CN110673474B - Intrusion-tolerant control method of networked motion control system based on event triggering - Google Patents
Intrusion-tolerant control method of networked motion control system based on event triggering Download PDFInfo
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Abstract
An event trigger-based intrusion tolerance control method for a networked motion control system comprises the steps of firstly modeling the networked motion control system, considering that the system is likely to be attacked by an actuator, and detecting the attack by using an attack detection filter; when the networked motion control system normally operates, a control strategy based on event triggering is adopted; when the networked motion control system is attacked by an actuator, an attack detection filter gives an alarm, an attack event can be regarded as event trigger, the system finishes event trigger control and is switched into intrusion tolerant control based on a compensation idea, and the specific implementation steps are as follows: an intermediate observer is constructed to estimate the attack and disturbance signals of an actuator in the system, and the state of the system is stabilized by adopting a feedback compensation mode. The invention adopts the event triggering technology, reduces the transmission frequency of signals and the control frequency, and switches into an intrusion tolerant control algorithm under the condition that a networked system is attacked, thereby ensuring the safe operation of the system.
Description
Technical Field
The invention belongs to the technical field of network security, and particularly provides an event-triggered networked motion control system intrusion-tolerant control method, which has two control strategies, wherein an attack detection filter is designed to detect an attack, and when no attack signal exists, a networked motion control algorithm based on event triggering is adopted; when an attack signal exists, the attack signal and external disturbance of the system can be estimated by adopting an intrusion-tolerant control algorithm of a compensation idea, so that the safe operation of the system is guaranteed.
Background
In the conventional networked motion control system, the sensor transmits a signal measured at each sampling time to the control center, however, continuous time control causes a large amount of communication resources to be wasted. Therefore, if the control algorithm triggered by the event is adopted, unnecessary control behaviors and signal transmission can be reduced, occupied communication bandwidth is reduced, and meanwhile the preset control performance index of the system can be met.
In the existing industrial network system, various communication protocols exist, and the security level is low, so that the networked motion control system is easily subjected to various network attacks, various performance indexes of the system are reduced, and even the system is directly paralyzed, thereby causing great potential safety hazard and great economic loss. Most of the existing research results on the aspect of security control of the networked control system are denial of service attacks, and the research on dummy data injection is less. Under the network attack, the event trigger control fails because the network attack can cause the state to frequently jump out of the threshold range, so that the event trigger control is changed into continuous trigger control, and meanwhile, the control system does not have the intrusion-tolerant control capability. Different from system faults, network attack signals may be occasionally absent, if a conventional intrusion tolerance control mode is adopted under the condition of no attack, communication resources are excessively wasted, and under the condition of attack, an event trigger control mode based on state feedback cannot sufficiently guarantee intrusion tolerance control performance. Therefore, a combined control strategy capable of freely switching event trigger control in a system non-attack state and intrusion-tolerant control in a false data injection attack state is designed, so that certain balance is obtained between communication resources and intrusion-tolerant control capacity, and the combined control strategy has certain practical significance.
Disclosure of Invention
Based on the problems, the invention provides an event-triggered networked motion control system intrusion tolerance control method, an attack detection filter detects whether a system is attacked or not in real time, and when the networked motion control system operates safely, a control strategy based on event triggering is applied to the system, so that the updating of control signals and the transmission of the signals are reduced, and the system can operate safely and achieve the preset control performance; when the networked motion control system is attacked by false data injection, the attack event can be regarded as an event trigger, an attack detection filter gives an alarm, and the system finishes the event trigger control strategy, switches into an intrusion-tolerant control strategy based on a compensation idea, ensures that the estimation error of the system is converged in a certain range, and ensures the safe operation of the system.
