Anti-interference elastic control method in network packet loss environment

Abstract

The invention discloses an anti-interference elastic control method under a network packet loss environment in the field of network security anti-interference. The method comprises the following steps: step 1) establishing a state equation of a system and modeling interference; step 2) giving an augmented composite system equation and elaborating a packet loss compensation algorithm based on sample-and-hold; 3) designing an interference observer based on sampling and holding and a controller for tracking interference and controlling the system; and step 4) through a Lyapunov stability analysis method and a stochastic system analysis method, obtaining gain parameters of the controller and the observer by solving a linear matrix inequality equation. The anti-interference elastic control method in the network packet loss environment can be designed under the condition that data packet loss in the network transmission process is unreliable due to the fact that a network control system is subjected to DoS attack and unknown interference, and the network control system is endowed with certain attack tolerance and anti-interference capacity.

Description

Technical Field

[0001] The present invention belongs to the technical field of network anti-interference control, and in particular relates to an anti-interference elastic control method in a network packet loss environment. Background Art

[0002] In the current situation, networked control systems have emerged. This system introduces computer networks in the control environment, so that components such as sensors, controllers and actuators can be connected through the network and exchange information and transmit data. Compared with traditional control systems, networked control systems do not need to build point-to-point dedicated lines, but can achieve information interconnection through wireless networks, thereby significantly reducing design and maintenance costs. In addition, this system also facilitates information sharing and simplifies the implementation of remote operation and control. At present, networked control systems have been widely used in many fields such as space exploration, industrial automation, remote monitoring and diagnosis, and drones.

[0003] Although networked systems use wireless networks for information transmission, which can greatly improve the flexibility of control systems, at the same time, this also brings many potential problems. Protecting the security of cyber-physical systems has always been a key area of ​​concern in academia. Denial of Service (DoS) attacks are a common means of network attacks. This attack occupies limited system resources by sending large amounts of data, thereby preventing legitimate users from accessing the system. The occurrence of data packet loss in the process of transmitting information in the facility structure that relies on network communication in the system will affect the performance of the system and may affect the stability of the system.

[0004] In addition, various interferences in the system can lead to poor system control performance or even system instability. Due to the universality of interference in various systems, anti-interference technology is also one of the current research hotspots. Observer-based control (DOBC) is a typical anti-interference control method, which is usually used to estimate unknown interference. As a control method, it can quickly compensate for interference. However, there are still some problems in how to apply anti-interference technology, such as interference observers, to network control systems. In particular, how interference observers can track interference and maintain system stability in the face of network packet loss in network control systems is still relatively lacking.

[0005] In view of these existing problems, it is very urgent to study the design of interference observers in network control systems to resist DoS attacks, which also requires comprehensive discussion and analysis from multiple aspects such as controller packet loss compensation design and interference observer. Summary of the invention

[0006] In response to existing problems and technical deficiencies, the present invention provides an anti-interference resilience control method in a network packet loss environment, which solves the problem of random packet loss in a network-physical system when encountering a denial of service (DoS) attack, and poor system control effect when facing unknown interference, improves the stability of the system and gives the system a certain attack tolerance.

[0007] To achieve the above object, the present invention adopts the following technical solution: a method for controlling anti-interference elasticity in a network packet loss environment, comprising the following steps:

[0008] Step 1) Establish the state equation of the system and model the disturbance;

[0009] Step 2) giving the augmented composite system equation and explaining the packet loss compensation algorithm based on sampling and holding;

[0010] Step 3) Design a disturbance observer based on sample-and-hold, and a controller for tracking the disturbance and controlling the system;

[0011] Step 4) The parameters of the controller and observer gain are obtained by solving linear matrix inequality equations through Lyapunov stability analysis method and stochastic system analysis method.

[0012] As a further improvement of the technical solution of the present invention, step 1) is specifically:

[0013] The state equation of the discrete linear steady-state system with disturbance is established as follows:

[0014]

[0015] In the formula, x(k) represents the actual state signal of the system at the kth moment, u(k) represents the control signal at the kth moment, d(k) represents the interference signal at the kth moment, and y(k) represents the output signal at the kth moment. 0 , B 0 and C 0 is a known constant matrix of suitable dimension;

[0016] The following interference model is established:

[0017]

[0018] Where d(k) represents the interference signal at the kth moment, w(k) represents the process variable of the interference at the kth moment, and E and F are known constant matrices of appropriate dimensions.

