Stochastic Control of Network Systems I: NETCAD State Space Structure & Dynamics

2006 ◽  
Author(s):  
Zhongjing Ma ◽  
Peter E. Caines ◽  
Roland P. Malhame
Keyword(s):  
State Space ◽  
Stochastic Control ◽  
Space Structure ◽  
Network Systems ◽  
Structure Dynamics

scholarly journals Mathematical modeling of transformable space structure dynamics

2019 ◽  
Vol 221 ◽  
pp. 01018 ◽  
Author(s):  
Vladimir Zimin ◽  
Alexey Krylov ◽  
Sergey Churilin ◽  
Zikun Zhang
Keyword(s):  
Strain State ◽  
Element Model ◽  
Space Structure ◽  
Space Structures ◽  
Elastic Rod ◽  
Stress Strain ◽  
Large Space ◽  
Structure Dynamics ◽  
Stress Strain State ◽  
Large Space Structure

Today large space structures are in focus of attention of engineers and designers of rocket and space equipment. In ground-based experiments, it is not always possible to carry out complex tests of large space structure functionality. Therefore, the development of mathematical models describing properly the transformable structure dynamics when they opened from the densely packed transport state to the operating position in the orbit becomes very important. To determine the stress-strain state of the frame elements when it is unfolding the shape of the framework is taken at the moments when relative velocities of the adjacent sections are maximal. Supposed, that at these moments the frame elements are getting on the stops limiting their relative angular displacements, and the structure behaves as an elastic rod with specified characteristics. Numerical analysis of the stress-strain state in the framework is carried out by means of a finite element model. Therefore, the represented mathematical model can be effectively used to predict the functional suitability of such transformable space structures already on the early stages of their development.

scholarly journals Modeling and Formal Analysis of Meta-Ecosystems with Dynamic Structure using Graph Transformation.

2021 ◽  
Author(s):  
Boris Flotterer ◽  
Maria Maximova ◽  
Sven Schneider ◽  
Johannes Dyck ◽  
Christian Zöllner ◽  
...  
Keyword(s):  
Graph Transformation ◽  
Formal Analysis ◽  
Dynamic Structure ◽  
Space Structure ◽  
Crucial Importance ◽  
Qualitative Properties ◽  
Ecological Dynamics ◽  
The Third ◽  
Structure Dynamics

Abstract The dynamics of ecosystems is of crucial importance. Various model-based approaches exist to understand and analyze their internal effects. In this paper, we model the space structure dynamics and ecological dynamics of meta-ecosystems using the formal technique of Graph Transformation (short GT). We build GT models to describe how a meta-ecosystem (modeled as a graph) can evolve over time (modeled by GT rules) and to analyze these GT models with respect to qualitative properties such as the existence of structural stabilities. As a case study, we build three GT models describing the space structure dynamics and ecological dynamics of three different savanna meta-ecosystems. The first GT model considers a savanna meta-ecosystem that is limited in space to two ecosystem patches, whereas the other two GT models consider two savanna meta-ecosystems that are unlimited in the number of ecosystem patches and only differ in one GT rule describing how the space structure of the meta-ecosystem grows. In the first two GT models, the space structure dynamics and ecological dynamics of the meta-ecosystem shows two main structural stabilities: the first one based on grassland-savanna-woodland transitions and the second one based on grassland-desert transitions. The transition between these two structural stabilities is driven by high-intensity fires affecting the tree components. In the third GT model, the GT rule for savanna regeneration induces desertification and therefore a collapse of the meta-ecosystem. We believe that GT models provide a complementary avenue to that of existing approaches to rigorously study ecological phenomena.

scholarly journals Assessment of Local Dynamic Stability in Gait Based on Univariate and Multivariate Time Series

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Henryk Josiński ◽  
Adam Świtoński ◽  
Agnieszka Michalczuk ◽  
Piotr Grabiec ◽  
Magdalena Pawlyta ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Dynamic Stability ◽  
Multivariate Time Series ◽  
Assessment Method ◽  
Space Structure ◽  
Largest Lyapunov Exponent ◽  
Local Dynamic ◽  
Short Term ◽  
Local Dynamic Stability

The ability of the locomotor system to maintain continuous walking despite very small external or internal disturbances is called local dynamic stability (LDS). The importance of the LDS requires constantly working on different aspects of its assessment method which is based on the short-term largest Lyapunov exponent (LLE). A state space structure is a vital aspect of the LDS assessment because the algorithm of the LLE computation for experimental data requires a reconstruction of a state space trajectory. The gait kinematic data are usually one- or three-dimensional, which enables to construct a state space based on a uni- or multivariate time series. Furthermore, two variants of the short-term LLE are present in the literature which differ in length of a time span, over which the short-term LLE is computed. Both a state space structure and the consistency of the observations based on values of both short-term LLE variants were analyzed using time series representing the joint angles at ankle, knee, and hip joints. The short-term LLE was computed for individual joints in three state spaces constructed on the basis of either univariate or multivariate time series. Each state space revealed walkers’ locally unstable behavior as well as its attenuation in the current stride. The corresponding conclusions made on the basis of both short-term LLE variants were consistent in ca. 59% of cases determined by a joint and a state space. Moreover, the authors present an algorithm for estimation of the embedding dimension in the case of a multivariate gait time series.

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