A single-link manipulator system memory dynamic event trigger control method based on deception attack

Abstract

This invention discloses a memory-based dynamic event triggering control method for a single-link robotic arm system based on spoofing attacks. The method first establishes a Markov model of the single-link robotic arm system based on Markov jump system theory, considering a system model with a general transition rate. Next, a mode-dependent memory controller is designed to overcome the influence of spoofing attacks and external disturbances on the system. A memory-based dynamic event triggering mechanism is also designed to reduce communication transmission frequency. Compared with existing memoryless event triggering schemes, this scheme utilizes a series of recently released signals and introduces a threshold function and an internal dynamic factor, which can automatically adjust according to the triggering error. Finally, vertex separator processing is introduced to address the uncertainty in the Markov transition rate. A mode-dependent state feedback controller is designed to control the stochastic stability of a single-link robotic arm system. When applied to a single-link robotic arm system, this method ensures the normal operation of the system under spoofing attacks and disturbances.

Description

Technical Field

[0001] This invention relates to a dynamic event triggering control method, specifically to a memory dynamic event triggering control method for a single-link robotic arm system based on deception attacks. Background Technology

[0002] Many real-world systems exhibit random fluctuations in their structure and parameters. These random fluctuations often arise from random failures and repairs of system components, changes in internal interconnections, sudden environmental changes, and variations in the operating point range of nonlinear systems after linearization. Single-link robotic arms are highly susceptible to factors such as temperature, humidity, and electromagnetic interference. Using Markov-based theory of jumping systems, a more accurate system model of the single-link robotic arm can be established. Furthermore, single-link robotic arms often struggle to detect measurement faults masked by interference during operation, which can lead to performance degradation. State feedback control, as a crucial component of robust control, is essential for improving system safety and reliability. State feedback involves feeding back any state of the system to the input in a specific proportion, combining it with the system's reference input to form a control law, which serves as the control input for the controlled system. Based on this concept, researchers have conducted extensive research on the design of state feedback controllers, achieving a series of results.

[0003] Furthermore, newly built intelligent control systems typically employ networked control methods that are easy to install and highly scalable. However, due to limited network bandwidth, data packets inevitably suffer from latency, packet loss, and timing discrepancies during network transmission. Event-triggered control becomes particularly important in reducing communication transmission frequency without sacrificing ideal stability and performance. In an event-triggered control environment, communication transmission only occurs when preset conditions are violated. Secondly, most event generators only use newly sampled data and recently released signals. However, at the peaks or troughs of a state, the error between two adjacent samples can be very small, easily causing some states to not be triggered. At these moments, the values ​​of these data packets are usually much larger than other data packets, requiring the controller to handle more data packets for more effective control; however, existing memoryless event-triggered mechanisms cannot achieve this.

[0004] However, the aforementioned research mainly focuses on memoryless controllers and memoryless event-triggered control, offering limited reduction in network load. Therefore, it is necessary to employ memory-based controllers to overcome the impact of spoofing attacks and external disturbances on the system, and to adopt memory-based dynamic event-triggered strategies to conserve communication resources. Summary of the Invention

[0005] The purpose of this invention is to propose a memory dynamic event triggering control method for a single-link robotic arm system based on deception attack, which can effectively reduce communication transmission frequency, improve control accuracy, and reduce bandwidth usage.

[0006] The specific technical solution of the present invention is as follows: A method for triggering control of dynamic events in a single-link robotic arm system based on deception attack, comprising the following steps:

[0007] Based on Markov jump system theory, a Markov model of a single-link robotic arm system is established, and a system model with a general transfer rate is also considered. The specific steps are as follows:

[0008] Based on the Markov jump system theory, the following dynamic model is established for the single-link robotic arm system in reference [1]:

[0009]

[0010] The above dynamic model can be modeled as the following state-space expression:

[0011]

[0012] In the formula, θ(t) represents the angle of the robotic arm, u(t) represents the control input, w(t) represents the external disturbance, M represents the mass of the load, J represents the moment of inertia, g represents the gravitational acceleration, L represents the length of the robotic arm, and D(t) represents the uncertainty coefficient of viscous friction.

[0013] The single-link robotic arm system is modeled as a Markov transition system with a general transfer rate, as follows:

[0014]

[0015] In the formula, A(r(t)), B(r(t)), C(r(t)), and D(r(t)) are known system matrices of appropriate dimensions, and g(t, r(t), x(t)) is a known nonlinear perturbation. For simplification, let A... i = A(r(t)), and other matrices are similarly abbreviated. r(t) is a right-continuous Markov process that takes values ​​from a finite set S = {1, 2, ..., N}. r(t) has the following properties:

[0016]

[0017] In the formula, δ>0, π ij It is the transition rate from mode i to mode j, and satisfies:

[0018]

[0019] Furthermore, when π in Λ ij When there is general uncertainty, the transfer rate matrix Λ can be expressed as:

[0020]

[0021] In the formula, and Δ ij It is known that Δ ij ∈[-δ ij δ ij ], δ ij "?" represents a known element, while "?" represents an unknown element.

