Dynamics of the f-divergence minimization processes based on the speed-gradient principle

2016 ◽  
Author(s):  
Dmitry S. Shalymov ◽  
Alexander L. Fradkov
Keyword(s):  
Gradient Principle ◽  
Divergence Minimization ◽  
Speed Gradient

scholarly journals GENERIC and Speed-Gradient Principle

2018 ◽  
Vol 51 (33) ◽  
pp. 121-126
Author(s):  
Dmitry S. Shalymov ◽  
Alexander L. Fradkov
Keyword(s):  
Gradient Principle ◽  
Speed Gradient

scholarly journals Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150324 ◽  
Author(s):  
Dmitry S. Shalymov ◽  
Alexander L. Fradkov
Keyword(s):  
Limit Distribution ◽  
Mass Conservation ◽  
Random Variable ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Stationary Processes ◽  
Entropy Principle ◽  
Gradient Principle ◽  
Probability Density Function Pdf ◽  
Speed Gradient

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

scholarly journals Evolution of non-stationary processes and some maximum entropy principles

2018 ◽  
Vol 56 (2) ◽  
pp. 43-70
Author(s):  
Vasile Preda ◽  
Irina Băncescu
Keyword(s):  
Maximum Entropy ◽  
Stationary Processes ◽  
Gradient Principle ◽  
Speed Gradient

AbstractThis paper studies, by using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rényi-Tsallis of order α entropies.

Speed-gradient principle for description of transient dynamics in systems obeying maximum entropy principle

2011 ◽  
Author(s):  
Alexander Fradkov ◽  
Anton Krivtsov ◽  
Ali Mohammad-Djafari ◽  
Jean-François Bercher ◽  
Pierre Bessiére
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Transient Dynamics ◽  
Entropy Principle ◽  
Gradient Principle ◽  
Speed Gradient

Adaptive control of time-varying non-linear plants by speed-gradient algorithms

2019 ◽  
pp. 37-44 ◽  
Author(s):  
O. P. Tomchina ◽  
D. N. Polyakhov ◽  
O. I. Tokareva ◽  
A. L. Fradkov
Keyword(s):  
Adaptive Control ◽  
Adaptive Systems ◽  
Reference Model ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Time Varying ◽  
System Solution ◽  
Non Linear ◽  
Initial Uncertainty ◽  
Speed Gradient

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

The Residual Generator: An Improved Divergence Minimization Framework for GAN

2021 ◽  
pp. 108222
Author(s):  
Aurele Tohokantche Gnanha ◽  
Wenming Cao ◽  
Xudong Mao ◽  
Si Wu ◽  
Hau-San Wong ◽  
...  
Keyword(s):  
Residual Generator ◽  
Divergence Minimization
Sign in / Sign up

Export Citation Format

Share Document