Asynchronous H-infinity control method based on hybrid scheduling

Abstract

The invention relates to an asynchronous H-infinity control method based on hybrid scheduling. The asynchronous H-infinity control method mainly comprises the following steps: S1, modeling a transient fault and circuit breaker switching of a power system into a hidden Markov jump system with an unknown transition probability matrix and an observation probability matrix; s2, dynamically adjusting the data transmission frequency of the sensor node in combination with an event triggering mechanism, reducing the communication load, and simultaneously defending denial of service attack and spoofing attack; s3, based on a mode-related Lyapunov function, deriving a mean square stability condition and an H infinity performance index of the closed-loop system; and S4, verifying the effectiveness of the method through a single-machine infinite bus power system case. According to the method, the network resource occupation is obviously reduced, and the robustness of the system under the hybrid attack is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system control, and particularly relates to an asynchronous H∞ control method for a hidden Markov jump power system, and is especially applicable to scenarios with cyber attacks and limited communication resources. Background Art

[0002] As a critical energy infrastructure, the power system faces multiple challenges such as the access of renewable energy, networked control, and cyber attacks. Existing research mostly describes the sudden change of system parameters based on Markov jump models, but in practice, the modal information is often not fully known. In addition, although the traditional event-triggered mechanism can reduce communication load, it is difficult to balance security and dynamic performance. The present invention effectively solves the above problems through a hybrid scheduling protocol and an asynchronous control strategy. Summary of the Invention

[0003] The following is an overview of the subject matter described in detail in this article. This overview is not intended to limit the scope of protection of the claims.

[0004] In order to solve the above technical problems, the present invention provides an asynchronous H∞ control method and system based on hybrid scheduling, aiming to reduce the data transmission requirements of the network control system, effectively alleviate network congestion, and enhance the robustness of the system under hybrid attacks.

[0005] In a first aspect, an asynchronous H∞ control method based on hybrid scheduling is characterized by including the following steps:

[0006] Step S1: Model the transient faults and breaker switching of the power system as a hidden Markov jump system with an unknown transition probability matrix and observation probability matrix;

[0007] Step S2: Dynamically adjust the data transmission frequency of sensor nodes in combination with the event-triggered mechanism to reduce communication load, and at the same time resist denial-of-service attacks and spoofing attacks;

[0008] Step S3: Derive the mean-square stability condition and H∞ performance index of the closed-loop system based on the mode-related Lyapunov function;

[0009] Step S4: Verify the effectiveness of the method through a single-machine infinite-bus power system case.

[0010] 1. An asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein the hidden Markov jump system model in step S1 is:

[0011] x(k + 1) = A(ψk)x(k) + B(ψk)u(k) + D(ψk)w(k),

[0012] Among them, ψk is a hidden Markov chain, and its transition probability matrix Π = [πab] and observation probability matrix Γ = [γmn] contain unknown information.

[0013] 2. The asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein the hybrid scheduling protocol in step S2 includes the following triggering conditions:

[0014] When ρi(k) ≥ Lmaxθi(k)yiT(k)Ωyi(k), the weighted time-ordered discard protocol is adopted;

[0015] When ρi(k) ≥ Lminθi(k)yiT(k)Ωyi(k), the polling protocol is adopted;

[0016] Among them, is the dynamic triggering threshold.

[0017] The data transmission signal of the hybrid scheduling protocol module when suffering from a DoS attack is:

[0018] yˉ(k) = {(1 - α(k))yi(k), if the triggering condition is satisfied and there is no attack

[0019] yˉ(k - 1), in other cases

[0020] Among them, α(k) follows a Bernoulli distribution, indicating the attack success probability.

[0021] 3. The asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein the asynchronous state feedback controller in step S3 is designed as:

[0022]

[0023] Among them, is the hidden Markov chain of the controller mode, which is asynchronously matched with the system mode ψk.

[0024] 4. The asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein the H∞ performance index in step S3 satisfies:

[0025] E{k = 0∑∞∥y(k)∥2} < μ2E{k = 0∑∞∥w(k)∥2},

[0026] And the controller gain Km = KmYm-1 is solved through linear matrix inequalities.

