scholarly journals Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
R. H. Huan ◽  
R. C. Hu ◽  
D. Pu ◽  
W. Q. Zhu
Keyword(s):  
Optimal Control ◽  
Stochastic Systems ◽  
Stochastic Averaging ◽  
Control Force ◽  
Dynamical Programming ◽  
Markovian Jump ◽  
Finite Set ◽  
Time Optimal ◽  
Set Up ◽  
Ito Equation

The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical programming equations is then set up based on the stochastic dynamical programming principle and Markovian jump rules, from which the optimal control force is obtained. The stationary response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy.

scholarly journals Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps

2015 ◽  
Vol 82 (5) ◽  
Author(s):  
Rong-Hua Huan ◽  
Wei-qiu Zhu ◽  
Fai Ma ◽  
Zu-guang Ying
Keyword(s):  
Stochastic Systems ◽  
Original System ◽  
Stochastic Averaging ◽  
Kolmogorov Equation ◽  
Markovian Jump ◽  
Nonlinear Stochastic Systems ◽  
Stationary Response ◽  
Set Up ◽  
Jump Systems ◽  
Stationary Probabilities

Systems whose specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the stationary response of multidegree, nonlinear, Markovian-jump, quasi-nonintegrable Hamiltonian systems subjected to stochastic excitation. Using stochastic averaging, the quasi-nonintegrable Hamiltonian equations are first reduced to a one-dimensional Itô equation governing the energy envelope. The associated Fokker–Planck–Kolmogorov equation is then set up, from which approximate stationary probabilities of the original system are obtained for different jump rules. The validity of this technique is demonstrated by using a nonlinear two-degree oscillator that is stochastically driven and capable of Markovian jumps.

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.

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.

scholarly journals Implementation lessons and pitfalls for real-time optimal control with stochastic systems

2014 ◽  
Vol 36 (2) ◽  
pp. 198-217 ◽  
Author(s):  
Steven M. Ross ◽  
Richard G. Cobb ◽  
William P. Baker ◽  
Frederick G. Harmon
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Stochastic Systems ◽  
Time Optimal Control ◽  
Time Optimal

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.

Nonstationary Response of Optimal Controlled Stochastic Van Der Pol Oscillator

2014 ◽  
Vol 875-877 ◽  
pp. 2000-2005
Author(s):  
Lu Yuan Qi ◽  
Wei Xu ◽  
Wei Ting Gao
Keyword(s):  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Van Der Pol Oscillator ◽  
Kolmogorov Equation ◽  
System Response ◽  
Control Law ◽  
Dynamical Programming ◽  
Control Constraint ◽  
Van Der Pol ◽  
Ito Equation

A procedure to calculate the transient response of optimal controlled stochastic Van Der Pol oscillator is proposed. The stochastic averaging method is employed to obtain a partially averaged Itô equation for the amplitude process. The dynamical programming equation is adopted to minimize the system response. An optimal control law with a control constraint is established. The completed averaged Itô equation is obtained. The transient probability density function is solved from Fokker-Planck-Kolmogorov equation by Galerkin method. Results obtained show the proposed method is accurate. The effective of the control strategy is significant.

Stochastic optimal semi-active control of stay cables by using magneto-rheological damper

2010 ◽  
Vol 17 (13) ◽  
pp. 1921-1929 ◽  
Author(s):  
M Zhao ◽  
WQ Zhu
Keyword(s):  
Active Control ◽  
Control Strategy ◽  
Mr Damper ◽  
Stochastic Averaging ◽  
Control Law ◽  
Control Force ◽  
Stay Cable ◽  
Dynamical Programming ◽  
Magneto Rheological ◽  
Bang Bang Control

Stochastic optimal semi-active control for stay cable multi-mode vibration attenuation by using magneto-rheological (MR) damper is developed. The Bingham model for an MR damper is used. The force produced by an MR damper is split into passive and active parts. The passive part is combined with structural damping forces into effective damping forces. The partially averaged Itô stochastic differential equations for controlled modal energies are derived by applying the stochastic averaging method for quasi-integrable Hamiltonian systems. Then the dynamical programming equation for controlled modal energies with an index involving control force is established by applying the stochastic dynamical programming principle, and a stochastic optimal semi-active control law is obtained by solving the dynamical programming equation. For controlled modal energies with an index not involving control force, bang-bang control law is obtained without solving a dynamical programming equation. A comparison between the two control laws shows that the stochastic optimal semi-active control strategy is superior to the bang-bang control strategy in the sense of higher control effectiveness and efficiency and less chattering.

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