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Recurrent Neural Networks for Stochastic Control Problems with Delay [article]

Jiequn Han, Ruimeng Hu
2021 arXiv   pre-print
In this paper, we propose and systematically study deep neural networks-based algorithms to solve stochastic control problems with delay features.  ...  Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions.  ...  neural networks to solve stochastic control problems with delay beyond the linear-quadratic case.  ... 
arXiv:2101.01385v2 fatcat:7plkmhbbabd2zjii2776vgvwyq

Stability Criteria for Stochastic Recurrent Neural Networks with Two Time-Varying Delays and Impulses

R. Raja, S.Marshal Anthoni
2010 International Journal of Computer Applications  
This paper is concerned with a stability problem for a class of stochastic recurrent impulsive neural networks with both discrete and distributed time-varying delays.  ...  Based on Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of impulsive neural networks.  ...  For the best of author's knowledge there were no global stability results for stochastic recurrent impulsive neural networks with both discrete and distributed delays.  ... 
doi:10.5120/514-831 fatcat:26wa6tvj4rglrpjx6yrwweahha

Stability Results for Uncertain Stochastic High-Order Hopfield Neural Networks with Time Varying Delays [chapter]

P. Balasubramaniam, R. Rakkiyapp
2008 Recurrent Neural Networks  
In this paper, we are concerned with the global stability for a class of uncertain stochastic high-order neural networks with time varying delays.  ...  Uncertain Stochastic High-Order Hopfield Neural Networks with Time Varying Delays 337 (42) Using the inequality technique, we have (43) Stability Results for Uncertain Stochastic High-Order  ...  Stability Results for Uncertain Stochastic High-Order Hopfield Neural Networks with Time Varying Delays, Recurrent Neural Networks, Xiaolin Hu and P.  ... 
doi:10.5772/5555 fatcat:cxa5xma2czhitkwpzwsjazqtiu

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Shuping He, Zhengguang Wu, Hao Shen, Yanyan Yin, Quanxin Zhu
2014 Abstract and Applied Analysis  
, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.  ...  As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits.  ...  Acknowledgments We first express our great appreciation to all the authors of this special issue for their high quality contributions.  ... 
doi:10.1155/2014/582549 fatcat:wamtzydcezhwfnwbo5vgcmhq5y

Input-to-State Stability of Stochastic Memristive Neural Networks with Time-Varying Delay

Xu Y. Lou, Qian Ye
2015 Mathematical Problems in Engineering  
This paper is concerned with the input-to-state stability problem of a class of memristive neural networks.  ...  We consider the neural networks that take into account both the stochastic effects and time-varying delay, and introduce the notions of meansquare exponential input-to-state stability.  ...  Acknowledgments This work is partially supported by National Natural Science Foundation of China (61473136), the Fundamental Research Funds for the Central Universities (JUSRP51322B), the 111 Project (  ... 
doi:10.1155/2015/140857 fatcat:xrdh5ko6nzg5lkfjgguafwvg3q

Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

Tianyu Wang, Quanxin Zhu, Jingwei Cai
2018 Mathematical Problems in Engineering  
We are interested in a class of stochastic fuzzy recurrent neural networks with multiproportional delays and distributed delays.  ...  By constructing suitable Lyapunov-Krasovskii functionals and applying stochastic analysis theory, Ito^'s formula and Dynkin's formula, we derive novel sufficient conditions for mean-square exponential  ...  Motivated by the above discussion, in this paper we investigate the problem of the input-to-state stability analysis for a class of the stochastic fuzzy delayed recurrent neural networks with multiproportional  ... 
doi:10.1155/2018/6289019 fatcat:nr6cy4mar5hhdfvszuvjwqi7si

Page 8427 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
stochastic stability and H., analysis for time-delay systems with Markovian jumping parameters.  ...  In this paper, sufficient conditions for stochastic stability of two families of feedback sig- moid neural networks are presented.  ... 

