scholarly journals Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
R. C. Hu ◽  
Q. F. Lü ◽  
X. F. Wang ◽  
Z. G. Ying ◽  
R. H. Huan
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Random Time ◽  
Nonlinear Stochastic System ◽  
Control Force ◽  
Markov Jump ◽  
Optimal Control Strategy ◽  
Vibrating Systems

A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, upon limiting averaging principle, the optimal control force is approximately expressed as probability-weighted summation of the control force associated with different modes of the system. Then, by using the stochastic averaging method and the dynamical programming principle, the control force for each mode can be readily obtained. To illustrate the effectiveness of the proposed control, the stochastic optimal control of a two degree-of-freedom nonlinear stochastic system with random time delay is worked out as an example.

Elastic-Plastic Time History Analysis of MR Damping Structure Based on LQG Algorithm

2016 ◽  
Vol 858 ◽  
pp. 145-150
Author(s):  
Yu Liang Zhao ◽  
Zhao Dong Xu
Keyword(s):  
Optimal Control ◽  
Time History ◽  
Mr Damper ◽  
Time History Analysis ◽  
Control Force ◽  
Control Effect ◽  
Damping Force ◽  
Optimal Control Strategy ◽  
Elastic Plastic ◽  
History Analysis

This paper discussed an elastic-plastic time-history analysis on a structure with MR dampers based on member model, in which the elastoplastic member of the structure is assumed to be single component model and simulated by threefold line stiffness retrograde model. In order to obtain better control effect, Linear Quadratic Gaussian (LQG) control algorithm is used to calculate the optimal control force, and Hrovat boundary optimal control strategy is used to describe the adjustable damping force range of MR damper. The effectiveness of the MR damper based on LQG algorithm to control the response of the structure was investigated. The results from numerical simulations demonstrate that LQG algorithm can effectively improve the response of the structure against seismic excitations only with acceleration feedback.

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.

Semi-Active Direct Velocity Control Method of Dynamic Response of Spatial Reticulated Structures Based on MR Dampers

2009 ◽  
Vol 12 (4) ◽  
pp. 547-558 ◽  
Author(s):  
Yan Bao ◽  
Cheng Huang ◽  
Dai Zhou ◽  
Yao-Jun Zhao
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Control Method ◽  
Optimal Placement ◽  
Feedback Gain ◽  
Control Force ◽  
Optimal Control Strategy ◽  
Integrated Method ◽  
Mr Dampers ◽  
Set Up

In this paper, a semi-active optimal control strategy for spatial reticulated structures (SRS) with MR dampers subjected to dynamic actions was proposed. The motion equation of SRS embedded with MR dampers was set up. The performance function of the optimal control strategy including both the structural responses and the control efforts was constituted for the optimization of feedback gain and MR damper placement in SRS, and an integrated method of genetic-gradient based algorithm was developed to solve this optimization problem. The clipped-optimal semi-active control strategy in the conjunction of velocity output feedback was applied to compute the desired control force from the MR dampers. Finally, a numerical example of SRS dealing with optimal placement of MR dampers and feedback gains of control system demonstrates the validity of the present semi-active optimal control strategy.

Stochastic Response of Nonlinear Viscoelastic Systems with Time-Delayed Feedback Control Force and Bounded Noise Excitation

2021 ◽  
pp. 2150181
Author(s):  
Xudong Gu ◽  
Fusen Jia ◽  
Zichen Deng ◽  
Rongchun Hu
Keyword(s):  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Stochastic Response ◽  
Bounded Noise ◽  
Strongly Nonlinear ◽  
Nonlinear Viscoelastic ◽  
Time Delayed Feedback

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method.

scholarly journals Asymptotic Stability of Delay-Controlled Nonlinear Stochastic Systems with Actuator Failures

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
N. Zhou ◽  
R. H. Huan
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Original System ◽  
Stochastic Averaging ◽  
Largest Lyapunov Exponent ◽  
Control Force ◽  
Nonlinear Stochastic Systems ◽  
Actuator Failures