The present invention provides the following solutions to solve the above technical problems:
an event trigger-based intrusion tolerance control method for a networked motion control system comprises the following steps:
step 1), establishing a state space equation of a networked motion control system:
considering the case where there is a disturbance in the system, the state space equation is shown as equation (1):
where A is the state matrix of the system, B is the input matrix, C is the output matrix, D 1 Perturbing the distribution matrix for the state, wherein the perturbation is a matching perturbation, D 2 For outputting disturbance distribution matrix, A, B, C, D 1 ,D 2 Is a matrix of constants of appropriate dimensions, x (t) E R n Represents the system state quantity, u (t) is the system input, y (t) is epsilon R p For system output, d (t) is belonged to R q Representing an external disturbance;
step 2), constructing an attack detection filter, wherein the process is as follows:
2.1 The core of the attack detection filter is a full order state observer, as shown in equation (2):
2.2 Consider a system under attack, the state space equation is shown as equation (3):
wherein f is a (t)∈R r Since B = E, then f a (t) is an attack signal of the actuator;
2.3 Simultaneous formula (2) and (3) definitions, the formula for the residual is simply defined as:
introducing variables
The residual equation is reduced to r (t) = Ce (t) + D 2 d(t)；
2.4 ) residual evaluation function J τ (τ) and threshold J th The design of (a) is as follows:
wherein r (t) has a residual characteristic when observer gain matrix L is selected to stabilize A-LC, τ represents time, and J represents time τ (τ)＞J th When the system is attacked, the system is attacked by the network, otherwise, the system is in a normal running state;
step 3), designing a networked motion control system based on event triggering, constructing an event generator between a sensor and a control center, and sending a state signal of the system to the control center when the following judgment algorithm is met:
t k+1 ＝t k +||e(t)|| 2 ＞δ||x(t k )|| 2 (6)
wherein, x (t) k ) The state at the last sampling instant, x (t) k+1 ) Triggering a time t for an event k+1 And e (t) = x (t) -x (t) k ) For deviations of the state of the controlled object from the current state at the previous sampling moment, so that the value of the controller u (t) changes only when an event triggers, i.e.
u(t)＝Kx(t k )t∈(t k t k+1 ] (7)
Step 4), designing an intrusion-tolerant control method of the networked motion control system, wherein the process is as follows:
4.1 The system is augmented according to the formula (3) to obtain an augmented state space equation, which is shown in the formula (8):
wherein the content of the first and second substances,
C a ＝[C D 2 ]，
is of f a (t) is an attack signal when θ 1 When v is greater than or equal to 0, there are
Suppose matrices E, D 2 Full rank, for each complex number s with a non-negative real part,
4.2 Design an intermediate observer, the process is as follows:
according to equation (8), an intermediate variable is defined:
where ω > 0, simultaneous equations (8) and (10), yields the following equation:
then
The estimated values are as follows:
wherein C is d ＝[0 I q ]，
Is to x a (t),f a (t),y(t),ζ a (t), d (t), and
the estimation error of the state is then shown by the following equation:
4.3 Controller design is as follows:
because D 1 Is a matching amount, therefore D 1 BN, N is a known matrix;
substituting equation (14) into equation (3) yields the following equation:
4.4 To construct a lyapunov energy function, as shown in equation (16) below:
in which a symmetric matrix P exists 1 ＞0,P 2 ＞0,P 3 If the formula (17) is satisfied, then (x (t) e) xa (t)e ζa (t)) exponential convergence;
therein II 11 ＝He[P 1 (A+BK)],
The invention relates to an intrusion-tolerant control method of a networked motion control system based on event triggering, which comprises the steps of firstly detecting an attack signal, and adopting a control strategy based on event triggering when the system is in safe operation; when the system is attacked, an attack signal and external disturbance of the system can be estimated, and the safe operation of the system is guaranteed.
The invention has the beneficial effects that: the event driving technology is adopted, so that unnecessary control signals can be reduced, and the transmission frequency of the control signals is reduced. Whether the networked motion control system is attacked or not can be detected in real time, the control strategy is actively switched, and an attack signal is estimated, so that the system can safely operate. And the design of the middle observer enables the error to be converged in a minimum energy boundary, so that the convergence error of the state is obtained.
