Stochastic Averaging for Practical Stability

2012 ◽  
pp. 57-78
Author(s):  
Shu-Jun Liu ◽  
Miroslav Krstic
Keyword(s):  
Stochastic Averaging ◽  
Practical Stability

On improved stochastic averaging procedure

1994 ◽  
Vol 9 (3) ◽  
pp. 203-211 ◽  
Author(s):  
W.Q. Zhu ◽  
J.S. Yu ◽  
Y.K. Lin
Keyword(s):  
Stochastic Averaging

Stochastic Response of SDOF Self-Centering System

2020 ◽  
Vol 20 (05) ◽  
pp. 2050062
Author(s):  
Huiying Hu ◽  
Lincong Chen
Keyword(s):  
Stochastic Averaging ◽  
Nonlinear Stochastic System ◽  
Amplitude Envelope ◽  
Stochastic Response ◽  
Equivalent Damping ◽  
Yield Displacement ◽  
Seismic Loadings ◽  
New Type ◽  
Stationary Probability Density Function ◽  
Energy Dissipation Coefficient

As a new type of seismic resisting device, the self-centering system is attractive due to its excellent re-centering capability, but research on such a system under random seismic loadings is quite limited. In this paper, the stochastic response of a single-degree-of-freedom (SDOF) self-centering system driven by a white noise process is investigated. For this purpose, the original self-centering system is first approximated by an auxiliary nonlinear system, in which the equivalent damping and stiffness coefficients related to the amplitude envelope of the response are determined by a harmonic balance procedure. Subsequently, by the method of stochastic averaging, the amplitude envelope of the response of the equivalent nonlinear stochastic system is approximated by a Markovian process. The associated Fokker–Plank–Kolmogorov (FPK) equation is used to derive the stationary probability density function (PDF) of the amplitude envelope in a closed form. The effects of energy dissipation coefficient and yield displacement on the response of system are examined using the stationary PDF solution. Moreover, Monte Carlo simulations (MCS) are used for ascertaining the accuracy of the analytical solutions.

On the Practical Stability of Incorporating Integral Compensation Into the Low-and-High Gain Control for a Class of Systems With Norm-Type Input Saturation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Shou-Tao Peng
Keyword(s):  
Input Saturation ◽  
Gain Control ◽  
High Gain ◽  
Output Regulation ◽  
Practical Stability ◽  
Design Parameters ◽  
Linear Matrix ◽  
Control Input ◽  
Chattering Effect ◽  
Practical Stabilization

This paper studies the practical stability of incorporating integral compensation into the original low-and-high gain feedback law. The motivation for the incorporation is for achieving output regulation in the presence of constant disturbances without the use of a very large high-gain parameter required in the original approach. Due to numerical accuracy, the employment of very large high-gain parameters to eliminate steady-state error has the potential for inducing undesirable chattering effect on the control signal. A set of linear matrix inequalities is formulated in this study to obtain the related design parameters, by which the incorporation can achieve both the practical stabilization and asymptotic output regulation in the presence of input saturation and constant disturbances. Furthermore, the saturation of the control input can be shown to vanish in finite time during the process of regulation. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

DIFFUSION APPROXIMATION FOR TRANSPORT PROCESSES WITH GENERAL REFLECTION BOUNDARY CONDITIONS

2006 ◽  
Vol 16 (05) ◽  
pp. 717-762 ◽  
Author(s):  
CRISTINA COSTANTINI ◽  
THOMAS G. KURTZ
Keyword(s):  
Boundary Conditions ◽  
Stochastic Averaging ◽  
Transport Processes ◽  
Collision Kernel ◽  
Diffusion Approximations ◽  
Transport Models ◽  
Scattering Kernel ◽  
Reflection Boundary ◽  
Averaging Techniques ◽  
Number Of Particles

Diffusion approximations are obtained for space inhomogeneous linear transport models with reflection boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the number of particles) and, in addition, to model the Debye sheath. The mathematical approach does not rely on Hilbert expansions, but rather on martingale and stochastic averaging techniques.

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