A Novel Fuzzy Approach for State Estimation of Nonlinear Hybrid Systems Using Particle Filtering Method

In this paper, a new particle smoother based on forward filtering backward simulation is developed to solve the nonlinear and non‐Gaussian smoothing problem when measurements are randomly delayed by one sampling time. The heart of the proposed particle smoother is computation of delayed posterior filtering density based on stochastic sampling approach, whose particles and corresponding weights are updated in Bayesian estimation framework by considering the one‐step randomly delayed measurement model. The superior performance of the proposed particle smoother as compared with existing methods is illustrated in a numerical example concerning univariate non‐stationary growth model.

p ({bold-italicx}_{0 : k} | {bold-italicy}_{1 : k}) \approx \overset{p}{true} ({bold-italicx}_{0 : k} | {bold-italicy}_{1 : k}) = \sum_{i = 1}^{N_{f}} {\overset{w}{true}}_{k}^{i} δ ([], {bold-italicx}_{0 : k} - {bold-italicx}_{0 : k}^{i})

where N f is the number of filter particles, and independent and identically distributed samples

{({}, {bold-italicx}_{0 : k}^{i})}_{i = 1}^{N_{f}}

are randomly drawn from q ( x 0: k | y 1: k ), and corresponding importance weights

w_{k}^{i}

and normalized weights

{\overset{w}{true}}_{k}^{i}

are given as

w_{k}^{i} = \frac{p ((), {bold-italicx}_{0 : k}^{i}, {bold-italicy}_{1 : k})}{q ((), {bold-italicx}_{0 : k}^{i} | {bold-italicy}_{1 : k})} {\overset{w}{true}}_{k}^{i} = \frac{w_{k}^{i}}{{falsefalse}_{\sum}^{i = 1} w_{k}^{i}}

To facilitate the online estimation, it is necessary to utilize the sequential importance sampling method. According to the Bayesian theorem, we have …”

Section: Ps For Nonlinear Systems With One‐step Randomly Delayed Measmentioning

confidence: 99%

“…w k − 1 = 1/ N f . Using () in (), w k can be reformulated as

w_{k} = \frac{1}{N_{f}} p ({bold-italicy}_{k} | {bold-italicx}_{k}, {bold-italicx}_{k - 1})

Note that the update of importance weights in () is different from conventional PF because the measurement y k may be z k − 1 when delay happens, thus it may be dependent on x k − 1 .…”

Section: Ps For Nonlinear Systems With One‐step Randomly Delayed Measmentioning

confidence: 99%

“…are randomly drawn from q(x 0∶k |y 1∶k ), and corresponding importance weights w i k and normalized weightsw i k are given as [15,16]…”

Section: Computation Of Delayed Filtering Densitymentioning

confidence: 99%

Section: Computation Of Delayed Filtering Densitymentioning

confidence: 99%

See 2 more Smart Citations

Particle Smoother for Nonlinear Systems With One‐Step Randomly Delayed Measurements

Huang

Zhang

2016

“…This means that the existing algorithms cannot solve the nonlinear mapping function in (20). This means that the existing algorithms cannot solve the nonlinear mapping function in (20).…”

Section: Algorithm For Control Loop Pre-setting Modelmentioning

confidence: 99%

Intelligent Setting Control for Clinker Calcination Process

Qiao¹,

Chai²,

Wang³

2013

In the process of clinker calcination, the target value of the raw meal decomposition rate (RMDR) is different in the easy and difficult calcination stages because the boundary conditions of raw meal (i.e., raw meal flow, raw meal ingredients, and particle size) change frequently, where RMDR cannot be guaranteed to be within its desirable range. To solve this problem, an intelligent setting control method is proposed in this paper for a clinker calcination process. The proposed approach is realized by on-line adjustment of the setpoints of control loops in line with the changes of raw meal boundary conditions. This method consists of five modules, namely an RMDR target value setting model, a control loop pre-setting model, a feedback compensation model based on the fuzzy rules, a feedforward compensation model based on the fuzzy rules, and a soft measurement model for RMDR. Successful application to the clinker calcination process of the Jiuganghongda Cement Plant in China has been made, where the efficiency of the proposed method has been validated by the results of the practical application.

Event‐triggered PCS Based Trajectory Tracking Control of Systems with Perturbation

Song

Wang

Tian

et al. 2017

This paper is aimed at reducing network load for saving bandwidth by designing appropriate trigger signals that decide when the transmission should be done. An event‐triggered piecewise continuous systems (PCS) based control for time‐varying trajectory tracking is proposed. By designing the sensor system and controller system, the communication between them is reduced while still retaining a satisfactory closed‐loop behavior of the whole system. The major idea behind a designed sensor system is the use of a Luenberger observer and planning of event‐triggered mechanism (ETM). The main principle behind the designed controller system is the proposal of a new event‐triggered PCS based controller. The development is motivated by consideration of variable network induced time delays. Tracking error is proved to be norm‐bounded in both the original and developed case. Finally, to show the proposed method's performance, we present the simulation results for a mobile cart.