Neural Networks Based Probability Density Function Control for Stochastic Systems

2009 ◽  
pp. 125-148
Author(s):  
Xubin Sun ◽  
Jinliang Ding ◽  
Tianyou Chai ◽  
Hong Wang
Keyword(s):  
Neural Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Stochastic Systems

Reshaping of the probability density function of nonlinear stochastic systems against abrupt changes

2019 ◽  
Vol 26 (7-8) ◽  
pp. 532-539
Author(s):  
Lei Xia ◽  
Ronghua Huan ◽  
Weiqiu Zhu ◽  
Chenxuan Zhu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Stochastic Systems ◽  
Stationary Probability ◽  
Markov Jump ◽  
Nonlinear Stochastic Systems ◽  
Stationary Probability Density ◽  
Abrupt Changes ◽  
Stationary Probability Density Function

The operation of dynamic systems is often accompanied by abrupt and random changes in their configurations, which will dramatically change the stationary probability density function of their response. In this article, an effective procedure is proposed to reshape the stationary probability density function of nonlinear stochastic systems against abrupt changes. Based on the Markov jump theory, such a system is formulated as a continuous system with discrete Markov jump parameters. The limiting averaging principle is then applied to suppress the rapidly varying Markov jump process to generate a probability-weighted system. Then, the approximate expression of the stationary probability density function of the system is obtained, based on which the reshaping control law can be designed, which has two parts: (i) the first part (conservative part) is designed to make the reshaped system and the undisturbed system have the same Hamiltonian; (ii) the second (dissipative part) is designed so that the stationary probability density function of the reshaped system is the same as that of undisturbed system. The proposed law is exactly analytical and no online measurement is required. The application and effectiveness of the proposed procedure are demonstrated by using an example of three degrees-of-freedom nonlinear stochastic system subjected to abrupt changes.

Rate of Convergence in Density Estimation Using Neural Networks

1996 ◽  
Vol 8 (5) ◽  
pp. 1107-1122 ◽  
Author(s):  
Dharmendra S. Modha ◽  
Elias Masry
Keyword(s):  
Neural Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Rate Of Convergence ◽  
Density Function ◽  
Density Estimation ◽  
Exponential Family ◽  
Density Estimator ◽  
Estimation Scheme ◽  
Hidden Layer

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.

scholarly journals The shape regulation of probability density function for stochastic systems

2014 ◽  
Vol 63 (24) ◽  
pp. 240508
Author(s):  
Yang Heng-Zhan ◽  
Qian Fu-Cai ◽  
Gao Yun ◽  
Xie Guo
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Stochastic Systems
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