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# RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems

## Abstract

This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.

- Authors:

- Univ. of Liverpool (United Kingdom)
- De Montfort Univ., Leicester (United Kingdom)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Manchester (United Kingdom)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1566993

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Automatic Control

- Additional Journal Information:
- Journal Volume: 65; Journal Issue: 3; Journal ID: ISSN 0018-9286

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Entropy; Stochastic processes; Estimation error; Probability density function; Nonlinear systems; Mathematical model; Neural networks

### Citation Formats

```
Yin, Xin, Zhang, Qichun, Wang, Hong, and Ding, Zhengtao. RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems. United States: N. p., 2019.
Web. doi:10.1109/TAC.2019.2914257.
```

```
Yin, Xin, Zhang, Qichun, Wang, Hong, & Ding, Zhengtao. RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems. United States. doi:10.1109/TAC.2019.2914257.
```

```
Yin, Xin, Zhang, Qichun, Wang, Hong, and Ding, Zhengtao. Tue .
"RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems". United States. doi:10.1109/TAC.2019.2914257.
```

```
@article{osti_1566993,
```

title = {RBFNN-based Minimum Entropy Filtering for a Class of Stochastic Nonlinear Systems},

author = {Yin, Xin and Zhang, Qichun and Wang, Hong and Ding, Zhengtao},

abstractNote = {This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.},

doi = {10.1109/TAC.2019.2914257},

journal = {IEEE Transactions on Automatic Control},

number = 3,

volume = 65,

place = {United States},

year = {2019},

month = {1}

}