scholarly journals pth Mean Practical Stability for Large-Scale Itô Stochastic Systems with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Yun ◽  
Huisheng Shu ◽  
Yan Che
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Practical Stability ◽  
Nonlinear Stochastic Systems ◽  
Deterministic Systems ◽  
The One

Motivated by the study of a class of large-scale stochastic systems with Markovian switching, this correspondence paper is concerned with the practical stability in thepth mean. By investigating Lyapunov-like functions and the basic comparison principle, some criteria are derived for various types of practical stability in thepth mean of nonlinear stochastic systems. The main contribution of these results is to convert the problem of practical stability in thepth mean of stochastic systems into the one of practical stability of the comparative deterministic systems.

A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems

1998 ◽  
Vol 65 (4) ◽  
pp. 867-869 ◽  
Author(s):  
J. Q. Sun
Keyword(s):  
Ad Hoc ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Nonlinear Stochastic Systems ◽  
Transition Probability Density ◽  
Generalized Cell Mapping ◽  
One Step ◽  
Step Transition ◽  
The One ◽  
Cell Partition

This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly from being linear to being strongly nonlinear. The nonuniform cell partition is shown to lead to more accurate steady-state solutions and enhance the computational efficiency of the GCM method.

scholarly journals Forward sensitivity analysis for contracting stochastic systems

2018 ◽  
Vol 50 (01) ◽  
pp. 102-130
Author(s):  
Thomas Flynn
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Systems ◽  
Wasserstein Distance ◽  
Gradient Estimation ◽  
Deterministic Systems ◽  
Continuous State Space ◽  
Continuous State ◽  
Sensitivity Analysis Method ◽  
One Step ◽  
The One

Abstract In this paper we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee differentiability of stationary costs. Then we show how to estimate the derivatives, deriving an estimator that can be seen as a generalization of the forward sensitivity analysis method used in deterministic systems. We apply the results to examples, including a neural network model.

scholarly journals Conditional Gaussian Systems for Multiscale Nonlinear Stochastic Systems: Prediction, State Estimation and Uncertainty Quantification

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 509 ◽  
Author(s):  
Nan Chen ◽  
Andrew Majda
Keyword(s):  
Large Scale ◽  
Stochastic Systems ◽  
Planck Equation ◽  
Reaction Diffusion ◽  
Small Scale ◽  
Model Errors ◽  
Nonlinear Stochastic Systems ◽  
Hybrid Strategy ◽  
Highly Nonlinear ◽  
Non Gaussian

A conditional Gaussian framework for understanding and predicting complex multiscale nonlinear stochastic systems is developed. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the non-Gaussian features of nature. The special structure of the system allows closed analytical formulae for solving the conditional statistics and is thus computationally efficient. A rich gallery of examples of conditional Gaussian systems are illustrated here, which includes data-driven physics-constrained nonlinear stochastic models, stochastically coupled reaction–diffusion models in neuroscience and ecology, and large-scale dynamical models in turbulence, fluids and geophysical flows. Making use of the conditional Gaussian structure, efficient statistically accurate algorithms involving a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry are developed for solving the Fokker–Planck equation in large dimensions. The conditional Gaussian framework is also applied to develop extremely cheap multiscale data assimilation schemes, such as the stochastic superparameterization, which use particle filters to capture the non-Gaussian statistics on the large-scale part whose dimension is small whereas the statistics of the small-scale part are conditional Gaussian given the large-scale part. Other topics of the conditional Gaussian systems studied here include designing new parameter estimation schemes and understanding model errors.

scholarly journals Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

2007 ◽  
Vol 49 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Zhenting Hou ◽  
Hailing Dong ◽  
Peng Shi
Keyword(s):  
Markov Chain ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Switching Systems ◽  
Switching System ◽  
Nonlinear Stochastic Systems ◽  
Semi Markov Process ◽  
Markovian Switching Systems ◽  
Semi Markov Processes

abstractIn this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.

Full-Order Distributed Fault Diagnosis for Large-Scale Nonlinear Stochastic Systems

2015 ◽  
Author(s):  
Elaheh Noursadeghi ◽  
Ioannis Raptis
Keyword(s):  
Particle Filtering ◽  
Large Scale ◽  
Stochastic Systems ◽  
Fault Detection And Isolation ◽  
Consensus Algorithm ◽  
Nonlinear Stochastic Systems ◽  
Graph Theoretic ◽  
Progression Model ◽  
Distributed Fault Detection ◽  
Distributed Average Consensus

This paper deals with the problem of designing a distributed fault detection and isolation algorithm for nonlinear large-scale systems that are subjected to multiple fault modes. To solve this problem, a network of detection nodes is deployed to monitor the monolithic system. Each node consists of an estimator with partial observation of the system’s state. The local estimator executes a distributed variation of the particle filtering algorithm; that process the local sensor measurements and the fault progression model of the system. In addition, each node communicates with its neighbors by sharing pre-processed information. The communication topology is defined using graph theoretic tools. The information fusion between the neighboring nodes is performed by a distributed average consensus algorithm to ensure the agreement on the value of the local estimates. The simulation results demonstrate the efficiency of the proposed approach.

Sign in / Sign up

Export Citation Format

Share Document