scholarly journals Hybrid-Driven Mechanism Based on Uncertain Network for Markov Jump System with Quantizations and Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Tian Tan ◽  
Jinfeng Gao ◽  
Jinxia Wang ◽  
Zhen Zhao ◽  
Miao Ma
Keyword(s):  
Communication Channel ◽  
Networked Control Systems ◽  
Transmission Rate ◽  
Packet Transmission ◽  
Finite Capacity ◽  
Markov Jump ◽  
Uncertain Network ◽  
Channel Quantization ◽  
Markov Jump System ◽  
The Stability

This paper investigates the hybrid-driven mechanism problem for Markov jump system, where both channel quantization (BCQ) and network-induced delay based on uncertain network are considered. Firstly, comparing with the traditional event-triggered scheme, a hybrid-driven mechanism is employed in networked control systems (NCSs) for the finite capacity of communication bandwidth resources and system performance in equilibrium. Then, the quantization technology is applied in the communication channel from sensor-to-controller and controller-to-actuator. The application of BCQ is for further investigation that mitigate data packet transmission rate. Thirdly, Markov jump system is modeled for the hybrid-driven mechanism and network-induced delay. By constructing the Lyapunov–Krasovskii function, a sufficient condition is derived as the stability criterion, and the controller is designed in which the nonlinear term is rewritten for simplifying the calculation. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

scholarly journals Control/Network Codesign Basics for IP-Based Shared Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Miguel Díaz-Cacho Medina ◽  
Emma Delgado Romero ◽  
Antonio Barreiro Blas
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Transmission Rate ◽  
Design Parameters ◽  
Control Network ◽  
Transport Protocol ◽  
Test Platform ◽  
Shared Networks ◽  
The Stability ◽  
And Control

Network and control relationship is an essential aspect in the design of networked control systems (NCSs). The design parameters are mainly centered in the transmission rate and in the packet structure, and some studies have been made to determine how transmission rate affects the network delay and consequently the stability of the control. In Internet, these analysis are mathematically complex due to the large number of different potential scenarios. Using empirical methods, this work deduces that the transmission scheduling problem of an NCS can be solved by designing an appropriate transport protocol, taken into account high and periodic sampling rates. The transport protocol features are determined by simulation, using a new test platform based on the NS2 network simulation suite, to develop control/network codesign solutions. Conclusions of this paper are that the transport features are packet-loss-based flow control, best effort, and fairness, supplemented by a packet priority scheme.

scholarly journals Networked Optimal Control with Random Medium Access Protocol and Packet Dropouts

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Chaoqun Zhu ◽  
Ge Guo ◽  
Bin Yang ◽  
Zhiwen Wang
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Networked Control Systems ◽  
Random Medium ◽  
Networked Control ◽  
Channel Access ◽  
Markov Jump ◽  
Access Protocol ◽  
Packet Dropouts ◽  
Markov Jump System

This paper is concerned with an optimal control framework for networked control systems in which the channel access of actuators is governed by a group random access protocol. The system is modeled as a switching Markov jump system with multiple modes according to channel-access status of the actuators, and an independent identical distribution Bernoulli process is used to describe the random packet dropouts of the channel. Then, an optimal control design methodology is addressed to satisfy the quadratic cost function by applying the well-developed theory for jump linear systems and stochastic optimal control while guaranteeing the mean-square exponential stability of networked control systems. And, finally, a numerical example is exploited to demonstrate the effectiveness of the proposed method.

Controller Design of Output Feedback MIMO Networked Control Systems with Multiple Packet Transmission

2009 ◽  
Vol 16-19 ◽  
pp. 935-940
Author(s):  
Cheng Xiang Xie ◽  
Wei Li Hu
Keyword(s):  
Control Systems ◽  
Periodic System ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sampling Period ◽  
Packet Transmission ◽  
Networked Control ◽  
Matrix Inequalities ◽  
Static Scheduling ◽  
The Stability

MIMO (mult-input multi-output) networked control systems (NCSs) with multiple packet transmission is considered. The network-induced delay is assumed to be time-varying and less than one sampling period. Suppose the data of sensor node is part of system outputs and is transferred with static scheduling strategy, then the NCS is modeled as uncertain periodic system. The uncertain periodic system theory is used for the stability sufficient condition. Then a control design approach is presented via bilinear matrix inequalities (BMIs) method. The simulation result shows the effectiveness of the proposed approach.

scholarly journals Directed Data-Processing Inequalities for Systems with Feedback

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 533
Author(s):  
Milan S. Derpich ◽  
Jan Østergaard
Keyword(s):  
Mutual Information ◽  
Data Processing ◽  
Channel Coding ◽  
Communication Channel ◽  
Closed Loop ◽  
Transmission Rate ◽  
Information Rate ◽  
Random Input ◽  
Directed Information ◽  
Stochastic Mapping

We present novel data-processing inequalities relating the mutual information and the directed information in systems with feedback. The internal deterministic blocks within such systems are restricted only to be causal mappings, but are allowed to be non-linear and time varying, and randomized by their own external random input, can yield any stochastic mapping. These randomized blocks can for example represent source encoders, decoders, or even communication channels. Moreover, the involved signals can be arbitrarily distributed. Our first main result relates mutual and directed information and can be interpreted as a law of conservation of information flow. Our second main result is a pair of data-processing inequalities (one the conditional version of the other) between nested pairs of random sequences entirely within the closed loop. Our third main result introduces and characterizes the notion of in-the-loop (ITL) transmission rate for channel coding scenarios in which the messages are internal to the loop. Interestingly, in this case the conventional notions of transmission rate associated with the entropy of the messages and of channel capacity based on maximizing the mutual information between the messages and the output turn out to be inadequate. Instead, as we show, the ITL transmission rate is the unique notion of rate for which a channel code attains zero error probability if and only if such an ITL rate does not exceed the corresponding directed information rate from messages to decoded messages. We apply our data-processing inequalities to show that the supremum of achievable (in the usual channel coding sense) ITL transmission rates is upper bounded by the supremum of the directed information rate across the communication channel. Moreover, we present an example in which this upper bound is attained. Finally, we further illustrate the applicability of our results by discussing how they make possible the generalization of two fundamental inequalities known in networked control literature.

FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS

2014 ◽  
Vol 56 (2) ◽  
pp. 138-149
Author(s):  
YANQING LIU ◽  
FEI LIU
Keyword(s):  
Predictive Control ◽  
Controller Design ◽  
Invariant Set ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Markov Jump System ◽  
Predictive Controller ◽  
Feasibility Region ◽  
Nonhomogeneous Markov Jump System ◽  
Jump Systems

AbstractWe consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

scholarly journals Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Hailay Weldegiorgis Berhe ◽  
Oluwole Daniel Makinde ◽  
David Mwangi Theuri
Keyword(s):  
Sensitivity Analysis ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Nonlinear Least Squares ◽  
Model Parameters ◽  
Nonlinear Least Squares Problem ◽  
The Stability ◽  
Diarrhea Disease ◽  
Effective Transmission ◽  
Disease Free

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0>1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0=1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

scholarly journals Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Ding Zhai ◽  
Liwei An ◽  
Jinghao Li ◽  
Qingling Zhang
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Markov Jump Linear System

This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

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