Identification of High Dimensional System by the General Parameter Method

1981 ◽  
Vol 14 (2) ◽  
pp. 637-642 ◽  
Author(s):  
A.A. Ashimov ◽  
D.J. Syzdykov
Keyword(s):  
High Dimensional ◽  
Parameter Method ◽  
Dimensional System ◽  
General Parameter

Asymptotic Stability of Controlled Nonlinear Stochastic Systems Considering the Dynamics of Sensors and Actuators

2021 ◽  
pp. 2150180
Author(s):  
Jiaojiao Sun ◽  
Zuguang Ying ◽  
Ronghua Huan ◽  
Weiqiu Zhu
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Stable Region ◽  
High Dimensional ◽  
Nonlinear Stochastic System ◽  
Dimensional System ◽  
Sensors And Actuators ◽  
Controlled System

A closed-loop controlled system usually consists of the main structure, sensors, and actuators. In this paper, asymptotic stability of trivial solutions of a controlled nonlinear stochastic system considering the dynamics of sensors and actuators is investigated. Considering the inherent and intentional nonlinearities and random loadings, the coupled dynamic equations of the controlled system with sensors and actuators are given, which are further formulated by a controlled, randomly excited, dissipated Hamiltonian system. The Hamiltonian of the controlled system is introduced, and, based on the stochastic averaging method, the original high-dimensional system is reduced to a one-dimensional averaged system. The analytical expression of Lyapunov exponent of the averaged system is derived, which gives the approximately necessary and sufficient condition of the asymptotic stability of trivial solutions of the original high-dimensional system. The validation of the proposed method is demonstrated by a four-degree-of-freedom controlled system under pure stochastically parametric excitations in detail. A comparative analysis, which is related to the stochastic asymptotic stability of the system with and without considering the dynamics of sensors and actuators, is carried out to investigate the effect of their dynamics on the motion of the controlled system. Results show that ignoring the dynamics of sensors and actuators will get a shrink stable region of the controlled system.

Nonlinear Dynamics and Bifurcations of an Axially Moving Beam

1999 ◽  
Vol 122 (1) ◽  
pp. 21-30 ◽  
Author(s):  
F. Pellicano ◽  
F. Vestroni
Keyword(s):  
High Dimensional ◽  
Axially Moving Beam ◽  
Dimensional System ◽  
Global Dynamics ◽  
Dimensional Phase Space ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method ◽  
Sample Case

The present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem: a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linear subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied. [S0739-3717(00)00501-8]

Sequential Sampling Based Reliability Analysis for High Dimensional Rare Events With Confidence Intervals

2020 ◽  
Author(s):  
Yanwen Xu ◽  
Pingfeng Wang
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Computational Efficiency ◽  
Rare Events ◽  
Computational Cost ◽  
Rare Event ◽  
Probability Analysis ◽  
High Dimensional ◽  
Dimensional System ◽  
Study Results

Abstract Analysis of rare failure events accurately is often challenging with an affordable computational cost in many engineering applications, and this is especially true for problems with high dimensional system inputs. The extremely low probabilities of occurrences for those rare events often lead to large probability estimation errors and low computational efficiency. Thus, it is vital to develop advanced probability analysis methods that are capable of providing robust estimations of rare event probabilities with narrow confidence bounds. Generally, confidence intervals of an estimator can be established based on the central limit theorem, but one of the critical obstacles is the low computational efficiency, since the widely used Monte Carlo method often requires a large number of simulation samples to derive a reasonably narrow confidence interval. This paper develops a new probability analysis approach that can be used to derive the estimates of rare event probabilities efficiently with narrow estimation bounds simultaneously for high dimensional problems. The asymptotic behaviors of the developed estimator has also been proved theoretically without imposing strong assumptions. Further, an asymptotic confidence interval is established for the developed estimator. The presented study offers important insights into the robust estimations of the probability of occurrences for rare events. The accuracy and computational efficiency of the developed technique is assessed with numerical and engineering case studies. Case study results have demonstrated that narrow bounds can be built efficiently using the developed approach, and the true values have always been located within the estimation bounds, indicating that good estimation accuracy along with a significantly improved efficiency.