[0019] As a further improvement of the technical solution of the present invention, step 2) is specifically as follows:

[0020] Step 2.1) First, the composite system obtained after augmenting x(k) and w(k) is:

[0021]

[0022] In the formula, It represents the state signal of the augmented system at the kth moment, z(k+1) represents the state signal of the augmented system at the k+1th moment, and u(k) represents the control signal at the kth moment;

[0023] in,

[0024] Step 2.2) describes the packet loss compensation algorithm:

[0025] If the network in the sensor-controller channel of the system is attacked by a denial of service at the kth moment, there is a possibility of random loss of data packets during transmission. Therefore, a signal detection device λ(·) is installed at the receiving end of the system controller, which is specifically defined as follows:

[0026]

[0027] Assuming that λ(·) follows a Bernoulli distribution, we have:

[0028]

[0029] In the formula, represents the probability of successful transmission of the output signal, is the variance of λ(·);

[0030] When packet loss occurs in the system, the output value of the previous moment in the zero-order holder is used. As the compensation output, the compensated output is recorded as If no packet loss occurs, the current output value y(k) is used as the output The specific form of the output compensation algorithm based on sampling and holding is as follows:

[0031]

[0032] Where λ(k) is the white sequence of Bernoulli distribution, represents the output signal of the system after compensation at the k-1th moment, Represents the output signal of the system after compensation at the kth moment.

[0033] As a further improvement of the technical solution of the present invention, step 3) is specifically as follows:

[0034] The specific design form of the observer based on the above compensation algorithm is as follows:

[0035]

[0036] In the formula, It represents the estimated value of the state signal of the augmented system at the k+1th moment, L is the observer gain, Represents the estimated value of the output signal of the augmented system at the kth moment.

[0037] Step 3.2) The controller design of the system is as follows:

[0038]

[0039] In the formula, is the estimated value of the disturbance signal at the kth moment, and K is the controller gain.

[0040] As a further improvement of the technical solution of the present invention, step 4) is specifically as follows:

[0041] Step 4.1) Define the estimated error as:

[0042]

[0043] Among them, e(k) is the augmented estimation error at the kth moment, e x (k) is the error between the actual state signal and the estimated value at the kth moment, e w (k) is the error between the actual interference signal and the estimated value at the kth moment, is the estimated value of the state signal at the kth moment, is the estimated value of the disturbance process variable at the kth moment;

[0044] The closed-loop function of the control system obtained by the controller and observer is as follows:

[0045]

[0046] in,

[0047] The error system of the control system is as follows:

[0048]

[0049] Step 4.2) According to Lyapunov stability theory and stochastic analysis theory, the control system gain must meet certain conditions to enable the system to maintain safe and stable operation when random packet loss occurs under a denial of service attack, specifically:

[0050] If there exists a matrix P 1 >0,P 2 >0,P 3 >0, and the known parameter α 1 , α 2 , α 3And the matrices Y and R satisfy the following linear matrix inequality:

[0051]

[0052] Where I is the identity matrix of appropriate dimensions,

[0053]

[0054]

[0055]

[0056] Then the error system and the closed-loop system are both stable, and the controller gain K and the observer gain L can be respectively expressed by K=YP 1 and L = P 2 -1 R is obtained.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] (1) Considering that some system states are difficult to measure directly, the present invention designs a discrete-time extended state observer. Different from the controller design method based on known system states, the present invention is more suitable for networked control systems with unknown system states in a computer context.

[0059] (2) The present invention uses a probability model based on Bernoulli distribution to describe the random packet loss phenomenon in the sensor-controller channel, and proposes a compensation control method based on sampling and holding;

[0060] (3) The present invention takes into account the situations where the system is subjected to denial of service DoS attacks and unknown disturbances, and designs an extended state observer based on sampling and holding, which enhances the system's ability to resist unknown interference while giving the system a certain attack tolerance and anti-interference characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0062] Figure 1 It is a control structure diagram of the system in the present invention.

[0063] Figure 2 Flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] like Figure 1-2 As shown, a method for controlling anti-interference elasticity in a network packet loss environment includes the following steps:

[0066] Step 1) Construction of system model:

[0067] Considering the network physical system in the computer environment, the discrete system model and the interference model are constructed respectively. Specifically, we assume that the state equation of a discrete linear steady-state system with interference is:

[0068]

[0069] In the formula, x(k) represents the actual state signal of the system at the kth moment, u(k) represents the control signal at the kth moment, d(k) represents the interference signal at the kth moment, y(k) represents the output signal at the kth moment, and A 0 , B 0 and C 0 is a known constant matrix of suitable dimension.