Drawings
FIG. 1 is an event trigger interval;
FIG. 2 is a system state x 1 ,x 2 The response curve of (a);
FIG. 3 is an estimation of an attack signal;
FIG. 4 is an estimate of a disturbance signal;
FIG. 5 is a residual signal response curve of an attack detection filter;
fig. 6 is an evaluation function response curve of a residual signal.
Detailed Description
In order to make the objects, technical solutions and points of the present invention clearer, the technical solutions of the present invention are further described below with reference to the accompanying drawings and embodiments.
Referring to fig. 1 to 6, an intrusion tolerance control method for a networked motion control system based on event triggering includes the following steps:
1) Establishing a state space equation of a networked motion control system;
2) Constructing an attack detection filter;
3) Constructing a networked motion control system based on event triggering;
4) And constructing an intermediate observer and estimating an attack signal.
In the step 1), a state space equation of the networked motion control system is established, as shown in formula (18):
x (t) represents the system state quantity, u (t) is the system input, y (t) is the system output, d (t) is the disturbance signal, d (t) =0.02sin (3 t);
when the system is under attack, the system state space equation is as shown in equation (19):
wherein f is a (t) is an actuator attack signal, f a (t)＝sin(2.5t)；
In the step 2), the process of constructing the attack detection filter is as follows:
2.1 Design a full-order state observer as shown in equation (20):
2.2 The residual signal is as follows:
set 15s later the system is under attack and J th As can be seen from fig. 5, the residual signal oscillates sharply after 15s, and as can be seen from fig. 6, the residual evaluation function exceeds the threshold J after 15s th Indicating that the system is under network attack, and therefore the attack detection filter alarms;
in the step 3), a networked motion control system based on event triggering is designed; when the following judgment algorithm is satisfied, the state signal of the system is sent to the control center:
t k+1 ＝t k +||e(t)|| 2 ＞δ||x(t k )|| 2 (6)
wherein, x (t) k ) X (t) being the state of the last sampling instant k+1 ) Triggering a time t for an event k+1 And e (t) = x (t) -x (t) k ) Selecting sigma =0.9 for the deviation between the state of the controlled object at the last sampling moment and the current state;
u(t)＝Kx(t k )t∈(t k t k+1 ] (7)
wherein K = [ -14.6698-23.5637 ]. It is known from fig. 1 that there is an event trigger control interval before 15s and there is no trigger interval after 15s, which means that the event trigger control is ended after 15s, and fig. 2 is a state response curve of the system, it can be seen that before 15s, the state converges to a minimum range, which satisfies the predetermined control performance index;
in the step 4), an intermediate observer is constructed, and the process is as follows:
the state space model is obtained by augmenting equation (19) as follows:
wherein
The intermediate observer is as follows:
C d ＝[0 0 1]；
fig. 3 is an estimation of an attack signal, fig. 4 is an estimation of a disturbance signal, and it is obvious that the estimation effect is very accurate;
the controller is designed as follows:
wherein
N =0.2905794153542, it is known from FIG. 2 that the system state is still stable after 15s, the state is converged in a very small range, and the system can run safely;
constructing a lyapunov energy function as shown in equation (16) below:
the criterion for lyapunov stability is as follows:
wherein II 11 ＝He[P 1 (A+BK)],
Selecting epsilon =1 and omega =10, and solving the formula (17) to obtain:
K＝[-14.6698 -23.5635]，
solving the formula (17) to obtain K and L values, and the formula (12) to obtain x a (t)，f a (t)，y(t)，ζ a The estimated values of (t), d (t) are obtained as u (t) by the formula (14). As shown in FIG. 1, after 15s, there is no event trigger interval, and the control is switched to intrusion tolerant control based on the end of the event trigger controlFig. 3 and 4 can see the estimation of the attack and disturbance signals by the intermediate observer after 15 s.
