Safe sliding mode control method and system for space manipulator under cyber attack

Abstract

The application discloses a safe sliding mode control method and system for a space manipulator under network attack, and comprises the following steps: considering the output shaft inertia under different loads and system parameter mutation, considering the case that the actuator of the manipulator is subjected to a false data injection attack, establishing a random model of the space manipulator subjected to the false data injection attack; using a double-layer hidden Markov process to describe the mode switching relationship between the space manipulator system subjected to the false data injection attack and a safety controller; designing a sliding mode surface based on the measurement output of the space manipulator and the double-layer hidden Markov process; and designing a safety output feedback sliding mode controller based on the mode switching relationship and the sliding mode surface. The application has the advantages that the random stability and control performance of the space manipulator are improved, and the difficulty of controller design is reduced.

Description

Technical Field

[0001] This invention relates to the fields of information security technology and intelligent control, specifically to a method and system for safe sliding mode control of a space robotic arm under network attack scenarios. Background Technology

[0002] With the in-depth development of new-generation information technology, cyber-physical systems (CPS), and robotics, industrial robots have wide applications in aerospace, military equipment, intelligent manufacturing, and digital healthcare. Cyber-physical systems integrate computing, communication, and control, enabling the interactive mapping and efficient collaboration of elements such as people, machines, objects, information, and the environment in both cyberspace and physical space. Space robotic arms, as a typical robotic system, are usually deployed at the physical layer of the CPS architecture and interact with the control center or other edge devices through the information layer to achieve precise control of maneuvers or collaboration among multiple devices.

[0003] On the other hand, frequent cyberattacks pose a significant threat to national security, infrastructure, and the economy and people's livelihoods, making the security and reliability of cyber-physical systems increasingly important. Furthermore, in many practical applications, only the output information of the space robotic arm is typically measurable. Therefore, research on how to perform output feedback safety control of a space robotic arm within a cyber-physical system framework using only the system's measured output information is of significant practical importance for ensuring the successful completion of predetermined control tasks. Relevant existing literature is as follows:

[0004] Existing technology 1 - A method for safe trajectory tracking and control of a robotic arm based on sliding mode (Publication No. CN112947293A)

[0005] (1) Technical solution of existing technology 1

[0006] This patent application discloses a sliding mode-based method for safe trajectory tracking control of a robotic arm. The method mainly involves: acquiring the current angle, angular velocity, and input torque estimation information of each joint within the robotic arm; determining the trajectory scaling function and calculating the actual tracking trajectory of the robotic arm; inputting the desired joint angle, angular velocity, and angular acceleration corresponding to the actual tracking trajectory into a sliding mode controller, and using the sliding mode controller to perform trajectory tracking control on the robotic arm. This control method can achieve trajectory tracking and collision avoidance even in the presence of external disturbances.

[0007] (2) Disadvantages of existing technology 1

[0008] 1) This patent application only suppresses external interference. The controller design does not take into account the adverse effects of malicious network attacks. When the actuator of the space robotic arm is attacked by false information injection, the method is no longer applicable.

[0009] 2) The parameter adjustment of the sliding mode controller proposed in this patent application is mainly based on human experience, and the controller design process is relatively complex.

[0010] Prior Art 2 - A Cyber-Physical System Security Control Method Based on Deep Reinforcement Learning (Publication No. CN113885330A)

[0011] (1) Technical solution of existing technology 2

[0012] This patent application discloses a cyber-physical system security control method based on deep reinforcement learning. The method's steps include using a Markov decision process to describe the cyber-physical system under attack conditions; proposing a flexible actor-critic reinforcement learning algorithm based on Lyapunov functions, and providing a deep neural network training framework. Lyapunov stability theory is incorporated into the design process to ensure the stability of the cyber-physical system. Finally, a single-link robotic arm example illustrates the effectiveness of the method.

[0013] (2) Disadvantages of existing technology 2

[0014] 1) The safety controller used in this patent application depends on the entire state of the system. This method is not applicable when only the output signal of the system is measurable.

[0015] 2) This patent application does not take into account the output shaft inertia under different loads and the different operating modes of the system caused by sudden changes in system parameters.

