CN115562241A - Event trigger prediction control method in networked control system - Google Patents

Event trigger prediction control method in networked control system Download PDF

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CN115562241A
CN115562241A CN202211310036.0A CN202211310036A CN115562241A CN 115562241 A CN115562241 A CN 115562241A CN 202211310036 A CN202211310036 A CN 202211310036A CN 115562241 A CN115562241 A CN 115562241A
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kalman filter
control system
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杨雪陶
段月月
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Nanjing University of Posts and Telecommunications
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Abstract

The invention belongs to the technical field of automatic control, in particular to an event triggering prediction control method in a networked control system, which comprises the following steps: constructing a networked control system model based on the state space; constructing an event trigger mechanism to decide whether to update the current sampling data; constructing a Kalman filter from the current actual output value; constructing a prediction control method of a networked control system model, and predicting according to a prediction algorithm; a closed loop system is formed by a networked control system model, an event trigger mechanism, a Kalman filter and a prediction control method, so that Schur stability of the system is obtained; the invention not only adopts a prediction control method, but also combines an event trigger mechanism with a Kalman filter, thereby greatly saving the control cost, improving the resource utilization rate, ensuring the stability of a networked control system and solving the problems of time delay and noise interference of the system.

Description

Event-triggered predictive control method in networked control system
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to an event triggering prediction control method in a networked control system.
Background
With the advent of the information age and the rapid development of computer technology and network technology, networked Control Systems (NCSs) have gained widespread attention. Compared with the traditional control system, the NCSs can realize resource sharing, remote operation and control, reduce the complexity, weight and power consumption of the system, reduce the required cost of the system, simplify the installation and maintenance of the system and improve the flexibility and reliability of the system. Network bandwidth in NCSs is limited, and therefore, in order to reduce occupation of network resources, transmission pressure of network bandwidth and control cost, many researchers reduce the number of data transmission times by referring to an event trigger mechanism. Compared with the conventional periodic sampling control, the event triggering control is a discontinuous and aperiodic communication control protocol, and the system feedback loop transmits information only when a triggering condition is met, so that the event triggering mechanism is undoubtedly an effective execution mode for improving the resource utilization rate. The existence of the double effect makes the design of an optimal controller more difficult, since the use of a state-based scheduler in a closed-loop system will cause the system to exhibit a double effect. Thus, some output-based event-triggered control takes place.
NCSs carry out data transmission through the network, and the intervention of unreliable communication networks with limited bandwidth can cause that certain network delay exists from a wireless communication transmitting end to a receiving end and from the receiving end to a terminal device. Therefore, the network delay phenomenon cannot be avoided in real life, and some adverse effects, such as damaging the stability of the system, reducing the performance of the system, etc., are brought. Among them, predictive control is an effective method for solving network delay. Currently, many researchers also combine event-triggering mechanisms with predictive control strategies. In the prior art, an event trigger mechanism is utilized to research the output-based predictive control problem of a network control system with time delay from a sensor to a controller, sufficient conditions for ensuring the stability of a closed-loop system are provided, and a model-based predictive control scheme and an event trigger control scheme are combined together aiming at the network control system with two kinds of DoS attacks, so that the pressure of network bandwidth is relieved, and the negative influence of the DoS attacks on the system performance can be effectively compensated.
In addition to unreliable communication channels, the actual communication process is often affected by channel noise, which may distort and error code the signal, so that complete status information of the system cannot be obtained, which is not considered in the prior art. Although a method for output feedback cooperative distributed model predictive control is provided in the prior art to process bounded disturbance and communication delay in a networked system, no event trigger mechanism is used, and communication resources may be wasted.
Disclosure of Invention
In order to solve the technical problem, the invention discloses an event-triggered predictive control method in a networked control system, which is based on a Kalman filter, wherein the Kalman filter is used for carrying out optimal estimation on the state of the system from a series of data with noise under the condition that the measurement variance is known.