[0022] Furthermore, a modality-dependent memory controller is designed to overcome the effects of spoofing attacks and external disturbances on the system. The specific steps are as follows:

[0023] First, the modality-dependent memory controller is designed as follows:

[0024]

[0025] In the formula, This indicates the state in which a deception attack has occurred. This indicates that no attack occurred. K indicated that he had been deceived and attacked. di The controller gain is represented by h, the sampling period is represented by m, and d are positive integers.

[0026] Furthermore, a memory-based dynamic event triggering mechanism is designed to reduce communication transmission frequency. Compared with existing memoryless event triggering schemes, this scheme utilizes a series of recently released signals and introduces a threshold function and an internal dynamic factor, which can automatically adjust according to the triggering error. The specific steps are as follows:

[0027] Establish the following memory dynamic event-triggered sampling mechanism:

[0028]

[0029]

[0030]

[0031]

[0032] In the formula, e d (t) represents the input trigger error, t k h represents the last trigger time, t k+1 h represents the next trigger time, μ d Indicates the weighted parameters. χ represents the internal dynamic variable, Ψ represents the participation of the internal dynamic variable, and χ represents the participation of the internal dynamic variable. i Let v and l represent the weighted matrix, where v and l are scalars, and σ is the weighted matrix. i (t) is the dynamic trigger parameter and is updated by the following formula:

[0033]

[0034]

[0035] In the formula, These represent the upper bounds of the trigger threshold, and ρ(t) is a scalar.

[0036] Furthermore, a vertex separator is introduced to address the uncertainty of the Markov transition rate. A modally dependent state feedback controller is designed to control the stochastic stability of a single-link robotic arm system. The specific steps are as follows:

[0037] C001: In the formula, the Lyapunov function of the following form is selected:

[0038] V(x(t),i)=V1(x(t),i)+V2(x(t),i)

[0039]

[0040]

[0041] C002: In the formula, i represents the mode, η is a scalar, and τ M Denotes the upper bound of the time delay, P, Q, R are Lyapunov variable matrices, ||U i x(τ)|| denotes the weighted matrix, ||g i (x(τ)), where τ|| represents the nonlinear perturbation;

[0042] C003: Calculate the derivative of V(t) and consider dynamic event triggering, where:

[0043]

[0044]

[0045] C004: In the formula, Indicates triggering error. This indicates a deceptive attack. It is a scalar;

[0046] C005: Based on the above transformation, consider H ∞ The upper bounds for performance and deception attacks can be obtained as follows:

[0047]

[0048]

[0049] C006: Select ξ T (t)=[x T (t)x T (t-τ(t))x T (t-τ M )g i T (x(t))E T (t)F T (x(t))w T (t)];

[0050] C007: In the formula, z(t) represents the control strategy, and γ represents H ∞ Performance level indicators;

[0051] C008: Furthermore, a vertex separator is introduced to address the uncertainty in Markov transition rates, as shown in the lemma below:

[0052]

[0053]

[0054]

[0055] C009: Further, Represents the vertex separator. Represents a set whose transition rate is unknown:

[0056] C010: Furthermore, by substituting the vertex separation method into the stability analysis, we can finally obtain the following equation:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] C011: In the formula, Δ ij ∈[-δ ij δ ij ], This represents a set whose transition rate is unknown. The single-link robotic arm system is stochastically stable under the state feedback controller designed in this invention. Attached Figure Description

[0070] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0071] Figure 2 This is a state diagram of a single-link robotic arm system using the method proposed in this invention under state feedback control, as shown in the embodiment.

[0072] Figure 3 The Markov mode transition diagram used in this embodiment employs the method proposed in this invention;

[0073] Figure 4 This is an example of an event triggering diagram using the method proposed in this invention;

[0074] Figure 5 This is an example of a denial-of-service attack diagram using the method proposed in this invention; Detailed Implementation

[0075] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0076] like Figure 1 As shown, a method for triggering control of dynamic events in a single-link robotic arm system based on deception attacks includes the following steps:

[0077] Step 1: Set initial values ​​for each parameter;

[0078] Step 2: Update the threshold parameter σ i (t);

[0079] Step 3: Discretely sample the system state x(t) to obtain x(kh);

[0080] Step 4: Use the threshold parameter σ i (t) verifies the event triggering condition with the system state x(kh), and updates the triggering state x(t). k h);

[0081] Step 5: Utilize trigger output x(t) k h), update controller input u(t) k h);

[0082] Step 6: Put u(t) k h) The data is transmitted to the ZOH and then sent to the controlled object via the actuator;

[0083] Step 7: Repeat steps 3, 4, 5, and 6 until the runtime ends.