[0016] In summary, existing space robotic arm control methods are not suitable for situations where the actuator of the space robotic arm is attacked by spoofed data injection or when only the output signal is measurable. Furthermore, they do not consider the output shaft inertia under different loads or the different operating modes caused by sudden changes in system parameters. As a result, it is difficult to guarantee the random stability and control performance of the space robotic arm, and the controller design is very difficult. Summary of the Invention

[0017] The technical problem to be solved by this invention is how to improve the random stability and control performance of a space robotic arm while reducing the design difficulty of the controller.

[0018] This invention solves the above-mentioned technical problems through the following technical means: a safe sliding mode control method for a space robotic arm under network attack conditions, comprising the following steps:

[0019] Step 1: Consider the output shaft inertia and system parameter mutations under different loads, establish the dynamic equation of the space manipulator system, and then consider the case where the actuator of the manipulator is attacked by false data injection, update the dynamic equation of the space manipulator system to obtain the stochastic model of the space manipulator attacked by false data injection.

[0020] Step 2: Use a two-layer hidden Markov process to characterize the modal switching relationship between the space robotic arm system and the safety controller under a false data injection attack;

[0021] Step 3: Design the sliding mode surface based on the measurement output of the space robot and the two-layer hidden Markov process;

[0022] Step 4: Based on the modal switching relationship and the sliding surface, design a safety output feedback sliding mode controller. Continuously adjust the parameters of the safety output feedback sliding mode controller so that the state of the space robot driven by the safety output feedback sliding mode controller reaches the sliding surface within a preset time and can resist false data injection attacks.

[0023] Further, step one includes:

[0024] The expression for the random switching model of the space robotic arm is:

[0025]

[0026] Where x1(t) = Ω, x3(t) = ε, Let x(t) be the four components of the system state vector, Ω be the joint angle of the inertial axis of the space manipulator, ε be the joint angle of the output axis of the space manipulator, u(t) be the control input, and A be the joint angle of the output axis of the space manipulator. r B and C are both system parameter matrices, y(t) is the measurement output, and u a (y(t), t) represents the injection of attack signals using fake data.

[0027] Furthermore, step two includes:

[0028] Define a Markov random process {α} t} represents three different working modes of the space robot, r∈{1,2,3} represents the three different working modes, and a Markov random process {β} is defined. t} represents the mode of the safety sliding mode controller / sliding surface, {β t The modal switching} takes values ​​in the finite set S2 = {1, 2, ..., n2}, where n2 > 0 is a positive integer representing the estimated number of modes, and satisfies the following mode switching relation.

[0029] Prob{β t =k|α t =r}=π r k,

[0030] Where k is a stochastic process {β} t The value of π is taken in set S2. rk It is a conditional probability and satisfies Due to β tIt takes values ​​within S2, therefore β t+Δt =l∈S2, then Prob{β t+Δt =l|α t+Δt =q}=π ql , where π ql Let α be the working mode of the robotic arm t+Δt =q when safety sliding mode controller / sliding surface mode β t+Δt = conditional probability of l, β t+Δt For the mode of the safety sliding mode controller / sliding surface at time t+Δt, β t+Δt =l represents the mode β of the safety sliding mode controller / sliding surface at time t+Δt. t+Δt The value of α is l. t+Δt Let α be the working mode of the robotic arm at time t+Δt, and let q be the working mode α of the robotic arm at time t+Δt. t+Δt The value of is q.

[0031] Furthermore, step three includes:

[0032] Based on the measured output signal y(t) and the two-layer hidden Markov process, the sliding surface is designed as follows:

[0033] s(β t ,t)=K(β) t )y(t),β t ∈S2,

[0034] Wherein, K(β) t ) represents the sliding surface gain.