The invention adopts the following specific technical scheme:
an event-triggered predictive control method in a networked control system, comprising the steps of:
step one, constructing a networked control system model based on a state space:
Figure BDA0003907655270000021
wherein x is k ∈R n ，u k ∈R l ，y k ∈R m Representing system state, control inputs and measurement outputs, respectively. Omega k ∈R m Represents measurement noise, and follows a normal distribution of (0, Q); upsilon is k ∈R m Representing process noise, compliance
Figure BDA0003907655270000022
And the measurement noise and the process noise are independent of each other. A, B, C are constant matrices of known appropriate dimensions, Q and
Figure BDA0003907655270000023
is the variance of the noise.
Step two, in order to ensure the performance of the closed-loop system and reduce the occupation of computing resources, network bandwidth resources and the like, an Event Triggering Mechanism (ETM) is constructed to select y k To determine whether to update the current sample data, define
Figure BDA0003907655270000024
If it is
Figure BDA0003907655270000025
Then
Figure BDA0003907655270000026
If it is
Figure BDA0003907655270000027
Then
Figure BDA0003907655270000028
Wherein the content of the first and second substances,
Figure BDA0003907655270000029
which represents the current actual state of the system,
Figure BDA00039076552700000210
an output value, y, representing the current actual transmission k Which is indicative of the current measured output value,
Figure BDA00039076552700000211
representing the value of the output actually transmitted at the last instant, sigma being an adjustable parameter,
Figure BDA00039076552700000212
representing process noise, compliance
Figure BDA00039076552700000213
Is normally distributed. The next trigger time is:
Figure BDA00039076552700000214
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00039076552700000215
is non-periodic.
Step three, outputting the value from the current actual value
Figure BDA0003907655270000031
Starting constructionThe Kalman filter is used for realizing the optimal estimation of the state of a networked control system containing noise, and comprises the following steps:
Figure BDA0003907655270000032
wherein the content of the first and second substances,
Figure BDA0003907655270000033
representing the state of the Kalman filter by actual output values
Figure BDA0003907655270000034
The updating process is carried out by the following steps,
Figure BDA0003907655270000035
representing the measurement output, M, of a Kalman filter k Is the gain matrix of the kalman filter, which is an adaptive quantity rather than a fixed value.
Figure BDA0003907655270000036
Is a covariance matrix of the kalman filter prediction error,
Figure BDA0003907655270000037
is the covariance matrix of the kalman filter estimation error.
The following assumptions are made for the coefficient matrices of the networked control system and the kalman filter:
assume 1, (a, B) is controllable, (a, C) is observable;
hypothesis 2. There is an invertible matrix C, such that M k-d C≥0。
Obtaining a Kalman filter gain matrix M according to assumption 1 and assumption 2 through an event triggering mechanism and a Kalman filter k The new updating mode is as follows:
Figure BDA0003907655270000038
and step four, constructing a prediction control method of the networked control system model, and predicting according to a prediction algorithm. The state prediction estimate of step d is constructed using the following sub-formula:
Figure BDA0003907655270000039
wherein the content of the first and second substances,
Figure BDA00039076552700000310
representing the state prediction of the information based on time k-d at time k-d + i, and
Figure BDA00039076552700000311
from the recursion we obtain:
Figure BDA0003907655270000041
the time delay of the invention takes the step d as an example, and d belongs to Z + Therefore, in the actual network control system, the control input information received by the controller at time k is
Figure BDA0003907655270000042
In order to enable the system to operate normally, the prediction controller is used for predicting output information of the controller at the moment k according to input information at the moment k-d, namely the controller is arranged:
Figure BDA0003907655270000043
step five, a closed loop system is formed by the networked control system model, the event trigger mechanism, the Kalman filter and the prediction control method, and Schur stability of the system is obtained: for a given event trigger parameter σ and delay d, under assumptions 1 and 2, when
Figure BDA0003907655270000044
e (A + BK) is Schur-stable (i.e., the modulus of the root of the maximum feature of T, e (A + BK) is less than 1), and is made by an event-triggered mechanism, a Kalman filter, and a predictive control strategyThe used networked control system is stable, wherein, the closed loop system is:
Figure BDA0003907655270000045
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003907655270000046
let X k ＝e k x k ，
Figure BDA0003907655270000047
Figure BDA0003907655270000048
The invention has the beneficial effects that:
(1) The invention constructs an event trigger mechanism based on output, reduces unnecessary measurement transmission, greatly saves control cost and improves the utilization rate of resources;
(2) The invention constructs a prediction control method based on a Kalman filter, and solves the problems of time delay and noise interference of a networked control system;
(3) According to the Schur stability of the networked control system model, an event trigger mechanism and a prediction control method based on a Kalman filter are combined together, and the Schur stability of the networked control system model is obtained.