[0027] The asynchronous state feedback controller module ensures the mean-square stability and H∞ performance of the closed-loop system through the mode-related Lyapunov function V(k) = xT(k)Pa-1x(k) + yˉT(k-1)Qm-1yˉ(k-1).

[0028] 5. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the single-machine infinite-bus power system case verification in step S4 includes the following parameters:

[0029] The system matrix A1 of mode 1 and the system matrix A2 of mode 2;

[0030] The attack probability αˉ = 0.8;

[0031] The controller gains K1 = [-1.4620, 1.7860, 11.7820, -0.8000] and K2 = [-0.9700, 1.5920, 10.7540, -0.7080]. Description of the Drawings

[0032] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the technical solutions of the present invention, and do not constitute a limitation to the technical solutions of the present invention.

[0033] Figure 1 is a flowchart of a hybrid-scheduling-based asynchronous H∞ control method of the present invention;

[0034] Figure 2 is the system state trajectory curve of the system provided by an embodiment of the present invention; Detailed Embodiments

[0035] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0036] It should be noted that although the functional modules are divided in the device schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order from the module division in the device or the order in the flowchart. Terms such as "first" and "second" in the specification, claims or the above drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence.

[0037] As Figure 1 shown, the present invention provides a flowchart of a hybrid-scheduling-based asynchronous H∞ control method, including the following steps:

[0038] Step S1: Model the transient faults of the power system and the circuit breaker switching as a hidden Markov jump system with unknown transition probability matrix and observation probability matrix;

[0039] Step S2: Combine the event-triggered mechanism to dynamically adjust the data transmission frequency of sensor nodes, reduce the communication load, and resist denial-of-service attacks and spoofing attacks at the same time;

[0040] Step S3: Based on the mode-related Lyapunov function, derive the mean-square stability condition and H∞ performance index of the closed-loop system;

[0041] Step S4: Verify the effectiveness of the method through a single-machine infinite-bus power system case.

[0042] 1. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the hidden Markov jump system model in step S1 is:

[0043] x(k + 1) = A(ψk)x(k) + B(ψk)u(k) + D(ψk)w(k),

[0044] where ψk is a hidden Markov chain, and its transition probability matrix Π = [πab] and observation probability matrix Γ = [γmn] contain unknown information.

[0045] 2. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the hybrid-scheduling protocol in step S2 includes the following triggering conditions:

[0046] When ρi(k) ≥ Lmaxθi(k)yiT(k)Ωyi(k), the weighted time-ordered discard protocol is adopted;

[0047] When ρi(k) ≥ Lminθi(k)yiT(k)Ωyi(k), the round-robin protocol is adopted;

[0048] where is the dynamic triggering threshold.

[0049] The data transmission signal of the hybrid-scheduling protocol module under a DoS attack is:

[0050] yˉ(k) = {(1 - α(k))yi(k), if the triggering condition is satisfied and there is no attack

[0051] yˉ(k - 1), otherwise

[0052] where α(k) follows a Bernoulli distribution, representing the attack success probability.

[0053] 3. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the asynchronous state feedback controller in step S3 is designed as:

[0054]

[0055] wherein, is the hidden Markov chain of the controller mode, which is asynchronously matched with the system mode ψk.

[0056] 4. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the H∞ performance index in step S3 satisfies:

[0057] E{k = 0∑∞∥y(k)∥2}<μ2E{k = 0∑∞∥w(k)∥2},

[0058] and the controller gain Km = KmYm-1 is solved by linear matrix inequality (LMI).

[0059] The asynchronous state feedback controller module ensures the mean-square stability and H∞ performance of the closed-loop system through the mode-related Lyapunov function V(k) = xT(k)Pa-1x(k)+yˉT(k - 1)Qm-1yˉ(k - 1).

[0060] 5. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, wherein the single-machine infinite bus power system case verification in step S4 includes the following parameters:

[0061] The system matrix A1 of mode 1 and the system matrix A2 of mode 2;

[0062] The attack probability αˉ = 0.8;

[0063] The controller gains K1 = [-1.4620, 1.7860, 11.7820, -0.8000] and K2 = [-0.9700, 1.5920, 10.7540, -0.7080].