[0035] Furthermore, step four includes:

[0036] The inertial axis joint angle and output axis joint angle of the space robotic arm are both bounded physical quantities. For a given upper bound δ>0, a bounded sliding mode region is introduced:

[0037]

[0038] Where Ξ represents the bounded sliding mode region. n x 3D space

[0039] Design a sliding mode controller with safety output feedback in the following form:

[0040]

[0041] Where S1 is the set of modal values ​​and S1 = {1, 2, 3}, n1 is the number of working modes of the robotic arm and n1 = 3, λ rqK represents the probability rate of mode transition from r to q of the spatial robotic arm system from time t to t+Δt. l Let f(y(t), t) be the gain of the sliding surface at time t+Δt, f(y(t), t) be a known bounded function, γ>0 be a given scalar; sgn(s(β) t ,t)) is the sliding surface s(β) t The sign function of t), and the variable K k Let v be the gain of the sliding surface at time t, and v be a known constant.

[0042] Furthermore, step four also includes:

[0043] By adjusting parameter γ, the safety output feedback sliding mode controller can drive the spatial robotic arm originating from the sliding mode region to reach the sliding surface within a preset time, and can resist spoofed data injection attacks. a The adverse effects of (y(t), t).

[0044] This invention also provides a safe sliding mode control system for a space robotic arm under network attack scenarios, including:

[0045] The model building module is used to consider the output shaft inertia and system parameter mutations under different loads, establish the dynamic equations of the space manipulator system, and then consider the case where the actuator of the manipulator is subjected to false data injection attack, update the dynamic equations of the space manipulator system to obtain the stochastic model of the space manipulator under false data injection attack.

[0046] The modal relationship acquisition module is used to characterize the modal switching relationship between a space robotic arm system subjected to a false data injection attack and a safety controller using a two-layer hidden Markov process.

[0047] The sliding surface design module is used for designing sliding surfaces based on the measurement output of a space robot and a two-layer hidden Markov process.

[0048] The controller design module is used to design a safety output feedback sliding mode controller based on the modal switching relationship and the sliding surface. It continuously adjusts the parameters of the safety output feedback sliding mode controller so that the state of the space robot driven by the safety output feedback sliding mode controller reaches the sliding surface within a preset time and can resist false data injection attacks.

[0049] Furthermore, the model building module is also used for:

[0050] The expression for the stochastic model of the space robotic arm is:

[0051]

[0052] Where x1(t) = Ω, x3(t) = ε, Let x(t) be the four components of the system state vector, Ω be the joint angle of the inertial axis of the space manipulator, ε be the joint angle of the output axis of the space manipulator, u(t) be the control input, and A be the joint angle of the output axis of the space manipulator. r B and C are both system parameter matrices, y(t) is the measurement output, and u a (y(t), t) represents the injection of attack signals using fake data.

[0053] Furthermore, the modal relationship acquisition module is also used for:

[0054] Define a Markov random process {α} t} represents three different working modes of the space robot, r∈{1,2,3} represents the three different working modes, and a Markov random process {β} is defined. t} represents the mode of the safety sliding mode controller / sliding surface, {β t The modal switching} takes values ​​in the finite set S2 = {1, 2, ..., n2}, where n2 > 0 is a positive integer representing the estimated number of modes, and satisfies the following mode switching relation.

[0055] Prob{β t =k|α t =r}=π rk ,

[0056] Where k is a stochastic process {β} t The value of π is taken in set S2. rk It is a conditional probability and satisfies

[0057] Due to β t It takes values ​​within S2, therefore β t+Δt =l∈S2, then Prob{β t+Δt =l|α t+Δt =q}=π ql , where π ql Let α be the working mode of the robotic arm t+Δt =q when safety sliding mode controller / sliding surface mode β t+Δt = conditional probability of l, β t+Δt For the mode of the safety sliding mode controller / sliding surface at time t+Δt, β t+Δt =l represents the mode β of the safety sliding mode controller / sliding surface at time t+Δt. t+Δt The value of α is l. t+Δt Let α be the working mode of the robotic arm at time t+Δt, and let q be the working mode α of the robotic arm at time t+Δt. t+Δt The value of is q.

[0058] Furthermore, the sliding surface design module is also used for:

[0059] Based on the measured output signal y(t) and the two-layer hidden Markov process, the sliding surface is designed as follows:

[0060] s(β t ,t)=K(β) t )y(t),β t ∈S2,

[0061] Wherein, K(β) t ) represents the sliding surface gain.

