nonlinear stochastic systems

Wang

Xie

Qian

et al. 2021

“…For instance, the external noises on DCNs are generally required to be energy-bounded or have Gaussian probability distributions so as to facilitate the utilization of the H ∞ filter or Kalman filter algorithms, respectively. However, the noises in real systems might be norm-bounded rather than energy-bounded, 9 and the Gaussian characteristics of noises are rarely met in practice. In the presence of norm-bounded noises, the traditional H ∞ and Kalman filter theories are no longer applicable and, in search of an alternative methodology, the moving-horizon estimation (MHE) appears to be particularly suitable to handle norm-bounded non-Gaussian noises whose summation/integral over time could tend to infinity.…”

Section: Introductionmentioning

confidence: 99%

Centralized moving‐horizon estimation for a class of nonlinear dynamical complex networks under event‐triggered transmission scheme

Gao

Wang

Sheng

et al. 2022

Self Cite

This article is concerned with the problem of event-triggered centralized moving-horizon state estimation for a class of nonlinear dynamical complex networks. An event-triggered scheme is employed to reduce unnecessary data transmissions between sensors and estimators, where the signal is transmitted only when certain condition is violated. By treating sector-bounded nonlinearities as certain sector-bounded uncertainties, the addressed centralized moving-horizon estimation problem is transformed into a regularized robust least-squares problem that can be effectively solved via existing convex optimization algorithms. Moreover, a sufficient condition is derived to guarantee the exponentially ultimate boundedness of the estimation error, and an upper bound of the estimation error is also presented. Finally, a numerical example is provided to demonstrate the feasibility and efficiency of the proposed estimator design method.

“…Over the past several decades, the nonlinear filtering or state estimation problem has drawn particular research attention due to its engineering insight in extensive applications such as control design, orbit determination and target tracking. A number of filtering algorithms have been developed for nonlinear systems including polynomial filtering, 1,2 extended Kalman filtering (EKF), 3 unscented Kalman filtering (UKF) 4 . EKF is developed for nonlinear systems by using the linearization technique, but it is not suitable for systems with high nonlinearities or parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Consensus‐based unscented Kalman filtering over sensor networks with communication protocols

Sheng

Huai

Niu

et al. 2021

Self Cite

This article is concerned with the consensus‐based distributed filtering problem for a class of general nonlinear systems over sensor networks with communication protocols. In order to avoid data collisions, the stochastic protocol and the Round‐Robin protocol are respectively introduced to schedule the data transmission between each node and its neighboring ones. A consensus‐based unscented Kalman filtering (UKF) algorithm is developed for the purpose of estimating the system states over sensor networks subject to communication protocols. Moreover, the exponential boundedness of estimation error in mean square is proved for the proposed algorithm. Finally, compared with the extended Kalman filtering, an experimental simulation example is provided to validate the effectiveness of the consensus‐based UKF algorithm.