[0064] As Figure 2 shown, the present invention also provides the system state trajectory curve of the system:

[0065] The effect of the single-machine infinite bus power system case:

[0066] Assume that the sampling time is Ts = 20μs, then the jump parameters of the mass-spring-damper system subject to the Markov chain are Rule 1:

[0067]

[0068] B1 = [-0.0001417 - 5.836×10 -5 0.06133 22.27],

[0069] C1 = diag{0.1, 0.7, 0.2, 0.1},

[0070] D1 = [0.2, 0.3, 0.4, 0.1] T

[0071] Rule 2:

[0072]

[0073] B2 = [-9.693e - 5 - 3.99×10 -5 0.06123 22.15],

[0074] C2 = diag{0.2, 0.5, 0.3, 0.1},

[0075] D2 = [0.1, 0.5, 0.3, 0.1] T .

[0076] F = [0.1 0.2 0.2 0.3] T , w(k) = 0.2cos(0.3k)exp(-0.56k), v(k) = cos(0.1k) / k,

[0077] ε = 2.5, L max = 6.5, L min = 3.5, α = 0.8.

[0078] The above has specifically described the preferred embodiments of the present invention, but the present invention is not limited to the above - mentioned embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included within the scope defined by the claims of the present invention.

Claims

1. An asynchronous H∞ control method based on hybrid scheduling, characterized in that, It includes the following steps: Step S1: Model the transient faults of the power system and the breaker switching as a hidden Markov jump system with unknown transition probability matrix and observation probability matrix; Step S2: Combine the event-triggered mechanism to dynamically adjust the data transmission frequency of sensor nodes, reduce the communication load, and resist denial-of-service attacks and spoofing attacks at the same time; Step S3: Based on the mode-dependent Lyapunov function, derive the mean-square stability condition and H∞ performance index of the closed-loop system; Step S4: Verify the effectiveness of the method through a single-machine infinite-bus power system case study.

2. The asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein The hidden Markov jump system model in the said Step S1 is: x(k + 1) = A(ψk)x(k) + B(ψk)u(k) + D(ψk)w(k), where ψk is a hidden Markov chain, and its transition probability matrix Π = [πab] and observation probability matrix Γ = [γmn] contain unknown information.

3. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, characterized in that The hybrid scheduling protocol in the said Step S2 includes the following triggering conditions: When ρi(k) ≥ Lmaxθi(k)yiT(k)Ωyi(k), adopt the weighted time-ordered discard protocol; When ρi(k) ≥ Lminθi(k)yiT(k)Ωyi(k), adopt the polling protocol; Among them, is the dynamic trigger threshold. The data transmission signal of the hybrid scheduling protocol module when suffering from a DoS attack is: yˉ(k) = {(1 - α(k))yi(k), if the triggering condition is satisfied and there is no attack yˉ(k - 1), otherwise where α(k) follows a Bernoulli distribution, representing the attack success probability.

4. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, characterized in that, The asynchronous state feedback controller in the said Step S3 is designed as: Among them, is a hidden Markov chain of the controller mode, which is asynchronously matched with the system mode ψk.

5. A hybrid-scheduling-based asynchronous H∞ control method according to claim 1, characterized in that, The H∞ performance index in the said Step S3 satisfies: E{k = 0∑∞∥y(k)∥2} < μ2E{k = 0∑∞∥w(k)∥2}, and solve the controller gain Km = KmYm-1 through linear matrix inequalities. The asynchronous state feedback controller module ensures the mean-square stability and H∞ performance of the closed-loop system through the mode-dependent Lyapunov function V(k) = xT(k)Pa-1x(k) + yˉT(k - 1)Qm-1yˉ(k - 1).

6. The asynchronous H∞ control method based on hybrid scheduling according to claim 1, wherein The single-machine infinite-bus power system case study in the said Step S4 includes the following parameters: The system matrix A1 of mode 1 and the system matrix A2 of mode 2; The attack probability αˉ = 0.8; The controller gains K1 = [-1.4620, 1.7860, 11.7820, -0.8000] and K2 = [-0.9700, 1.5920, 10.7540, -0.7080].

Images