[0062] Furthermore, the controller design module is also used for:

[0063] The inertial axis joint angle and output axis joint angle of the space robotic arm are both bounded physical quantities. For a given upper bound δ>0, a bounded sliding mode region is introduced:

[0064]

[0065] Where Ξ represents the bounded sliding mode region. n x 3D space

[0066] Design a sliding mode controller with safety output feedback in the following form:

[0067]

[0068] Where S1 is the set of modal values ​​and S1 = {1, 2, 3}, n1 is the number of working modes of the robotic arm and n1 = 3, λ rq K represents the probability rate of mode transition from r to q of the spatial robotic arm system from time t to t+Δt. l Let f(y(t), t) be the gain of the sliding surface at time t+Δt, f(y(t), t) be a known bounded function, γ>0 be a given scalar; sgn(s(β) t ,t)) is the sliding surface s(β) t The sign function of t), and the variable K k Let v be the gain of the sliding surface at time t, and v be a known constant.

[0069] Furthermore, the controller design module is also used for:

[0070] By adjusting parameter γ, the safety output feedback sliding mode controller can drive the spatial robotic arm originating from the sliding mode region to reach the sliding surface within a preset time, and can resist spoofed data injection attacks. a The adverse effects of (y(t), t).

[0071] The advantages of this invention are as follows: This invention considers the output shaft inertia under different loads and the different operating modes of the system caused by sudden changes in system parameters, establishing the dynamic equations of the space manipulator system. A two-layer Hidden Markov Process (HMM) is used to characterize the mode switching relationship between the space manipulator system and the safety controller mode when the actuator is subjected to a spoofed data injection attack. A sliding mode surface is designed based on the space manipulator's measurement output and the HMM. A safety output feedback sliding mode controller is designed based on the mode switching relationship and the sliding mode surface. Therefore, this method is applicable when the space manipulator's actuator is subjected to a spoofed data injection attack, and it is also applicable when only the output signal is measurable, ensuring the random stability of the space manipulator and improving control performance. Furthermore, optimized control can be achieved simply by adjusting the parameters of the safety output feedback sliding mode controller, reducing the difficulty of controller design while expanding the scope of application of this invention. Attached Figure Description

[0072] Figure 1 This is a flowchart of a safe sliding mode control method for a space robotic arm under network attack scenarios, as disclosed in an embodiment of the present invention.

[0073] Figure 2 This is a schematic diagram of the space robotic arm structure in the safe sliding mode control method for space robotic arms under network attack scenarios disclosed in the embodiments of the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] Example 1

[0076] like Figure 1 As shown, a safe sliding mode control method for a space robotic arm under network attack conditions includes the following steps:

[0077] S1. Considering the output shaft inertia and sudden changes in system parameters under different loads, establish the dynamic equations of the space manipulator system. Then, considering the case where the actuator of the manipulator is subjected to a false data injection attack, update the dynamic equations of the space manipulator system to obtain a stochastic model of the space manipulator under false data injection attack. The specific process is as follows:

[0078] Space robotic arm as attached Figure 2 As shown, its dynamic characteristics can be characterized by the following Euler-Lagrange dynamic equations:

[0079]

[0080] The parameters involved in system (1) are given in Table 1 below (it should be noted that, for the convenience of referencing the formula, the numbers enclosed in parentheses in this embodiment all represent formula numbers. For example, system (1) represents formula (1)):

[0081] Table 1 Parameters of the spatial robotic arm (1)

[0082]

[0083] Where the subscript r∈{1,2,3} represents the three different working modes of the robotic arm, and correspondingly, the output axis inertia coefficient is I. out，1 =400kgm 2 I out，2 =600kgm 2 I out，3 =200kgm 2 .

[0084] Let x1(t) = Ω, x3(t) = ε, Let u(t) = i be the four components of the system state vector x(t). c To control the input, consider the three working modes of the robotic arm and use a Markov process to model the system (1), resulting in the following spatial robotic arm system model:

[0085]

[0086] Among them, A r B and C are system parameter matrices, and are...