[0070] In addition, interference needs to be modeled. The specific interference model is as follows:

[0071]

[0072] Where w(k) represents the process variable of the disturbance at the kth moment, and E and F are known constant matrices of appropriate dimensions.

[0073] Step 2) giving the augmented composite system equation and explaining the packet loss compensation algorithm based on sampling and holding;

[0074] First, for discrete systems, the composite system obtained by augmenting x(k) and w(k) is as follows:

[0075]

[0076] In the formula, It represents the state signal of the augmented system at the kth moment, z(k+1) represents the state signal of the augmented system at the k+1th moment, and u(k) represents the control signal at the kth moment;

[0077] in, C=[C 00].

[0078] Considering that the discrete system sensor-controller channel suffers from DoS attack, resulting in the loss of communication data packets, a detection device λ(·) is set at the receiving end of the controller, which is specifically defined as follows:

[0079]

[0080] Assuming that λ(·) follows a Bernoulli distribution, we have:

[0081]

[0082] In the formula, represents the probability of successful transmission of the output signal, is the variance of λ(·).

[0083] Secondly, the packet loss compensation algorithm is explained. When packet loss occurs in the system, we use the output value of the previous moment in the zero-order holder As the compensation output, the compensated output is recorded as If no packet loss occurs, the current output value y(k) is used as the output The specific form of the output compensation algorithm based on sampling and holding is as follows:

[0084]

[0085] Where λ(k) is the white sequence of Bernoulli distribution, represents the output signal of the system after the k-1 step compensation, Represents the output signal of the system after compensation at the kth moment.

[0086] Step 3) Design a disturbance observer and controller based on sample-and-hold:

[0087] The specific design form of the observer based on the above compensation algorithm is as follows:

[0088]

[0089] In the formula, It represents the estimated value of the state signal of the augmented system at the k+1th moment, L is the observer gain, Represents the estimated value of the output signal of the k-th step of the augmented system.

[0090] At the same time, the controller design of the system is as follows:

[0091]

[0092] In the formula, is the estimated value of the disturbance signal at the kth moment, and K is the controller gain.

[0093] Step 4) Stability analysis:

[0094] First, define the estimation error as:

[0095]

[0096] Among them, e(k) is the augmented estimation error at the kth moment, e x (k) is the error between the actual state signal and the estimated value at the kth moment, e w (k) is the error between the actual interference signal and the estimated value at the kth moment, is the estimated value of the state signal at the kth moment, is the estimated value of the disturbance process variable at the kth moment.

[0097] The closed-loop function of the control system obtained by the above controller and observer is as follows:

[0098]

[0099] In the formula,

[0100] The error system of the control system is as follows:

[0101]

[0102] Then, according to Lyapunov stability theory and stochastic analysis theory, the control system gain must meet certain conditions to enable the system to maintain safe and stable operation when random packet loss occurs under denial of service attacks, specifically:

[0103] Theorem 1: If there exists a matrix P 1 >0,P 2 >0,P 3 >0, and parameter α 1 , α 2 , α 3 , ε, η 1 , η 2 , η 3 And the matrices Y and R satisfy the following linear matrix inequality:

[0104]

[0105] Where I is the identity matrix of appropriate dimensions,

[0106]

[0107]

[0108] Lemma 1: For any initial state x 0 , if the system satisfies:

[0109]

[0110] Then the system is stochastically stable.

[0111] Proof: Define the following Lyapunov function:

[0112]

[0113] It can be obtained that the expectation is:

[0114]

[0115] In the formula,

[0116]

[0117] in,

[0118]

[0119] To facilitate subsequent analysis, we define a new augmented variable get:

[0120]

[0121] Among them, η 1 , η 2 , η 3 are all positive numbers, α 1 , α 2 are known parameters.