Drawings
Fig. 1 is a schematic diagram of a networked control system according to the present invention, in which ETM represents an event trigger mechanism, and Observe represents a kalman filter.
FIG. 2 shows the prediction control u of the present invention k State trajectory diagram of (2).
FIG. 3 is a diagram illustrating the predicted control u of the networked control system according to the present invention k State trace diagram of the following.
Detailed Description
For the purpose of enhancing understanding of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and examples, which are provided for illustration only and are not intended to limit the scope of the present invention.
Example (b): as shown in fig. 1, an event-triggered predictive control method in a networked control system includes the following steps:
step one, constructing a networked control system model based on a state space:
Figure BDA0003907655270000051
wherein x is k ∈R n ，u k ∈R l ，y k ∈R m Representing system state, control inputs and measurement outputs, respectively. Omega k ∈R m Represents the measurement noise, obeying a normal distribution of (0, Q); v is a cell k ∈R m Representing process noise, compliance
Figure BDA0003907655270000052
And the measurement noise and the process noise are independent of each other. A, B, C are constant matrices of known appropriate dimensions, Q and
Figure BDA0003907655270000053
is the variance of the noise.
Step two, in order to ensure the performance of the closed-loop system and reduce the occupation of computing resources, network bandwidth resources and the like, an Event Trigger Mechanism (ETM) is constructed to select y k To determine whether to update the current sample data, define
Figure BDA0003907655270000054
If it is
Figure BDA0003907655270000055
Then the
Figure BDA0003907655270000056
If it is
Figure BDA0003907655270000057
Then
Figure BDA0003907655270000058
Wherein the content of the first and second substances,
Figure BDA0003907655270000059
which represents the current actual state of the system,
Figure BDA00039076552700000510
an output value, y, representing the current actual transmission k Which is indicative of the current measured output value,
Figure BDA00039076552700000511
representing the value of the output actually transmitted at the last instant, sigma is an adjustable parameter,
Figure BDA00039076552700000512
representing process noise, compliance
Figure BDA00039076552700000513
Is normally distributed. The next trigger time is:
Figure BDA00039076552700000514
wherein the content of the first and second substances,
Figure BDA0003907655270000061
is non-periodic.
Step three, outputting the value from the current actual value
Figure BDA0003907655270000062
Starting to construct a Kalman filter to realize the optimal estimation of the state of a networked control system containing noise, wherein the Kalman filter is as follows:
Figure BDA0003907655270000063
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003907655270000064
representing the state of the Kalman filter by actual output values
Figure BDA0003907655270000065
The updating process is carried out by the following steps,
Figure BDA0003907655270000066
representing the measured output value, M, of the Kalman filter k Is the gain matrix of the kalman filter, which is an adaptive quantity, rather than a fixed value.
Figure BDA0003907655270000067
Is a covariance matrix of the kalman filter prediction error,
Figure BDA0003907655270000068
is the covariance matrix of the kalman filter estimation error.
