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Mathematical Theories and Applications for Nonlinear Control Systems

Xue-Jun Xie, Ju H. Park, Hiroaki Mukaidani, Weihai Zhang
2019 Mathematical Problems in Engineering  
Lin et al. entitled " ∞ Robust Tracking Control of Stochastic T-S Fuzzy Systems with Poisson Jumps" designs a robust adaptive ∞ tracking control for nonlinear stochastic systems with both Brownian motion  ...  Wang studies adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances.  ...  The editors also wish to thank the anonymous reviewers for their careful reading of the manuscripts submitted to this special issue collection and their many insightful comments and suggestions.  ... 
doi:10.1155/2019/2065786 fatcat:qx66v5pu3fgo7ee4rt7rn6rcj4

Intermittent process analysis with scattering moments

Joan Bruna, Stéphane Mallat, Emmanuel Bacry, Jean-François Muzy
2015 Annals of Statistics  
Scattering moments of Poisson processes, fractional Brownian motions, Lévy processes and multifractal random walks are shown to have characteristic decay.  ...  Numerical applications are shown on financial time-series and on energy dissipation of turbulent flows.  ...  For most classes of random processes, including fractional Brownian motions and multifractal random walks, we observe numerically that ϵ(j 1 ) converges to zero as the averaging scale 2 M goes to ∞.  ... 
doi:10.1214/14-aos1276 fatcat:glc7xogqivf7nihkh4pidcfyie

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

Kamsing Nonlaopon, Naveed Ahmad Khan, Muhammad Sulaiman, Fahad Sameer Alshammari, Ghaylen Laouini
2022 Nanomaterials  
Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in  ...  The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg  ...  Acknowledgments: We would like to thank the referees for their valuable comments and helpful advice on our manuscript. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/nano12132273 pmid:35808108 pmcid:PMC9268436 fatcat:5nnxn2b6b5dgjfxh4vxdolsj7m

p-th moment exponential convergence analysis for stochastic networked systems driven by fractional Brownian motion

Jiaxin Shi, Huaiqin Wu
2017 Complex & Intelligent Systems  
In this paper, the existence, uniqueness and asymptotic behavior of mild solutions of stochastic neural network systems driven by fractional Brownian motion are investigated.  ...  By applying the Banach fixed point theorem, the existence and uniqueness of mild solution are analytically proved in a Hilbert space.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s40747-017-0049-5 fatcat:i3cyvg4d5zd3jeffn22xn22mda

Fractional Underdamped Langevin Dynamics: Retargeting SGD with Momentum under Heavy-Tailed Gradient Noise [article]

Umut Şimşekli, Lingjiong Zhu, Yee Whye Teh, Mert Gürbüzbalaban
2020 arXiv   pre-print
We support our theory with experiments conducted on a synthetic model and neural networks.  ...  We observe that the Euler discretization of FULD has noteworthy algorithmic similarities with natural gradient methods and gradient clipping, bringing a new perspective on understanding their role in deep  ...  The contribution of Umut Ş imşekli to this work is partly supported by the French National Research Agency (ANR) as a part of the FBIMATRIX (ANR-16-CE23-0014) project, and by the industrial chair Data  ... 
arXiv:2002.05685v2 fatcat:226fijes3jfjvm5t36sp4cxkbm

2013 Index IEEE Transactions on Automatic Control Vol. 58

2013 IEEE Transactions on Automatic Control  
-L., see Yue, D., TAC Feb. 2013 475-481 Han, S., see Wang, X., TAC April 2013 975-988 Hariharan, S., Zheng, Z., and Shroff, N. B  ...  ., see Dominguez- Garcia, A. D., TAC March 2013 1696-1706 Hammouri, H., see Nadri, M., TAC March 2013 757-762 Hammouri, H., see Benachour, M. S., TAC Dec. 2013 3011-3023 Han, Q.  ...  ., +, TAC March 2013 757-762 On Mean-Square Boundedness of Stochastic Linear Systems With Quan- tized Observations.  ... 
doi:10.1109/tac.2013.2295962 fatcat:3zpqog4r4nhoxgo4vodx4sj3l4

Master Index Volumes 1-100

2002 Stochastic Processes and their Applications  
convergence of an infinite neuron model with local connections 73 (1998) 173 Turova, T.S., Mommaerts, W., van der Meulen, E.C., Synchronization of firing times in a stochastic neural network model with  ...  antipersistent fractional Brownian motion 60 (1995) 1 Cioczek-Georges, R., Mandelbrot, B.B., Alternative micropulses and fractional Brownian motion 64 (1996) 143 Cioczek-Georges, R., Taqqu, M.S., How  ...  Sequential methods; Sequential estimation of parameter in a certain class of stochastic processes 18 (1984) 59 (1995) (2000) 12 (1982) (1985) 71 Yamada, K., A stability theorem for stochastic  ... 
doi:10.1016/s0304-4149(02)00154-0 fatcat:5zmghyapt5d5fp272vy3x63bbq