The experimental result shows that the attack detection method can detect attack signals in time, adopts a control strategy based on event triggering when the system runs safely, sends an alarm by an attack detection filter when the system is attacked, actively switches a control mode by the system, and accurately estimates the attack and disturbance signals by adopting an intrusion-tolerant control algorithm. The running result can meet the requirements of precision and real-time performance of practical application, and the networked motion control system can be stable when being attacked, so that greater economic loss is avoided.
The embodiments of the present invention have been described and illustrated in detail above with reference to the accompanying drawings, but are not limited thereto. Many variations and modifications are possible which remain within the knowledge of a person skilled in the art, given the concept underlying the invention.
Claims (1)
1. An event trigger-based intrusion tolerance control method for a networked motion control system, the method comprising the following steps:
step 1), establishing a state space equation of a networked motion control system:
considering the case where there is a disturbance in the system, the state space equation is shown as equation (1):
where A is the state matrix of the system, B is the input matrix, C is the output matrix, D 1 Perturbing the distribution matrix for the state, wherein the perturbation is a matching perturbation, D 2 For outputting disturbance distribution matrix, A, B, C, D 1 ,D 2 Is a matrix of constants of appropriate dimensions, x (t) E R n Representing the system state quantity, u (t) being the controller, as system input, y (t) e R p For system output, d (t) is belonged to R q Representing an external disturbance;
step 2), constructing an attack detection filter, wherein the process is as follows:
2.1 The core of the attack detection filter is a full order state observer, as shown in equation (2):
2.2 Consider a system under attack, the state space equation is shown as equation (3):
y(t)＝Cx(t)+D 2 d(t)
B＝E (3)
wherein f is a ∈R r Since B = E, it is an actuator attack signal;
2.3 Simultaneous equations (2) and (3), the residual equation is simply defined as:
introducing variables
The residual equation is reduced to r (t) = Ce (t) + D 2 d(t)；
2.4 ) residual evaluation function J τ (τ) and threshold Jth are as follows:
wherein r (t) has a residual characteristic when the observer gain matrix L is selected to stabilize A-LC, τ represents time, and J is when τ If the (tau) > Jth indicates that the system is attacked by the network, otherwise, the system is in a normal operation state;
and 3), constructing a networked motion control system based on event triggering, constructing an event generator between the sensor and the control center, and sending a state signal of the system to the control center when the following judgment algorithm is met:
t k+1 ＝t k +||e k (t)|| 2 ＞δ||x(t k )|| 2 (6)
wherein, x (t) k ) X (t) being the state of the last sampling instant k+1 ) Triggering a time t for an event k+1 Adopted state of (e) and k (t)＝x(t)-x(t k ) For deviations of the state of the controlled object from the current state at the previous sampling moment, so that the value of the controller u (t) changes only when an event triggers, i.e.
u(t)＝Kx(t k ) t∈(t k t k+1 ] (7)
Step 4), designing an intrusion-tolerant control method of the motion control system, wherein the process is as follows:
4.1 The system is augmented according to formula (3) to obtain an augmented state space equation, as shown in formula (8):
wherein the content of the first and second substances,
C a ＝[C D 2 ]，
f a (t) is an actuator attack signal when theta 1 When v is greater than or equal to 0, there are
Suppose matrices E, D 2 Full rank, for each complex number s with a non-negative real part,
4.2 Design an intermediate observer, the procedure is as follows:
defining an intermediate variable according to equation (8)
Simultaneous equations (8) and (10) yield equation (11)
Then
The estimated values are as follows:
wherein C is d ＝[0 I q ]，
Is to x a (t),f a (t),y(t),ζ a (t), estimation of d (t), and
then the estimation error of the state is shown by the following equation:
4.3 Controller design as follows:
because D 1 To match the amount, therefore D 1 N is a known matrix, and substituting equation (14) into equation (3) yields
4.4 To construct a Lyapunov energy function, as shown in equation (13):
in which a symmetric matrix P exists 1 ＞0,P 2 ＞0,P 3 If the formula (17) is satisfied, then (x (t) e) xa (t) e ζa (t)) exponential convergence;
therein II 11 ＝He[P 1 (A+BK)],
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