Control of Recurrent Neural Networks Using Differential Minimax Game: The Stochastic Case

2010 ◽  
Author(s):  
Ziqian Liu ◽  
Nirwan Ansari
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
New Approach ◽  
Numerical Example ◽  
Inverse Optimality ◽  
Stochastic Case ◽  
Stochastic Input ◽  
Minimax Game ◽  
Unknown Covariance ◽  
Lyapunov Technique

As a continuation of our study, this paper extends our research results of optimality-oriented stabilization from deterministic recurrent neural networks to stochastic recurrent neural networks, and presents a new approach to achieve optimally stochastic input-to-state stabilization in probability for stochastic recurrent neural networks driven by noise of unknown covariance. This approach is developed by using stochastic differential minimax game, Hamilton-Jacobi-Isaacs (HJI) equation, inverse optimality, and Lyapunov technique. A numerical example is given to demonstrate the effectiveness of the proposed approach.

Design of Globally Robust Control for Biologically-Inspired Noisy Recurrent Neural Networks

2011 ◽  
pp. 116-135
Author(s):  
Ziqian Liu
Keyword(s):  
Neural Networks ◽  
Robust Control ◽  
Recurrent Neural Networks ◽  
Disturbance Attenuation ◽  
Biologically Inspired ◽  
Inverse Optimality ◽  
Modeling Errors ◽  
Minimax Game ◽  
Biological Motor ◽  
Lyapunov Technique

This chapter presents a theoretical design of how a global robust control is achieved in a class of noisy recurrent neural networks which is a promising method for modeling the behavior of biological motor-sensor systems. The approach is developed by using differential minimax game, inverse optimality, Lyapunov technique, and the Hamilton-Jacobi-Isaacs equation. In order to implement the theory of differential games into neural networks, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The proposed design achieves global inverse optimality with respect to some meaningful cost functional, global disturbance attenuation, as well as global asymptotic stability provided no disturbance. Finally, numerical examples are used to demonstrate the effectiveness of the proposed design.

Optimality-Oriented Stabilization for Recurrent Neural Networks

2011 ◽  
pp. 93-115
Author(s):  
Ziqian Liu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Jacobi Equation ◽  
Control Design ◽  
Optimal Stabilization ◽  
Numerical Examples ◽  
Differential Game Theory ◽  
Inverse Optimality ◽  
Hamilton Jacobi Equation ◽  
Lyapunov Technique

This chapter presents an approach of how optimality-oriented stabilization is achieved for recurrent neural networks, which includes both the input-to-state stabilization for deterministic recurrent neural networks and the noise-to-state stabilization for stochastic recurrent neural networks. Owing to the difficulty in solving the Hamilton-Jacobi equation for nonlinear systems, optimal regulation seems to be an unachievable goal in control design for recurrent neural networks. However, a methodology proposed in this chapter solves the problem and obtains optimal stabilization by using the knowledge of Lyapunov technique, inverse optimality, and differential game theory. Numerical examples demonstrate the effectiveness of the proposed design.

scholarly journals General methods of forecasting nonlinear nonstationary processes based on mathematical models using statistical data

2021 ◽  
pp. 79-86
Author(s):  
Oleg Belas ◽  
Andrii Belas
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Mathematical Models ◽  
Recurrent Neural Networks ◽  
Statistical Data ◽  
Economic Systems ◽  
Nonstationary Processes ◽  
General Technique ◽  
New Approach ◽  
Advantages And Disadvantages

The article considers the problem of forecasting nonlinear nonstationary processes, presented in the form of time series, which can describe the dynamics of processes in both technical and economic systems. The general technique of analysis of such data and construction of corresponding mathematical models based on autoregressive models and recurrent neural networks is described in detail. The technique is applied on practical examples while performing the comparative analysis of models of forecasting of quantity of channels of service of cellular subscribers for a given station and revealing advantages and disadvantages of each method. The need to improve the existing methodology and develop a new approach is formulated.

Towards an Embedding-Based Approach for the Geolocation of Texts and Users on Social Networks

2021 ◽  
pp. 206-234
Author(s):  
Sarra Hasni
Keyword(s):  
Neural Networks ◽  
Social Networks ◽  
Spatial Analysis ◽  
Recurrent Neural Networks ◽  
Contextual Information ◽  
Language Models ◽  
New Approach ◽  
Textual Data ◽  
Word Forms ◽  
Statistical Language Models

The geolocation task of textual data shared on social networks like Twitter attracts a progressive attention. Since those data are supported by advanced geographic information systems for multipurpose spatial analysis, new trends to extend the paradigm of geolocated data become more emergent. Differently from statistical language models that are widely adopted in prior works, the authors propose a new approach that is adopted to the geolocation of both tweets and users through the application of embedding models. The authors boost the geolocation strategy with a sequential modelling using recurrent neural networks to delimit the importance of words in tweets with respect to contextual information. They evaluate the power of this strategy in order to determine locations of unstructured texts that reflect unlimited user's writing styles. Especially, the authors demonstrate that semantic proprieties and word forms can be effective to geolocate texts without specifying local words or topics' descriptions per region.

scholarly journals Gene Expression Analysis using Markov Chains extracted from RNNs

2007 ◽  
Vol 10 (2) ◽  
Author(s):  
Igor Lorenzato Almeida ◽  
Denise Regina Pechmann ◽  
Adelmo Luis Cechin
Keyword(s):  
Gene Expression ◽  
Neural Networks ◽  
Markov Chains ◽  
Microarray Data ◽  
Recurrent Neural Networks ◽  
Gene Expression Analysis ◽  
Data Sets ◽  
New Approach ◽  
Several Variables ◽  
Gene Expression Levels

This paper present a new approach for the analysis of gene expres- sion, by extracting a Markov Chain from trained Recurrent Neural Networks (RNNs). A lot of microarray data is being generated, since array technologies have been widely used to monitor simultaneously the expression pattern of thou- sands of genes. Microarray data is highly specialized, involves several variables in which are complex to express and analyze. The challenge is to discover how to extract useful information from these data sets. So this work proposes the use of RNNs for data modeling, due to their ability to learn complex temporal non-linear data. Once a model is obtained for the data, it is possible to ex- tract the acquired knowledge and to represent it through Markov Chains model. Markov Chains are easily visualized in the form of states graphs, which show the influences among the gene expression levels and their changes in time

Control of Recurrent Neural Networks Using Differential Minimax Game: The Deterministic Case

2010 ◽  
Author(s):  
Ziqian Liu ◽  
Nirwan Ansari
Keyword(s):  
Neural Networks ◽  
Dynamic Systems ◽  
Recurrent Neural Networks ◽  
Large Scale ◽  
Nonlinear Dynamic Systems ◽  
Deterministic Case ◽  
Stability Margins ◽  
Theoretical Design ◽  
Modeling Errors ◽  
Minimax Game

This paper presents a theoretical design of how a minimax equilibrium of differential game is achieved in a class of large-scale nonlinear dynamic systems, namely the recurrent neural networks. In order to realize the equilibrium, we consider the vector of external inputs as a player and the vector of internal noises (or disturbances or modeling errors) as an opposing player. The purpose of this study is to construct a nonlinear H∞ optimal control for deterministic noisy recurrent neural networks to achieve an optimal-oriented stabilization, as well as to attenuate noise to a prescribed level with stability margins. A numerical example demonstrates the effectiveness of the proposed approach.

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