An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters

Usa Humphries, Grienggrai Rajchakit, Ramalingam Sriraman, Pramet Kaewmesri, Pharunyou Chanthorn, Chee Peng Lim, Rajendran Samidurai
2020 Symmetry  
The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of  ...  time-varying delays and Markovian jumping parameters (MJPs).  ...  Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/sym12061035 fatcat:jtaqi7ay7rbo3f7wolpxlh27yq

Discrete scaling and criticality in a chain of adaptive excitable integrators [article]

Mario Martinez-Saito
2022 arXiv   pre-print
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible  ...  Activity and energy are released as intermittent avalanches of pulses with a discrete scaling distribution largely independent of the exogenous input form.  ...  Alternatively, it can be construed as a discrete version of Brownian motion with stochastic resetting [220] : since ε (t) has a well defined variance, in the scaling limit a (t) l behaves as a Brownian  ... 
arXiv:2201.07075v10 fatcat:32cizc7ayngbxey6b6evdgdqzq

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

Bruce J. West
2022 Fractal and Fractional  
For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies  ...  ) into a single-body fractional stochastic rate equation.  ...  Acknowledgments: The author acknowledges the many investigators whose work are freely drew from and cited herein.  ... 
doi:10.3390/fractalfract6040225 fatcat:7scxmerm2recjlopc5g72oeaxu

How disorder originates and grows inside order [article]

S.E. Kurushina, E.A. Shapovalova
2017 arXiv   pre-print
Mean-field results are compared with numerical simulations of the evolution of the model under study.  ...  Our research is based on the study of solutions of the nonlinear self-consistent Fokker-Planck equation for a stochastic spatially extended model of a chemical reaction.  ...  A neural network consisting of interacting neurons is another example. The nonequilibrium properties of a neural network which models the dynamics of the neocortex are considered in Ref. [4] .  ... 
arXiv:1703.04480v1 fatcat:6rveuaak5ndnbdzgpczmkwuaqa

Driven dissipative dynamics and topology of quantum impurity systems

Karyn Le Hur, Loïc Henriet, Loïc Herviou, Kirill Plekhanov, Alexandru Petrescu, Tal Goren, Marco Schiro, Christophe Mora, Peter P. Orth
2018 Comptes rendus. Physique  
In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures.  ...  In these situations, the non-perturbative stochastic Schroedinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields h_z(t) of arbitrary time-dependence  ...  Acknowledgements This work has been initiated by lectures given at Yale University, at Jouvence in Quebec and at CIFAR meetings, and at small classes at "École polytechnique" (Palaiseau, France).  ... 
doi:10.1016/j.crhy.2018.04.003 fatcat:vzay47eltnbgbbz6cfqhigdcca

Robustness: confronting lessons from physics and biology

Annick Lesne
2008 Biological Reviews  
and novel frameworks are required to account for the robustness properties of living systems.  ...  A distinction between dynamic selection and natural selection in the establishment of a robust behaviour is underlined.  ...  and mean squares identified with square averages (Lesne, 2007) .  ... 
doi:10.1111/j.1469-185x.2008.00052.x pmid:18823391 fatcat:jt7gtj7fefdpndg6geptk2oauq

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

S. Senthilraj, T. Saravanakumar, R. Raja, J. Alzabut
2021 Advances in Difference Equations  
AbstractThis work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete  ...  Finally, we propose numerical simulations to show the efficiency of the proposed method.  ...  Alzabut would like to thank Prince Sultan University and OSTİM Technical University for their support. Funding Not applicable.  ... 
doi:10.1186/s13662-021-03504-8 fatcat:jsh4oznmdjg2lhrtvie6oebleq

Passivity Analysis of Coupled Stochastic Neural Networks with Multiweights

Min Cao, Xun-Wu Yin, Wen-He Song, Xue-Mei Sun, Cheng-Dong Yang, Shun-Yan Ren, Ya Jia
2021 Discrete Dynamics in Nature and Society  
In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions.  ...  By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can  ...  Acknowledgments is work was supported by the Natural Science Foundation of Tianjin, China, under Grant 19JCYBJC18700.  ... 
doi:10.1155/2021/9688627 fatcat:f6b6qkkzhbbjjfi644ae3j6gwq
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