The mean square stability analysis of a stochastic dynamic model for electricity market

2015 ◽  
Vol 8 (4) ◽  
pp. 1071-1079 ◽  
Author(s):  
Zhanhui Lu ◽  
Weijuan Wang ◽  
Quanxin Zhu ◽  
Gengyin Li
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Electricity Market ◽  
Stochastic Dynamic ◽  
Mean Square ◽  
Mean Square Stability ◽  
The Mean

Stochastic Response and Stability Analysis of Two-Point Mooring System

2011 ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Stability Analysis ◽  
Probability Density Function ◽  
Probability Density ◽  
Mooring System ◽  
Mean Square ◽  
Stochastic Response ◽  
Sea State ◽  
Mean Square Response ◽  
Linear Damping ◽  
The Mean

The stochastic response and stability of a two-point mooring system are investigated for random sea state represented by the P-M sea spectrum. The two point mooring system is modeled as a SDOF system having only stiffness nonlinearity; drag nonlinearity is represented by an equivalent linear damping. Since no parametric excitation exists and only the linear damping is assumed to be present in the system, only a local stability analysis is sufficient for the system. This is performed using a perturbation technique and the Infante’s method. The analysis requires the mean square response of the system, which may be obtained in various ways. In the present study, the method using van-der-Pol transformation and F-P-K equation is used to obtain the probability density function of the response under the random wave forces. From the moment of the probability density function, the mean square response is obtained. Stability of the system is represented by an inequality condition expressed as a function of some important parameters. A two point mooring system is analysed as an illustrative example for a water depth of 141.5 m and a sea state represented by PM spectrum with 16 m significant height. It is shown that for certain combinations of parameter values, stability of two point mooring system may not be achieved.

A Mean-Square Stability Analysis of the Least Mean Fourth Adaptive Algorithm

2007 ◽  
Vol 55 (8) ◽  
pp. 4018-4028 ◽  
Author(s):  
Pedro InÁcio Hubscher ◽  
JosÉ Carlos M. Bermudez ◽  
VÍtor H. Nascimento
Keyword(s):  
Stability Analysis ◽  
Adaptive Algorithm ◽  
Mean Square ◽  
Mean Square Stability

scholarly journals Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

2021 ◽  
Author(s):  
Seiji Miyoshi
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Asymptotic Analysis ◽  
Adaptive Filter ◽  
Adaptive System ◽  
Adaptive Signal Processing ◽  
Mean Square ◽  
Mean Square Stability ◽  
Statistical Mechanical ◽  
The Mean

Adaptive signal processing is used in broad areas. In most practical adaptive systems, there exists substantial nonlinearity that cannot be neglected. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. To represent the macroscopic state of the system, we introduce two macroscopic variables. By considering the limit in which the number of taps of the unknown system and adaptive filter is large, we derive the simultaneous differential equations that describe the system behaviors in the deterministic and closed form. Although the derived simultaneous differential equations cannot be analytically solved, we discuss the dynamical behaviors and steady state of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it becomes clear that the saturation value S has the critical value SC at which the mean-square stability of the adaptive system is lost. That is, when S > SC, both the mean-square error (MSE) and mean-square deviation (MSD) converge, i.e., the adaptive system is mean-square stable. On the other hand, when S < SC, the MSD diverges although the MSE converges, i.e., the adaptive system is not mean-square stable. In the latter case, the converged value of the MSE is a quadratic function of S and does not depend on the step size. Finally, SC is exactly derived by asymptotic analysis.<br>

scholarly journals A Comparison Theorem for Stability of Linear Stochastic Implicit Difference Equations of Index-1

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Nguyen Hong Son
Keyword(s):  
Comparison Theorem ◽  
Difference Equations ◽  
Mean Square ◽  
Mean Square Stability ◽  
Method Of Solution ◽  
The Mean ◽  
Definition Of

In this paper we study linear stochastic implicit difference equations (LSIDEs for short) of index-1. We give a definition of solution and introduce an index-1 concept for these equations. The mean square stability of LSIDEs is studied by using the method of solution evaluation. An example is given to illustrate the obtained results.

Cooperative guidance law considering the randomness of the unreliable communication network

2018 ◽  
Vol 233 (9) ◽  
pp. 3313-3322
Author(s):  
Chunyan Zhang ◽  
Jianmei Song ◽  
Lan Huang ◽  
Gaohua Cai
Keyword(s):  
Communication Network ◽  
Consensus Algorithm ◽  
Mean Square ◽  
Cooperative System ◽  
Proportional Navigation ◽  
Impact Time ◽  
Guidance Law ◽  
Mean Square Stability ◽  
Cooperative Guidance ◽  
The Mean

The cooperative attack problem of multiple missiles considering the randomness of the unreliable communication network is investigated. Firstly, the stochastic communication network is described by a Bernoulli random model. And the cooperative guidance law with unreliable communication network is proposed, which is composed of the upper consensus algorithm of desired impact time and the local proportional navigation with time-varying navigation gain. Each node of the upper cooperative system uses different update gain to adjust the desired impact time to improve the cooperative performance. Secondly, the mean square stability of the upper cooperative system is analyzed and proved. The explicit necessary and sufficient conditions of the mean square stability are presented for the two-missile cooperative attack system. And the analytic expression of the mean of the cooperative impact time is derived since it influences the attack precision directly and significantly. Thirdly, the effectiveness of the proposed cooperative guidance law with unreliable communication network is verified by simulation. And the influence of the update gain, the communication step, and the mean of link probability on the cooperative attack precision is analyzed.

scholarly journals Numerical Study on Stochastic Diabetes Mellitus Model with Additive Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Zhifang Zhang ◽  
Qingyi Zhan ◽  
Xiangdong Xie
Keyword(s):  
Diabetes Mellitus ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Stability And Convergence ◽  
Mean Square ◽  
Existence And Uniqueness Theorem ◽  
Mean Square Stability ◽  
The Mean

This article focuses on the numerical analysis and simulation of the stochastic diabetes mellitus model with additive noise. The existence and uniqueness theorem of the solution under some appropriate assumptions is established. And, the mean square stability and convergence of numerical solutions are proposed, too. The practical use of these theorems is demonstrated in the numerical computations of the stochastic diabetes mellitus model and the value for the forecast of the tendency of diabetes mellitus in a given time.

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