OPTIMAL SYNTHESIS OF PROCESSOR ARRAYS WITH PIPELINED ARITHMETIC UNITS

1994 ◽  
Vol 04 (03) ◽  
pp. 339-350
Author(s):  
KUMAR GANAPATHY ◽  
BENJAMIN W. WAH
Keyword(s):  
Design Method ◽  
Parameter Method ◽  
Systematic Design ◽  
Processing Elements ◽  
Processor Arrays ◽  
Data Flows ◽  
Matrix Products ◽  
Efficient Scheme ◽  
General Parameter ◽  
Additional Constraints

Two-level pipelining in processor arrays (PAs) involves pipelining of operations across processing elements (PEs) and pipelining of operations in functional units in each PE. Although it is an attractive method for improving the throughput of PAs, existing methods for generating PAs with two-level pipelining are restricted and cannot systematically explore the entire space of feasible designs. In this paper, we extend a systematic design method, called General Parameter Method (GPM), we have developed earlier to find optimal designs of PAs with two-level pipelines. The basic idea is to add new constraints on periods of data flows to include the effect of internal functional pipelines in the PEs. As an illustration, we present pipelined PA designs for computing matrix products. For n-dimensional meshes and other symmetric problems, we provide an efficient scheme to obtain a pipelined PA from a non-pipelined PA using a reindexing transformation. This scheme is used in GPM as a pruning condition to arrive at optimal pipelined PAs efficiently. For pipelines with minimum initiation interval (MII) greater than unity, we show additional constraints that ensure correctness of the synthesized PAs.

STATE SPACE MODELING OF YEAST GENE EXPRESSION DYNAMICS

2007 ◽  
Vol 05 (01) ◽  
pp. 31-46 ◽  
Author(s):  
OLLI HAAVISTO ◽  
HEIKKI HYÖTYNIEMI ◽  
CHRISTOPHE ROOS
Keyword(s):  
Gene Expression ◽  
State Space ◽  
Dynamic Models ◽  
System Modeling ◽  
Dynamic State ◽  
Yeast Genome ◽  
High Dimensional ◽  
Dimensional System ◽  
Yeast Saccharomyces Cerevisiae ◽  
Space Modeling

Combined interaction of all the genes forms a central part of the functional system of a cell. Thus, especially the data-based modeling of the gene expression network is currently one of the main challenges in the field of systems biology. However, the problem is an extremely high-dimensional and complex one, so that normal identification methods are usually not applicable specially if aiming at dynamic models. We propose in this paper a subspace identification approach, which is well suited for high-dimensional system modeling and the presented modified version can also handle the underdetermined case with less data samples than variables (genes). The algorithm is applied to two public stress-response data sets collected from yeast Saccharomyces cerevisiae. The obtained dynamic state space model is tested by comparing the simulation results with the measured data. It is shown that the identified model can relatively well describe the dynamics of the general stress-related changes in the expression of the complete yeast genome. However, it seems inevitable that more precise modeling of the dynamics of the whole genome would require experiments especially designed for systemic modeling.

scholarly journals Triangular System of Higher Order Singular Fractional Differential Equations

2021 ◽  
Vol 45 (01) ◽  
pp. 81-101
Author(s):  
AMELE TAIEB ◽  
ZOUBIR DAHMANI
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
High Dimensional ◽  
Dimensional System ◽  
Stability Of Solutions ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
The Banach Contraction Principle

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, we prove an existence result. We also investigate the uniqueness of solution using the Banach contraction principle. Moreover, we study the Ulam-Hyers stability and the generalized-Ulam-Hyers stability of solutions. Some illustrative examples are also presented.

scholarly journals A Monte Carlo method for in silico modeling and visualization of Waddington’s epigenetic landscape with intermediate details

2018 ◽  
Author(s):  
Xiaomeng Zhang ◽  
Ket Hing Chong ◽  
Jie Zheng
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Time Course ◽  
Initial Conditions ◽  
High Dimensional ◽  
Dimensional System ◽  
Global Dynamics ◽  
Epigenetic Landscape ◽  
Cellular Dynamics ◽  
Gene Regulatory

AbstractWaddington’s epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington’s epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington’s epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U (xi, xj) = −ln P (xi, xj), where P (xi, xj) is the estimated probability of an equilibrium steady state or a non-equilibrium state. A state with locally maximal probability corresponds to a locally minimal potential and such a state is called an attractor. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The same topography of landscape can be produced from deterministic or stochastic time-course simulations. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN. Besides GRN-driven landscapes of cellular dynamics, the algorithm proposed can also be applied to studies of global dynamics (or emergence behavior) of other dynamical systems.

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