[0122] If the above equation holds, then there exists a positive constant η 3 , and the matrix P that meets the conditions 1 and Make

[0123]

[0124] in

[0125] The above formula is equivalent to the parameter α 1 and α 2 are all less than 0, then α 1 +α 2 <0. Therefore, there is a parameter Such that ΔE{V(φ(k))}<-ε||φ(k)|| 2 ,in other words,

[0126] E{V(φ(k+1))}-V(φ(k))≤ε||φ(k)|| 2 ,

[0127] Assume that there is an integer M. For any M>1, adding from 0 to M on both sides of the above equation yields This means If M→∞, according to Lemma 1, the closed-loop system and the estimation error dynamics under DoS attack are both stochastically stable. Proof completed.

[0128] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A method for controlling anti-interference elasticity in a network packet loss environment, characterized in that: The following steps are involved: Step 1) Establish the state equation of the system and model the disturbance; Step 2) giving the augmented composite system equation and explaining the packet loss compensation algorithm based on sampling and holding; Step 3) Design a disturbance observer based on sample-and-hold, and a controller for tracking the disturbance and controlling the system; Step 4) The parameters of the controller and observer gain are obtained by solving linear matrix inequality equations through Lyapunov stability analysis method and stochastic system analysis method.

2. The anti-interference elastic control method in a network packet loss environment according to claim 1, characterized in that: Step 1) is specifically as follows: The state equation of the discrete linear steady-state system with disturbance is established as follows: Where x(k) represents the actual state signal of the system at the kth moment, u(k) represents the control signal of the kth step, d(k) represents the interference signal at the kth moment, y(k) represents the output signal at the kth moment, A0, B0 and C0 are known constant matrices of appropriate dimensions; The following interference model is established: Where w(k) represents the process variable of the disturbance at the kth moment, and E and F are known constant matrices of appropriate dimensions.

3. The anti-interference elastic control method in a network packet loss environment according to claim 2, characterized in that: Step 2) is specifically as follows: Step 2.1) First, the composite system obtained after augmenting x(k) and w(k) is: In the formula, represents the state signal of the augmented system at the kth moment, z(k+1) represents the state signal of the augmented system at the k+1th moment, and u(k) represents the control signal at the kth moment; in, C = [C00]; Step 2.2) describes the packet loss compensation algorithm: If the network in the sensor-controller channel of the system is attacked by a denial of service at the kth moment, there is a possibility of random loss of data packets during transmission. Therefore, a signal detection device λ(·) is installed at the receiving end of the system controller, which is specifically defined as follows: Assume that λ(·) follows a Bernoulli distribution: In the formula, represents the probability of successful transmission of the output signal, is the variance of λ(·); When packet loss occurs in the system, the output value of the previous moment in the zero-order holder is used. As the compensation output, the compensated output is recorded as If no packet loss occurs, the current output value y(k) is used as the output The specific form of the output compensation algorithm based on sampling and holding is as follows: Where λ(k) is the white sequence of Bernoulli distribution, represents the output signal of the system after the k-1 step compensation, Represents the output signal of the system after the k-th step compensation.

4. The anti-interference elastic control method in a network packet loss environment according to claim 3, characterized in that: Step 3) is specifically: Step 3.1) The specific design form of the observer based on the compensation algorithm is as follows: In the formula, It represents the estimated value of the state signal of the augmented system at the k+1th moment, L is the observer gain, represents the estimated value of the output signal of the augmented system at the kth moment; Step 3.2) The controller design of the system is as follows: In the formula, is the estimated value of the disturbance signal at the kth moment, and K is the controller gain.

5. The anti-interference elastic control method in a network packet loss environment according to claim 4, characterized in that: Step 4) is specifically as follows: Step 4.1) Define the estimated error as: Among them, e(k) is the augmented estimation error at the kth moment, e x (k) is the error between the actual state signal and the estimated value at the kth moment, e w (k) is the error between the actual interference signal and the estimated value at the kth moment, is the estimated value of the state signal at the kth moment, is the estimated value of the disturbance process variable at the kth moment; The closed-loop function of the control system obtained by the controller and observer is as follows: In the formula, The error system of the control system is as follows: Step 4.2) According to Lyapunov stability theory and random analysis theory, the control system gain must meet certain conditions to enable the system to maintain safe and stable operation when random packet loss occurs under a denial of service attack, specifically: If there exists a matrix P1>0, P2>0, P3>0, Q=P1 -1 >0 and parameters α1, α2, α3 and matrices Y and R satisfy the following linear matrix inequality: Where I is the identity matrix of appropriate dimensions, Then the error system and the closed-loop system are both stable, and the controller gain K and the observer gain L can be respectively expressed by K=YP1 and L=P2 -1 R is obtained.

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