CN116760603B - Multi-rate information physical system safety control method based on prediction information under network attack - Google Patents
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Abstract
The invention discloses a multi-rate information physical system safety control method based on prediction information under network attack, which comprises the following steps: 1) Firstly, establishing a multi-rate system model under the DoS attack; 2) Constructing a sampling data state observer, an output predictor and an output feedback controller for reconstructing the system state; 3) Establishing an augmentation model of system state and error under DoS attack; 4) By means of Lyapunov stability analysis, the asymptotic stability of the control system is ensured under certain standard conditions. Compared with the network security control of the existing information physical system, the invention can ensure the system to have excellent control performance and ensure the safe and stable operation under the influence of DoS attack under the condition that the sensor and the controller are asynchronous in speed.
Description
Technical Field
The invention relates to the field of network control and information prediction, in particular to a multi-rate information physical system safety control method based on prediction information under network attack.
Background
With the rapid development of the internet information technology and control field, in the modern control field, such as a power network system, a transportation system, a chemical production system, etc., the physical change evolution process of an object system and the information processing transmission process are often mutually influenced and deeply coupled, and an information physical system (CyberPhysical System, CPS) is a system for describing the close connection between the generation of such information and the physical dynamic process. In essence, CPS can be viewed as a networked system containing control mechanisms. Therefore, according to the viewpoint of control theory, the characteristics and strategies of potential attacks in the information physical system are analyzed, and particularly, the actions of the attacks need to be described by adopting a unified method or mode; and the safety control method of the information physical system under various attack conditions, particularly the feasibility condition and method of attack detection and the feasibility condition and method of safety state estimation are researched.
Although there have been many studies on the above-mentioned safety control methods, there are still many improvements that can be made, for example: at present, few researches relate to the condition that a sensor and a controller in an information physical system are asynchronous in sampling, and when the periods of the sensor and the controller are inconsistent, the original controller cannot work with high performance; among different sensors, different sampling periods mean that the price, the shape, the size and the function of the sensors are inconsistent, the pursuit of consistency of sampling frequency is the most important for common devices in terms of comparison of functions, prices and the like, and for a spacecraft or a sampler in some other field, the sensors with different periods are necessary in consideration of weight and cost, and the design of a controller under the condition is a significant research direction; secondly, dos attacks may cause paralysis of the information physical system and service unavailability, and an attacker makes the system unable to normally process requests of legal users by sending a large amount of requests to the system or occupying system resources, which may cause service interruption, resulting in delay and interruption of user access to the system or data transmission. In some typical systems, such as unmanned systems or emergency communication systems, serious economic and safety risks may be posed. In view of the above, the invention provides an alternative prediction control method for network security of the multi-rate information physical system, which can ensure that the multi-rate information physical system can still keep stable and high-efficiency operation under the condition of facing DoS attack.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides a multi-rate information physical system safety control method based on prediction information under network attack, which solves the problems of poor control effect, bao Pin transmission loss when encountering DoS attack and the like of the existing multi-rate information physical system.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a multi-rate information physical system safety control method based on prediction information under network attack includes the following steps:
step 1), firstly, constructing a multi-rate continuous system model and a DoS attack model according to the principle that the update rate of a sensor in a multi-rate control system is slower than that of a controller and the problem of packet loss of an information physical system under DoS attack;
step 2) constructing an alternate prediction state observer for reconstructing the system state according to a typical Robert observer and combining prediction knowledge, and designing a controller by combining feedback control;
step 3) establishing an augmentation model of system state and error under DoS attack;
and step 4) finally, establishing asymptotic stability of the control system under a certain standard condition by using a Lyapunov stability theory, so that the controlled multi-rate dynamic network control system can still safely and stably operate under the condition of facing a DoS attack.
