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.

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.

Compensating Random Time Delays in a Feedback Networked Control System With a Kalman Filter

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Alexander C. Probst ◽  
Mario E. Magaña ◽  
Oliver Sawodny
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
Time Delays ◽  
Padé Approximation ◽  
Networked Control System ◽  
Random Time ◽  
Pade Approximation ◽  
Time Stamps ◽  
The Mean ◽  
Measurement And Control

This paper presents procedures to handle time delays in a feedback control loop in which both measurement and control signals are sent through a network, where random time delays occur. Even when time stamps are utilized, for example, the control signal time delay still must be estimated. Using a Padé approximation and a Kalman filter, we can estimate the mean time delay. Furthermore, methods are described to estimate the time delay of every packet instead of the mean for the measurement channel, which greatly enhances the performance of the Padé approximation approach. This is done by matching the measurements to the expected measurements provided by the filter with maximum likelihood. The methods are applied to an inverted pendulum to assess performance.

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 Robust Sliding Mode Predictive Control of Uncertain Networked Control System with Random Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Zhang ◽  
Shousheng Xie ◽  
Ledi Zhang ◽  
Litong Ren
Keyword(s):  
Control System ◽  
Time Delay ◽  
Sliding Mode ◽  
Networked Control System ◽  
Networked Control ◽  
Random Time ◽  
System Stability ◽  
Sliding Surface ◽  
Predictive Controller ◽  
Global Sliding Surface

This paper proposes a sliding mode predictive controller with a new robust global sliding surface for a certain networked control system with random time delay, mismatched parametric uncertainty, and external disturbances. First, the model of the networked control system is established, based on which linear transformation is made to get a new form of the system which does not have time delay term in expression. Then a global sliding surface is proposed followed by the sufficient condition given in the form of linear matrix inequality (LMI) to guarantee system stability and robustness. Subsequently, a sliding mode predictive controller is proposed with modified reaching law as its reference trajectory and the rolling optimization method is combined to provide optimal control input for each step so that chattering can be minimized. Finally, simulations have been made and the results indicate the advantages of the proposed controller in the aspect of convergence speed, chattering suppression, and robustness to uncertainties.

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