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Scheduling policy based on model prediction error is presented to reduce energy consumption and network conflicts at the actuator node, where the characters of networked control systems are considered, such as limited network bandwidth, limited node energy, and high collision probability. The object model is introduced to predict the state of system at the sensor node. And scheduling threshold is set at the controller node. Control signal is transmitted only if the absolute value of prediction error is larger than the threshold value. Furthermore, the model of networked control systems under scheduling policy based on predicted error is established by taking uncertain parameters and long time delay into consideration. The design method of

Networked control systems (NCS) are frequently encountered in practice for widespread fields of applications due to their suitable and flexible structure [

Literatures in the aspects of NCS have got plenty of achievements on stability analysis and controller design considering uncertain parameters, time delay, noise, and other factors [

With the rapid development of computer technology, sensors sampling frequency and the processing speed of the controller are being improved continually; network conflict is becoming more and more serious at actuators side because of the limited channels of network during the transmission of information. So, it is important to explore a reasonable scheduling policy to reduce the network conflict at actuator node and to avoid the loss of important information. This motivates us to conduct the research work.

In this paper, scheduling policy based on model prediction error is presented to reduce energy consumption and network conflicts at the actuator node, in which the characters of NCS are considered, such as limited network bandwidth, limited node energy, and high collision probability. The prediction model is introduced to predict the state of system at the sensor node, and then referential value of control signal is obtained after the predicted value of state is calculated by the controller. And scheduling threshold is set at the controller node. Control signal is not transmitted if the absolute value of prediction error is lower than the threshold value. Moreover, the design method of

The paper is organized in 5 sections including the introduction. Section

The structure of networked control systems under scheduling policy based on predicted error is shown in Figure

The structure of networked control systems under scheduling policy based on predicted error.

Consider the NCS model with uncertain parameters as follows:

To facilitate discussion, some assumptions are employed as follows.

The state of NCS is completely measurable.

The cache devices are not used both at actuators end and at sensors end.

Sensors, controllers, and actuators are all time driving. Before the first controlled input reaches the actuator, controlled input always maintains

Forward channel delay caused by the network is denoted by

Based on assumption 2, system information obtained by controller is only the state of system object, namely,

Based on assumption 4, the feedback information received by system controller at time

The controller nodes use the

The predicted error of control signal produced by the model is shown as follows:

With the rapid development of computer technology, sensors sampling frequency and the processing speed of the controller are being improved continually; network conflict is becoming more and more serious at actuators side because of the limited channels of network during the transmission of information. So it is important to introduce reasonable scheduling policy to reduce the network conflict at actuator node. Here we introduce the restrained condition of transmission as

According to the description above, piecewise function as follows is introduced:

Moreover, we introduce

According to the description about

Obviously, different from the previous method, such as [

Based on the description of equalities (

For the system model established above, performance indicator is given as follows:

For system (

For a symmetric matrix

For matrices

Given symmetric positive definite matrices

Because system (

From zero initial condition, we know

Because the process above elucidated that the system is asymptotically stable, we have

Inequality (

Uncertain system forms like

Given symmetric positive definite matrices

It is called that system (

The proof is based on a suitable congruence transformation and a change of variables allowing us to obtain inequality (

From

Consider the parameters of system (

It can be obtained that

By taking advantage of inequality (

The following two group thresholds of restrained transmission will be selected for simulation experiments.

Select

if

if

Select

if

if

the performance index of the system in the threshold condition (1) is

the performance index of the system in the threshold condition (2) is

The system under scheduling policy based on predicted error is stable according to the state response curve shown in Figure

The state response curves of NCS.

State response of NCS in the threshold condition (1)

State response of NCS in the threshold condition (2)

After entering the steady state, data will stop being transmitted and calculated unless interference makes the value of prediction error surpass the value of threshold. In order to facilitate comparison, the number of data packet losses at time

The packet losses curves of NCS.

Packet losses of NCS in the threshold condition (1)

Packet losses of NCS in the threshold condition (2)

In addition, we apply the method proposed by Longo et al. [

The state response curves of NCS.

State response of NCS in the threshold condition (1)

State response of NCS in the threshold condition (2)

In this paper, scheduling policy based on model prediction error is presented to reduce energy consumption and network conflicts at the actuator node, where the characters of NCS are considered, such as limited network bandwidth, limited node energy, and high collision probability. The object model is introduced to predict the state of system at the sensor node. And scheduling threshold is set at the controller node. Control signal is transmitted only if the absolute value of prediction error is larger than the threshold value. And the model of NCS under scheduling policy based on predicted error is established by taking uncertain parameters and long time delay into consideration. The design method of

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was partly supported by the National Nature Science Foundation of China (61164014 and 51375323), the China Postdoctoral Science Foundation (20100480131), the Science and Technology Support Project Plan of Jiangxi Province, China (2010BGB00607), and the Natural Science Foundation of Jiangxi Province, China (2010GZC0118).