As a further improvement of the present technical solution, step 1) specifically includes:
the following multi-rate information physical system model is established:
where x (-) is the system state vector, u (-) is the control input, y (-) is the system output, y a (. Cndot.) is the sensor sample output, A, B and C are known constant matrices of appropriate dimensions, T is the system controller fast update period, MT is the sensor slow sample period, P is the prediction horizon, k=1, 2,3, …, m=1, 2,3 …, p=1, 2, …, M-1;
wherein kMT +pt=ρt, z (ρt) = [ x ] T (ρT)u T (ρT)] T The multi-rate information physical system model is as follows:
wherein the method comprises the steps of
The following DoS attack model is established:
wherein the method comprises the steps ofFor the system state information after being attacked, θ (·) is a DoS attack detector located at the controller end, when the system is detected to be attacked, θ (·) =0, otherwise θ (·) =1, the DoS attack model obeys Bernoulli distribution, and can be obtained:
as a further improvement of the present technical solution, step 2) specifically includes:
first, according to a typical leber observer, the following state observer is constructed:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>Representing the estimated output, L being the observer gain; two input quantities u (ρT) and y of the state observer a There is a considerable difference in the update rate of (ρT), which is kT, which is the time series {0, T,2T, … }, y a (ρT) has an update rate of kMT, said kMT being the time series {0, MT,2MT, … };
constructing a plurality of virtual output points during the slow sampling period of the sensor, so that the output rate is matched with the update rate of the controller, and obtaining an alternate prediction state observer based on the Luneberg observer and combined with a model prediction method, wherein the alternate prediction state observer is as follows:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>Representing the estimated output, y p (. Cndot.) represents the predicted output value, (. Cndot.)>For mixed output, the specific expression is:
wherein φ (·) is a detector at the sensor end for detecting whether the sensor has an actual measurement y a (. Cndot.) output; with the actual measurement output then phi (·) =1, whereas phi (·) =0, let
Said y p (. Cndot.) is derived from the following predictors:
wherein the method comprises the steps ofIs a predicted state;
the controller is as follows:
wherein K= [ K ] 1 K 2 ]，K 1 ，K 2 Is the gain.
As a further improvement of the present technical solution, step 3) specifically includes:
defining an estimation error as:
defining a closed loop system as:
wherein the method comprises the steps of
As a further improvement of the present technical solution, step 4) specifically includes:
given the controller gain matrix K and the observer gain matrix L, the positive definite matrices P and S satisfy the following linear matrix inequality:
wherein gamma is 1 ＝-P，Υ 2 ＝-S，Υ 5 ＝-P，Υ 7 ＝-S，/>
And the mean square stability of the system index is enhanced under the designed composite controller by the linear matrix inequality.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention selects a discrete time system model, and provides a method which is more direct and easier to realize on a digital computer platform for engineers;
(2) The invention researches the problem of DoS attack in the multi-rate information physical system for the first time, and provides an effective defending mechanism, thereby improving the safety of the multi-rate information physical system;
(3) The invention provides an alternate prediction observer which can simultaneously solve the problems of state deficiency in a sensor output interval and influence of DoS attack on a system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a control method of the present invention.
FIG. 2 is a schematic diagram of the system and attack modeling of the present invention.
FIG. 3 is a schematic diagram of the design principle of the multi-rate alternative prediction observer under the DoS attack in the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The multi-rate information physical system security control method based on the prediction information under the network attack shown in fig. 1 comprises the following steps:
step 1) analyzing the difference between the sampling rate of the sensor and the update rate of the controller in the multi-rate information physical network control system. Often the sensor update rate is much slower than the controller update rate, making the control performance of the multi-rate control system poor. Aiming at the phenomenon, the invention uniformly sets the virtual output point position in the period of slow sampling and updating of the sensor, takes the virtual output point position as a system reference period, and is based on the system and attack modeling process as follows:
firstly, establishing the following multi-rate information physical system model:
where x (-) is the system state vector, u (-) is the control input, y (-) is the system output, y a (. Cndot.) is the sensor sample output, A, B and C are known constant matrices of appropriate dimensions, T is the system controller fast update period, MT is the sensor slow sample period, P is the prediction horizon, k=1, 2,3, …, m=1, 2,3 …, p=1, 2, …, M-1;
for convenience of expression, let kMT +pt=ρt, z (ρt) = [ x ] T (ρT) u T (ρT)] T . The following system is obtained:
wherein the method comprises the steps of
The following DoS attack model is established:
wherein the method comprises the steps ofFor the system state information after being attacked, θ (·) is a DoS attack detector located at the controller end, when the system is detected to be attacked, θ (·) =0, otherwise, θ (·) =1. Assuming that it obeys the Bernoulli distribution, it is available:
step 2) because the internal state information of the system is unknown, a state observer is firstly required to be constructed to obtain the state of the system, but in a multi-rate information physical system, because the output information part of the system is unknown, a predictor is required to be constructed by combining prediction knowledge to obtain the prediction output of the system, and an alternate prediction observer is constructed by combining the actual measured value of a sensor, and the specific steps are as follows:
step 2.1) firstly, constructing the following state observer according to a typical leber observer:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>The estimated output is represented, L being the observer gain. It should be emphasized that the two inputs u (ρT) and ρT of the observer arey a There is a considerable difference in the update rate (ρt). In particular, the update rate of u (ρT) is kT, which is the time series {0, T,2T, … }, and y a The update rate of (ρT) is kMT, and kMT is the time series {0, MT,2MT, … }.