The following assumptions are made for the coefficient matrices of the networked control system and the kalman filter:
assume 1, (a, B) is controllable, (a, C) is observable;
hypothesis 2. There is an invertible matrix C, such that M k-d C≥0。
Obtaining a Kalman filter gain matrix M according to hypothesis 1 and hypothesis 2 through an event trigger mechanism and a Kalman filter k The new updating mode is as follows:
Figure BDA0003907655270000069
and step four, constructing a prediction control method of the networked control system model, and predicting according to a prediction algorithm. The state prediction estimate of step d is constructed using the following sub-formula:
Figure BDA00039076552700000610
wherein the content of the first and second substances,
Figure BDA00039076552700000611
represents the state prediction of the information based on time k-d at time k-d + i, and
Figure BDA00039076552700000612
from the recursion we obtain:
Figure BDA0003907655270000071
the time delay of the invention takes the step d as an example, and d belongs to Z + Therefore, in the actual network control system, the control input information received by the controller at time k is
Figure BDA0003907655270000072
In order to enable the system to operate normally, the prediction controller is used for predicting output information of the controller at the moment k according to input information at the moment k-d, namely the controller is arranged:
Figure BDA0003907655270000073
step five, a closed loop system is formed by the networked control system model, the event trigger mechanism, the Kalman filter and the prediction control method, and Schur stability of the system is obtained: for a given event trigger parameter σ and time delay d, under assumptions 1 and 2, when
Figure BDA0003907655270000074
e (a + BK) is Schur stable (i.e. the modulus of the maximum characteristic root of T, e (a + BK) is less than 1), and the networked control system acted on by the event-triggered mechanism, kalman filter and predictive control strategy is stable, wherein the closed-loop system is:
Figure BDA0003907655270000075
wherein the content of the first and second substances,
Figure BDA0003907655270000076
let X k ＝e k x k ，
Figure BDA0003907655270000077
Figure BDA0003907655270000078
Aiming at a networked control system, the following parameters are adopted:
Figure BDA0003907655270000079
this is obtained by the pole arrangement principle: k = [ 3.1957.0324)]. Assuming a time delay d =3, a time length k =200, an event trigger parameter σ =0.125, and an initial state x of the system, present on the sensor-to-controller channel 0 ＝[2.5 0] T Initial control input u 0 =0, noise ω k 、υ k 、
Figure BDA00039076552700000710
Are random sequences that follow a uniform distribution over the (0, 1) interval.
Let G = [ B, AB.,. A ] n-1 B]，H＝[C,CA,...,CA n-1 ] T . Matlab calculation shows that the ranks of G and H are both 2, namely G and H are full ranks, so that (A and B) are controllable, and (A and C) are observable and satisfy the hypothesis 1; for all k e N, M k-d C is greater than or equal to 0, and the hypothesis 2 is satisfied; the modulus of the e (A + BK) maximum feature root is 0.998<1；
Figure BDA0003907655270000081
The modulus of the largest feature root is 0.9669<1, so e (A + BK), the modulus of all characteristic roots of T are less than 1, i.e., both are Schur stable.
FIG. 2 shows the predictive control u k Fig. 3 shows the state trajectory of the networked control system in predictive control u k The state trace of the lower case can be seen from the figureThe state trajectory gradually approaches 0 after the time k =30, so that it can be shown that when e (a + BK) and T are Schur stable, the networked control system is stable under the predictive control action based on the kalman filter.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. An event-triggered predictive control method in a networked control system, comprising the steps of:
firstly, constructing a networked control system model based on a state space;
step two, constructing an event trigger mechanism to determine whether to update the current sampling data;
thirdly, constructing a Kalman filter from the current actual output value;
step four, constructing a prediction control method of the networked control system model, and predicting according to a prediction algorithm;
and step five, forming a closed-loop system by a networked control system model, an event trigger mechanism, a Kalman filter and a prediction control method, and obtaining Schur stability of the system.
2. The method for event-triggered predictive control in a networked control system according to claim 1, wherein in the first step, the model of the networked control system is constructed based on the state space as follows:
Figure FDA0003907655260000011
wherein x is k ∈R n ，u k ∈R l ，y k ∈R m Respectively representing system state, control input and measurement output, ω k ∈R m Represents measurement noise, and follows a normal distribution of (0, Q); upsilon is k ∈R m Representing process noise, compliance
Figure FDA0003907655260000012
And the measurement noise and the process noise are independent of each other, A, B, C are constant matrices of known appropriate dimensions, Q and
Figure FDA0003907655260000013
is the variance of the noise.