[0087]

[0088] Note that the robotic arm system (2) contains 3 modes, and the stochastic process {α} is defined. t} represents these 3 modes, and takes values ​​within the set S1 = {1, 2, 3}. The corresponding mode transition probabilities are:

[0089]

[0090] Where r and q represent parameters taking values ​​in the set S1 = {1, 2, 3}, Δt represents the small time increment, o(Δt) represents the higher-order infinitesimal of Δt, and λ rq The transition probability rate of the mode of system (1) from r to q from time t to t+Δt represents the transition probability rate.

[0091] Considering that the actuator of the robotic arm system (1) is subjected to a fake data injection attack, the attacker usually injects the attack signal u to increase the stealth. a (y(t), t) is designed in the form of system state dependency, and satisfies the condition without loss of generality: ||u a (y(t), t)||≤ν||x(t)||+f(y(t), t), where f(y(t), t) is a known bounded function and v is a known constant. In summary, the stochastic model of the space robotic arm subjected to a fake data injection attack is shown below:

[0092]

[0093] S2. A two-layer Hidden Markov Process (HMM) is used to characterize the mode-switching relationship between the space robotic arm system and the safety controller under a false data injection attack; the specific process is as follows:

[0094] Considering that the actual operating modes of the robotic arm under cyberattacks may not be known in real time to the defender, a two-layer hidden Markov process is used to characterize the modal relationship between the actual modes of the system and the modes of the safety sliding mode controller / sliding surface. The Markov random process {α} is defined as follows: t} represents three different working modes of the space robot, r∈{1,2,3} represents the three different working modes, and a Markov random process {β} is defined. t} represents the mode of the safety sliding mode controller / sliding surface, {β t The values ​​are taken within the finite set S2 = {1, 2, ..., n2}, where n2 > 0 is a positive integer representing the estimated number of modes, and the following relationship is satisfied.

[0095] Prob{β t =k|α t =r}=π rk (6)

[0096] Where k is a stochastic process {β} t The value of π is taken in set S2. rk It is a conditional probability and satisfies

[0097] Due to β t It takes values ​​within S2, therefore β t+Δt =l∈S2, then Prob{β t+Δt =l|α t+Δt =q}=π gl , where π ql Let α be the working mode of the robotic arm t+Δt =q when safety sliding mode controller / sliding surface mode β t+Δt = conditional probability of l, β t+ΔtFor the mode of the safety sliding mode controller / sliding surface at time t+Δt, β t+Δt =l represents the mode β of the safety sliding mode controller / sliding surface at time t+Δt. t+Δt The value of α is l. t+Δt Let α be the working mode of the robotic arm at time t+Δt, and let q be the working mode α of the robotic arm at time t+Δt. t+Δt The value of is q.

[0098] S3. Design of sliding mode surface based on measurement output from a space robotic arm and a two-layer hidden Markov process; the specific process is as follows:

[0099] The sliding surface is designed as follows:

[0100] s(β t ,t)=K(β) t )y(t),β t ∈S2, (7)

[0101] in, Let be the sliding surface gain. For an ideal sliding mode, we have s(β). t Since matrix B is of full column rank, there exists a full row rank matrix Q such that QB = 0. Therefore, a 4×4 matrix N = [Q] can be constructed. T B] T And satisfy QN -1 =[I3 O 3×1 Multiply the matrix N on both sides of the stochastic model (5) of the space robotic arm, noting that QB = 0 and B T The nonsingularity of B can be obtained from the sliding mode.

[0102]

[0103] Where E is a singular matrix, Let be the system matrix after the singular transformation, and

[0104]

[0105] The purpose of this invention is to design a safe output feedback sliding mode controller for a stochastic model (5) of a spatial joint manipulator that is attacked by false data injection, based on the output signal and a two-layer hidden Markov process, to ensure the stochastic stability of the closed-loop manipulator system and improve control performance.