Step 2.2) constructing a plurality of virtual output points during sensor slow sampling such that the output rate matches the controller update rate, thereby solving u (ρT) and y a (ρT) the update rate difference is large. Based on this, the following alternate prediction observer is proposed:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>Representing the estimated output, y p (. Cndot.) represents the predicted output value, (. Cndot.)>For mixed output, the specific expression is:
wherein φ (·) is a detector at the sensor end for detecting whether the sensor has an actual measurement y a (. Cndot.) output. If there is an actual measurement output then phi (·) is=1, otherwise phi (·) is=0, and letIn addition y p (. Cndot.) is derived from the following predictors:
wherein the method comprises the steps ofIs the predicted state.
Therefore, we design the following controller:
wherein K= [ K ] 1 K 2 ]，K 1 ，K 2 Is the gain.
And 3) comprehensively considering the state space model and the attack model provided by the invention and the designed alternative prediction observer and controller to establish an augmentation model of system state and error under DoS attack. The method comprises the following steps:
defining an estimation error as:
the closed loop system can thus be expressed as:
wherein the method comprises the steps of
And 4) finally solving parameters such as each gain of the structural controller by using a Lyapunov stability analysis method and solving a linear matrix inequality equation, and meanwhile, proving that the system index is stable in mean square.
The linear matrix inequality for solving the controller and observer gains is:
theorem 1: considering the proposed multi-rate information physical system, an alternate prediction controller consisting of an alternate prediction observer and a feedback controller is used to measure the DoS interference attack of the channel with unknown attack strategy. Given the controller gain matrix K and the observer gain matrix L, the closed-loop system index is stable squared if positive definite matrices P and S exist that satisfy the inequality below.
Wherein gamma is 1 ＝-P，Υ 2 ＝-S，Υ 5 ＝-P，Υ 7 ＝-S，/>
Lemma 1: let V (x (k)) be the Lyapunov function. If lambda > 0, mu > 0, v > 0 andthe method meets the following conditions:
μ||x(k)|| 2 ≤V(x(k))≤v||x(k)|| 2 ,
then x (k) satisfies
And (3) proving: let η (ρt) = [ z T (ρT) e T (ρT)]Constructing a Lyapunov function: v (η (ρt))=z T (ρT)Pz(ρT)+e T (ρT) Se (ρT). According to step 3, it is possible to:
wherein ψ is 1 ＝[Ψ 11 Ψ 12 ]，
Ψ 2 ＝diag{P,S,σ 2 S,σ 3 S,σ 4 S}，
Ψ 3 ＝diag{-P,-S}，
Using the matrix diag { I, I, P -1 ,S -1 ,S -1 ,S -1 ,S -1 The matrix in the } left-and right-multiply theorem 1 is available:
wherein Ω 1 ＝-P，Ω 2 ＝-S，Ω 5 ＝-P -1 ，Ω 7 ＝-S -1 ，/> It is not difficult to understand the matrix Λ 1 And lambda 2 Equivalently, from the schulb theorem, Λ 2 Equivalent to Θ < 0. Two scalar quantities α and β are defined to satisfy:
α＝max{λ max (P),λ max (S)},0＜β＜min{λ min (-Θ),α}
the combination Θ < 0 can be obtained:
Ε{V(η(ρT+T))}-V(η(ρT))＝η T (ρT)Θη(ρT)≤λ min (-Θ)η T (ρT)η(ρT)＜-βη T (ρT)η(ρT)
further:
β||η(ρT)|| 2 ≤V(η(ρT))≤α||η(ρT)|| 2
according to lemma 1:
therefore, the index of the closed loop system is stable in mean square, and the phenomenon is verified.
The above description of the embodiments is only for aiding in the understanding of the method of the present invention and its core ideas. It should be noted that it will be apparent to those skilled in the art that various modifications and adaptations of the invention can be made without departing from the principles of the invention and these modifications and adaptations are intended to be within the scope of the invention as defined in the following claims.