[0084] An embodiment of the present invention is described below:

[0085] Consider a single-link robotic arm system from reference [1], whose corresponding dynamic model is:

[0086]

[0087]

[0088] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; applying the proposed method, the state of the single-link robotic arm system under state feedback control is as follows: Figure 2 As shown, the Markov mode transition is as follows Figure 3 As shown, the event triggering graph is as follows: Figure 4 As shown in the diagram, the denial-of-service attack is as follows: Figure 5 As shown, the proposed memory-based controller overcomes the impact of deception attacks and external disturbances on the system. The proposed event-triggered mechanism effectively reduces communication transmission. Compared with existing memoryless event-triggered schemes, this scheme utilizes a series of recently released signals and introduces a threshold function and an internal dynamic factor, which can automatically adjust according to the triggering error.

[0089] References

[0090] [1]Cao Z,Niu Y,Song J.Finite-time sliding-mode control of Markovianjump cyber-physical systems against randomly occurring injection attacks[J].IEEE Transactions on Automatic Control,2019,65(3):1264-1271,DOI:10.1109 / tac.2019.2926156

[0091] [2]Gu Y,Shen M,Ahn C K.Dynamic event-triggered fault-tolerant controlthrough a new intermediate observer[J].International Journal of Robust andNonlinear Control,2023,DOI:10.1002 / rnc.6869 。

Claims

1. A method for dynamic event-triggered control of a single-link manipulator system based on deception attack, characterized in that, Includes the following steps: Based on the Markov jump system theory, a Markov model of a single-link robotic arm system is established, and a system model with a general transfer rate is also considered. Design a modality-dependent memory controller to overcome the effects of spoofing attacks and external disturbances on the system. The modality-dependent memory controller design is as follows: wherein denotes a state in which a spoofing attack occurs, denotes a state in which no attack occurs, denotes a state in which a spoofing attack is received, denotes a controller gain, denotes a sampling period, denotes a positive integer; Design a memory dynamic event triggering mechanism to reduce communication transmission frequency. Utilize a series of recently released signals, and introduce a threshold function and an internal dynamic factor to automatically adjust based on triggering error. Establish the following memory dynamic event-triggered sampling mechanism: ， wherein denotes the input trigger error, denotes the last trigger time, denotes the next trigger time, denotes the weighting parameter, denotes the internal dynamic variable, denotes the contribution of the internal dynamic variable, denotes the weighting matrix, is a scalar, is a dynamic trigger parameter and is updated by In the formula, These represent the upper bounds of the trigger threshold, It is a scalar; A vertex separator is introduced to handle the uncertainty of the Markov transition rate, and a modally dependent state feedback controller is designed to control the stochastic stability of the single-link robotic arm system.

2. The method for memory dynamic event triggering control of a single-link robotic arm system based on deception attack according to claim 1, characterized in that, Based on the Markov transition system theory, a Markov transition model of a single-link robotic arm with a general transfer rate is established: Dynamic equations of a single-link robotic arm system: The above dynamic equations can be rewritten as the following state-space expression: In the formula, Indicates the angle of the robotic arm. Indicates control input, Indicates external disturbance. The mass of the load, Represents the moment of inertia. Represents gravitational acceleration. Indicates the length of the robotic arm. The uncertainty factor representing viscous friction; Furthermore, the system is modeled as a Markov jump model with a general transition rate: In the formula, , , , It is a known system matrix of appropriate dimensions. It is a known nonlinear perturbation; for simplicity, let Other matrices are also abbreviated. It is a right-continuous Markov process and originates from a finite set. Take the value from the middle. It has the following properties: In the formula, , , From modality To mode The transfer rate, and satisfies: when In When there is general uncertainty, the transfer rate matrix It can be represented as In the formula, and It is known. , "?" represents a known element, while "?" represents an unknown element.

3. The method for memory dynamic event triggering control of a single-link robotic arm system based on deception attack according to claim 2, characterized in that, A vertex separator is introduced to handle the uncertainty of the Markov transition rate. A modally dependent state feedback controller is designed to control the stochastic stability of a single-link robotic arm system. The specific steps are as follows: B001: Select a Lyapunov function of the following form: B002: In the formula, Represents mode, It is a scalar. Indicates the upper bound of the delay. , , It is a Lyapunov variable matrix. Represents a weighted matrix. Indicates nonlinear perturbation; B003: Calculation The derivative of and considering dynamic event triggering, where B004: In the formula, Indicates triggering error. This indicates a deceptive attack. It is a scalar; B005: Based on the above transformation, consider The upper bounds for performance and deception attacks can be obtained as follows: B006: Select B007: In the formula, , Indicates the control strategy. express Performance level indicators; B008: Furthermore, a vertex separator is introduced to address the uncertainty in Markov transition rates, as shown in the lemma below: B009: Further, , , Represents the vertex separator. Represents a set whose transition rate is unknown: B010: Furthermore, substituting the vertex separation method into the stability analysis, we can finally obtain the following equation: B011: In the formula, , Let represent the set of unknown transfer rates. The single-link robotic arm system is stochastically stable under the designed state feedback controller.

Images