3. The method according to claim 1, wherein in the second step, the event trigger mechanism is constructed to select y k To determine whether to update the current sample data, define
Figure FDA0003907655260000014
If it is
Figure FDA0003907655260000015
Then the
Figure FDA0003907655260000016
If it is
Figure FDA0003907655260000017
Then
Figure FDA0003907655260000018
Wherein the content of the first and second substances,
Figure FDA0003907655260000019
which represents the current actual state of the system,
Figure FDA00039076552600000110
an output value, y, representing the current actual transmission k Which is indicative of the current measured output value,
Figure FDA00039076552600000111
representing the value of the output actually transmitted at the last instant, sigma being an adjustable parameter,
Figure FDA00039076552600000112
representing process noise, compliance
Figure FDA00039076552600000113
Is normally distributed.
4. The method for controlling event-triggered prediction in a networked control system according to claim 3, wherein in the step two, the next triggering time is:
Figure FDA0003907655260000021
wherein the content of the first and second substances,
Figure FDA0003907655260000022
is non-periodic.
5. The method according to claim 1, wherein the step three is performed from the current actual output value
Figure FDA0003907655260000023
Starting to construct a Kalman filter to realize the optimal estimation of the state of a networked control system containing noise, wherein the Kalman filter is as follows:
Figure FDA0003907655260000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003907655260000025
representing the state of the Kalman filter by actual output values
Figure FDA0003907655260000026
The updating process is carried out by the following steps,
Figure FDA0003907655260000027
representing the measured output value, M, of the Kalman filter k Is a matrix of gains of the kalman filter,
Figure FDA0003907655260000028
is a covariance matrix of the kalman filter prediction error,
Figure FDA0003907655260000029
is the covariance matrix of the kalman filter estimation error.
6. The method for controlling event-triggered prediction in a networked control system according to claim 5, wherein in the third step, the following settings are made for the coefficient matrices of the networked control system and the kalman filter:
setting 1. (A, B) is controllable, (A, C) is observable;
setting 2. There is an invertible matrix C, such that M k-d C≥0；
Obtaining a Kalman filter gain matrix M according to a setting 1, a setting 2, an event trigger mechanism and a Kalman filter k The new updating mode is as follows:
Figure FDA00039076552600000210
7. the method according to claim 6, wherein in the fourth step, a predictive control method of the networked control system model is constructed, and prediction is performed according to a predictive algorithm: the state prediction estimate of step d is constructed using the following sub-formula:
Figure FDA0003907655260000031
wherein the content of the first and second substances,
Figure FDA0003907655260000032
representing the state prediction of the information based on time k-d at time k-d + i, and
Figure FDA0003907655260000033
from the recursion we obtain:
Figure FDA0003907655260000034
wherein d ∈ Z + The control input information received by the controller at time k is
Figure FDA0003907655260000035
The prediction controller predicts and obtains output information of the controller at the time k according to the input information at the time k-d, namely the prediction controller is arranged:
Figure FDA0003907655260000036
8. the method according to claim 7, wherein in the step five, for the given event trigger parameters σ and d, under setting 1 and setting 2, when
Figure FDA0003907655260000037
e (A + BK) is Schur stable, closed loop system:
Figure FDA0003907655260000038
wherein the content of the first and second substances,
Figure FDA0003907655260000039
let X k ＝e k x k ，
Figure FDA00039076552600000310
Figure FDA00039076552600000311
CN202211310036.0A 2022-10-25 2022-10-25 Event trigger prediction control method in networked control system Pending CN115562241A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116527060A (en) * 2023-05-29 2023-08-01 北京理工大学 Information compression and anomaly detection method based on event trigger sampling

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116527060A (en) * 2023-05-29 2023-08-01 北京理工大学 Information compression and anomaly detection method based on event trigger sampling
CN116527060B (en) * 2023-05-29 2024-01-05 北京理工大学 Information compression and anomaly detection method based on event trigger sampling

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