Claims (1)
1. The multi-rate information physical system safety control method based on the prediction information under the network attack is characterized by comprising the following steps:
step 1) firstly, constructing a multi-rate continuous system model and a DoS attack model according to the principle that the update rate of a sensor in a multi-rate control system is slower than that of a controller and the problem of packet loss of an information physical system under DoS attack, wherein the method specifically comprises the following steps:
the following multi-rate information physical system model is established:
where x (-) is the system state vector, u (-) is the control input, y (-) is the system output, y a (. Cndot.) is the sensor sample output, A, B and C are known constant matrices of appropriate dimensions, T is the system controller fast update period, MT is the sensor slow sample period, P is the prediction horizon, k=1, 2,3, …, m=1, 2,3 …, p=1, 2, …, M-1;
wherein kMT +pt=ρt, z (ρt) = [ x ] T (ρT) u T (ρT)] T The multi-rate information physical system model is as follows:
wherein the method comprises the steps of
The following DoS attack model is established:
wherein the method comprises the steps ofFor the system state information after being attacked, θ (·) is a DoS attack detector located at the controller end, when the system is detected to be attacked, θ (·) =0, otherwise θ (·) =1, the DoS attack model obeys Bernoulli distribution, and can be obtained:
step 2) constructing an alternate prediction state observer for reconstructing the state of the system according to a typical leber observer and combining prediction knowledge, and designing a controller by combining feedback control, wherein the method specifically comprises the following steps:
first, according to a typical leber observer, the following state observer is constructed:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>Representing the estimated output, L being the observer gain; two input quantities u (ρT) and y of the state observer a There is a considerable difference in the update rate of (ρT), which is kT, which is the time series {0, T,2T, … }, y a (ρT) has an update rate of kMT, said kMT being the time series {0, MT,2MT, … };
constructing a plurality of virtual output points during the slow sampling period of the sensor, so that the output rate is matched with the update rate of the controller, and obtaining an alternate prediction state observer based on the Luneberg observer and combined with a model prediction method, wherein the alternate prediction state observer is as follows:
wherein the method comprises the steps ofIs an estimate of z (·), is +.>Representing the estimated output +.>For mixed output, y p (. Cndot.) represents a predicted output value, and the specific expression is:
wherein φ (·) is a detector at the sensor end for detecting whether the sensor has an actual measurement y a (. Cndot.) output; with the actual measurement output then phi (·) =1, whereas phi (·) =0, let
Said y p (. Cndot.) is derived from the following predictors:
wherein the method comprises the steps ofIs a predicted state;
the controller is as follows:
wherein K= [ K ] 1 K 2 ]，K 1 ，K 2 Is gain;
step 3) establishing an augmentation model of system state and error under DoS attack, which specifically comprises the following steps:
defining an estimation error as:
defining a closed loop system as:
wherein the method comprises the steps of
And step 4) finally, establishing asymptotic stability of the control system under a certain standard condition by using a Lyapunov stability theory, so that the controlled multi-rate dynamic network control system can still safely and stably operate under the condition of facing a DoS attack, and the method specifically comprises the following steps:
given the controller gain matrix K and the observer gain matrix L, the positive definite matrices P and S satisfy the following linear matrix inequality:
wherein gamma is 1 ＝-P，Υ 2 ＝-S，Υ 5 ＝-P，Υ 7 ＝-S，/>
And the mean square stability of the system index is enhanced under the designed composite controller by the linear matrix inequality.
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| CN110213115A (en) * | 2019-06-25 | 2019-09-06 | 南京财经大学 | A kind of Multi net voting attacks the method for controlling security of lower event-driven network control system |
| CN115718427A (en) * | 2022-11-16 | 2023-02-28 | 哈尔滨理工大学 | Security-guaranteed non-fragile networked prediction control method |
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| CN110213115A (en) * | 2019-06-25 | 2019-09-06 | 南京财经大学 | A kind of Multi net voting attacks the method for controlling security of lower event-driven network control system |
| CN115718427A (en) * | 2022-11-16 | 2023-02-28 | 哈尔滨理工大学 | Security-guaranteed non-fragile networked prediction control method |
Non-Patent Citations (1)
| Title |
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| Resilient Predictive Control for Cyber–Physical Systems Under Denial-of-Service Attacks;Longjie Zhang et al;IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS,;第69卷(第1期);全文 * |
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