Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high-speed train control system

Abstract

In order to control the nonlinear high-speed train with high robustness, the fractional order control of nonlinear switching systems is studied. The fractional order controller is designed for a class of nonlinear switching systems by the fractional order backstepping method. In this paper, a simple and effective online updating scheme of model coefficients is proposed by using the flexibility of the model predictive control algorithm and its wide range of model accommodation. A stochastic discrete nonlinear state space model describing the mechanical behavior of a single particle in a high-speed train is constructed, and the maximum likelihood estimation of the parameters of a high-speed train is transformed into an optimization problem with great expectations. Finally, numerical comparison experiments of motion characters of two high-speed trains are given. The results show the effectiveness of the proposed identification method.

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

“…7 Dai and Sinha utilized the block functions for parameter estimation of the bilinear system. 10 Parameter estimation methods and state filtering can be applied to many areas, 11,12 such as information fusion and fault diagnosis, 13,14 system modelling, 15,16 and signal processing. 9 Nowadays, the Carleman linearization is an approach to reach the approximation, and the bilinear model is proven to be an effective approximator for some nonlinear systems, which can solve the nonlinear system state filtering problems in signal processing and control.…”

Highly computationally efficient state filter based on the delta operator

“…5. Compute the gain vector K(s + 1) by (35) and the posteriori state estimation error covariance matrix P(s + 1) by (36). Increase s by 1.…”

“…Parameter estimation and state filtering are basic for system identification [27][28][29] and system analysis and design, [30][31][32][33] and can be applied to many areas. [34][35][36][37][38][39] The Kalman filter (KF) is known as the optimal state filter for linear systems under the Gaussian white noise and has been extended to study the parameter estimation for bilinear systems. [40][41][42] For nonlinear systems, its modifications such as the particle filter, the extended KF, and the unscented KF give approaches for nonlinear filtering problems.…”

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

“…However, the increased amount of computation can be borne by computers. The proposed methods in this paper can be extended and be applied to many areas [37][38][39][40] such as linear systems [41][42][43][44][45][46] bilinear systems, [47][48][49] and nonlinear systems. 50,51…”