A discrete state-space controller for superconducting turbogenerators

1988 ◽  
Vol 3 (2) ◽  
pp. 300-304 ◽  
Author(s):  
M.A.A.S. Alyan ◽  
Y.H. Rahim
Keyword(s):  
State Space ◽  
Discrete State ◽  
Discrete State Space

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

A novel recursive T-S fuzzy semantic modeling approach for discrete state-space systems

2019 ◽  
Vol 340 ◽  
pp. 222-232 ◽  
Author(s):  
Liang-Qun Li ◽  
Xiao-Li Wang ◽  
Wei-Xin Xie ◽  
Zong-Xiang Liu
Keyword(s):  
State Space ◽  
Space Systems ◽  
Semantic Modeling ◽  
Discrete State ◽  
Modeling Approach ◽  
State Space Systems ◽  
Discrete State Space

scholarly journals Aggregation of Markov flows I: theory

2018 ◽  
Vol 376 (2118) ◽  
pp. 20170232 ◽  
Author(s):  
R. S. MacKay ◽  
J. D. Robinson
Keyword(s):  
State Space ◽  
Efficient Computation ◽  
Theme Issue ◽  
Discrete State ◽  
Mean First Passage Times ◽  
Hierarchical Aggregation ◽  
Semi Markov Process ◽  
Potential Benefits ◽  
Discrete State Space ◽  
Passage Times

A Markov flow is a stationary measure, with the associated flows and mean first passage times, for a continuous-time regular jump homogeneous semi-Markov process on a discrete state space. Nodes in the state space can be eliminated to produce a smaller Markov flow which is a factor of the original one. Some improvements to the elimination methods of Wales are given. The main contribution of the paper is to present an alternative, namely a method to aggregate groups of nodes to produce a factor. The method can be iterated to make hierarchical aggregation schemes. The potential benefits are efficient computation, including recomputation to take into account local changes, and insights into the macroscopic behaviour. This article is part of the theme issue ‘Hilbert’s sixth problem’.

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