The problem of asymptotic stability of delay-controlled nonlinear stochastic systems with actuator failures is investigated in this paper. Such a system is formulated as a continuous-discrete hybrid system based on the random switch model of failure-prone actuator. Time delay control force is converted into delay-free one by randomly periodic characteristic of the system. Using limit theorem and stochastic averaging, an approximate formula for the largest Lyapunov exponent of the original system is then derived, from which necessary and sufficient conditions for asymptotic stability are obtained. The validity and utility of the proposed procedure are demonstrated by using a stochastically driven nonlinear two-degree system with time delay feedback and actuator failure.

scholarly journals Applying higher order stochastic averaging method to the Van der Pol system with timedelay under random excitation

2019 ◽  
Vol 2 (2) ◽  
pp. 102-109
Author(s):  
Hao Ngoc Duong ◽  
Anh Dong Nguyen ◽  
Dung Quang Nguyen
Keyword(s):  
Time Delay ◽  
Averaging Method ◽  
Order Approximation ◽  
Original System ◽  
Stochastic Averaging ◽  
Random Excitation ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
Van Der Pol ◽  
System With Time Delay

The paper investigated the Van der Pol system with time-delay under random excitation by the higher stochastic averaging method. The original system was expressed in terms without time-delay under the assumption that the state variabled of the system were slowly varying processed. Then the higher stochastic averaging method was applied on the approximation system. By this technique, the analytical expression of the stationary probability density function for the Van der Pol system with time-delay under random excitation was showed in higher order approximation for the first time. Effects of the parameter time-delay on the system’s response were investigated. The analytical results were suited well to numerical ones obtained by Monte-Carlo method. It was also showed that the higher order averaging solution was better than the one obtained by the traditional stochastic averaging method.

Nonlinear Stochastic Optimal Control of Quasi Hamiltonian Systems

2005 ◽  
Author(s):  
W. Q. Zhu
Keyword(s):  
Optimal Control ◽  
Hamiltonian Systems ◽  
Stochastic Optimal Control ◽  
Control Strategies ◽  
First Passage Time ◽  
Stochastic Averaging ◽  
Passage Time ◽  
Stochastic Averaging Method ◽  
Dynamic Programming Principle ◽  
Stochastic Dynamic

In recent years, a class of nonlinear stochastic optimal control strategies were developed by the present author and his co-workers for minimizing the response, stabilization and maximizing the reliability and mean first-passage time of quasi Hamiltonian systems based on the stochastic averaging method for quasi Hamiltonian systems and the stochastic dynamic programming principle. This review summaries the basic idea, procedures and applications of these strategies and pointes out necessary further work.

Asymptotic Stability With Probability One of Random-Time-Delay-Controlled Quasi-Integrable Hamiltonian Systems

2016 ◽  
Vol 83 (9) ◽  
Author(s):  
R. H. Huan ◽  
W. Q. Zhu ◽  
R. C. Hu ◽  
Z. G. Ying
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Hybrid System ◽  
Networked Control System ◽  
Random Time ◽  
Largest Lyapunov Exponent ◽  
Integrable Hamiltonian Systems ◽  
Markov Jump ◽  
Solution Property

A new procedure for determining the asymptotic stability with probability one of random-time-delay-controlled quasi-integrable Hamiltonian systems is proposed. Such a system is formulated as continuous–discrete hybrid system and the random time delay is modeled as a Markov jump process. A three-step approximation is taken to simplify such hybrid system: (i) the randomly periodic approximate solution property of the system is used to convert the random time delay control into the control without time delay but with delay time as parameter; (ii) a limit theorem is used to transform the hybrid system with Markov jump parameter into one without jump parameter; and (iii) the stochastic averaging method for quasi-integrable Hamiltonian systems is applied to reduce the system into a set of averaged Itô stochastic differential equations. An approximate expression for the largest Lyapunov exponent of the system is derived from the linearized averaged Itô equations and the necessary and sufficient condition for the asymptotic stability with probability one of the system is obtained. The application and effectiveness of the proposed procedure are demonstrated by using an example of stochastically driven two-degrees-of-freedom networked control system (NCS) with random time delay.

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