Mathematical Problems for Complex Networks

Zidong Wang, Jinling Liang, Yurong Liu
2012 Mathematical Problems in Engineering  
Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication  ...  Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet.  ...  Acknowledgments This special issue is a timely reflection of the research progress in the area of mathematical problems for complex networks.  ... 
doi:10.1155/2012/934680 fatcat:kd3rfwztpzbv7bbzq3sqmkc3ci

On general systems with randomly occurring incomplete information

Zidong Wang, Jun Hu, Hongli Dong
2016 International Journal of General Systems  
In the paper entitled "H ∞ State Estimation for Discrete-time Memristive Recurrent Neural Networks with Stochastic Time-delays" by H.  ...  ., the robust H ∞ state estimation problem is investigated for a class of memristive recurrent neural networks with randomly occurring time-delays.  ... 
doi:10.1080/03081079.2015.1106734 fatcat:3uvg6qgeu5bipn7cbon3lfovyy

Quantum Neural Machine Learning: Backpropagation and Dynamics

Carlos Pedro Gonçalves
2016 NeuroQuantology  
The results are extended to general architectures including recurrent networks that interact with an environment, coupling with it in the neural links' activation order, and self-organizing in a dynamical  ...  The current work addresses quantum machine learning in the context of Quantum Artificial Neural Networks such that the networks' processing is divided in two stages: the learning stage, where the network  ...  Recurrence frequencies calculated for the three neuron neural network, the frequencies were calculated for a delay embedding with dE=7 for a 5000 iterations series taken from a 6000 iterations simulation  ... 
doi:10.14704/nq.2017.15.1.1008 fatcat:k7aur5gayzgtlkktw3reyodbf4

Stochastic Systems: Modeling, Analysis, Synthesis, Control, and Their Applications to Engineering

Weihai Zhang, M. D. S. Aliyu, Yun-Gang Liu, Xue-Jun Xie
2012 Mathematical Problems in Engineering  
The next paper deals with the synchronization of stochastic neural networks and is entitled "Master-slave synchronization Mathematical Problems in Engineering 3 of stochastic neural networks with mixed  ...  Gao; "Iterative learning control for remote control systems with communication delay and data dropout," by C.  ...  Acknowledgments As the Lead Guest Editor of this special issue, I wish to express my profound gratitude to my three coeditors for accepting to undertake this project with me and the wonderful accomplishment  ... 
doi:10.1155/2012/745065 fatcat:pntcptknizcazhajqfrlvrwlpi

Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays

Zidong Wang, Yurong Liu, Maozhen Li, Xiaohui Liu
2006 IEEE Transactions on Neural Networks  
In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed  ...  It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs  ...  In this letter, we deal with the global asymptotic stability analysis problem for a class of stochastic Cohen-Grossberg neural networks with discrete and distributed time-delays.  ... 
doi:10.1109/tnn.2006.872355 pmid:16722186 fatcat:x6jsa5lr3jba3ds3saivhph2gq

Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

Deyi Li, Yuanyuan Wang, Guici Chen, Shasha Zhu
2018 Mathematical Problems in Engineering  
This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay.  ...  Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities  ...  for inertial neural networks with time-delay [20] .  ... 
doi:10.1155/2018/2939425 fatcat:7ljrbge4ufh2lgt57pew6vnkny

Synchronization Control for Stochastic Neural Networks with Mixed Time-Varying Delays

Qing Zhu, Aiguo Song, Shumin Fei, Yuequan Yang, Zhiqiang Cao
2014 The Scientific World Journal  
Synchronization control of stochastic neural networks with time-varying discrete and continuous delays has been investigated.  ...  Sufficient conditions have been derived to ensure the global asymptotical mean-square stability for the error system, and thus the drive system synchronizes with the response system.  ...  Acknowledgments The authors would like to thank the editor and the reviewers for their helpful and valuable comments and suggestions, which have improved the presentation. This work is sup-  ... 
doi:10.1155/2014/840185 pmid:25110747 pmcid:PMC4106077 fatcat:hkei5vupzbashhz6o67dokyi24

Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

Wenwu Yu, Jinde Cao
2007 Neural Processing Letters  
In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered.  ...  Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks  ...  Up to now, most works on delayed neural networks have focused on the stability analysis problem for neural networks with constant or time-varying delays.  ... 
doi:10.1007/s11063-007-9045-x fatcat:jdtmm7ckvbfgrj5kx76mkm77ca
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