[0106] S4. Based on the modal switching relationship and sliding surface, a safety output feedback sliding mode controller is designed. The parameters of the safety output feedback sliding mode controller are continuously adjusted to ensure that the state of the space robot driven by the controller reaches the sliding surface within a finite time, and to resist spoofed data injection attacks. The specific process is as follows:

[0107] Without loss of generality, the joint angles of the robotic arm's inertial axis and output axis are both bounded physical quantities. For a given upper bound δ>0, a bounded sliding mode region is introduced:

[0108]

[0109] Where Ξ represents the bounded sliding mode region. n x 3D space

[0110] Design a sliding mode controller with safety output feedback in the following form:

[0111]

[0112] Where S1 is the set of modal values ​​and S1 = {1, 2, 3}, n1 is the number of working modes of the robotic arm and n1 = 3, Kl is the gain of the sliding surface at time t + Δt, γ > 0 is a given scalar, and sgn(s(β) t ,t)) is the sliding surface s(β) t The sign function of t), and the variable

[0113]

[0114] Among them, K k Let be the gain of the sliding surface at time t.

[0115] The performance of the safety output feedback sliding mode controller designed in this invention is demonstrated below by constructing a Lyapunov function. The specific proof process is as follows:

[0116] Construct Lyapunov functions of the following form.

[0117]

[0118] Taking the weak derivative of the Lyapunov function (13) yields...

[0119]

[0120] Without loss of generality, due to β t It takes values ​​within S2, therefore β t+Δt =l∈S2, then Prob{η t+Δt =l|r t+Δt =q}=π ql Therefore, (14) can be further obtained as follows:

[0121]

[0122] Substituting the safety output feedback sliding mode controller (11) into formula (15), we have

[0123]

[0124] According to the sliding region (10) and achievable

[0125]

[0126] By adjusting the appropriate parameter γ, we can ensure... Therefore, the safe output feedback sliding mode controller (11) can drive the state of the space robot (5) starting from the sliding mode region (10) to reach the sliding surface within a finite time, and can resist false data injection attacks. a The adverse effects of (y(t), t) were mitigated, ensuring the control performance of the space robotic arm (5).

[0127] Then, by integrating Lyapunov stability theory, using singular systems methods, and designing a structured matrix, the stochastic stability of the sliding mode of the space robot is proved. The specific process is as follows:

[0128] Construct the following Lyapunov function:

[0129] V(x(t), α) t ,t)=x T (t)E T P(α t x(t) (18)

[0130] Wherein, P(α) t ) is a Lyapunov matrix and satisfies ETP(α) t ) = P T (α t E > 0.

[0131] The weak derivative of the Lyapunov function (18) is,

[0132]

[0133] For each α t =r∈S1 and β t =k∈S2, therefore,

[0134]

[0135] Where n1 = 3 represents the number of working modes of the robotic arm.

[0136] Based on formula (20), if the following equation holds, then the closed-loop robotic arm system (8) has stochastic stability.

[0137]

[0138] in, It is α t =r∈S1 and β t The system matrix when k∈S2, and

[0139] Since the Lyapunov matrix is ​​multiplied by the singular matrix E, the two should have structural consistency. Design the Lyapunov matrix P. r The structure is as follows:

[0140]

[0141] in, Note and QN -1 =[I3 0 3×1 Therefore, we can obtain P. 4r =0, P 1r >0. Therefore

[0142] Equation (21) can be rewritten as:

[0143]

[0144] Applying the matrix projection theorem to equation (23) and introducing matrices Y1 and Y2 of appropriate dimensions, we have

[0145]

[0146] Define new matrix variables And specify that matrices Y1 and Y2 have the following structure,

[0147]

[0148] in, It is an adjustable parameter matrix, parameters It is a non-zero adjustable parameter.

[0149] The matrices Y1 and Y2 in equation (25) and the matrix variables Substituting into formula (24), the following equation can be made true by adjusting the parameters.

[0150]

[0151] in,

[0152]

[0153] At this point, the sliding mode of the closed-loop flexible robotic arm system is stochastically stable and the gain of the sliding surface (7) can be parameterized by the following equation:

[0154]

[0155] Based on the above technical solutions, considering the output shaft inertia and abrupt changes in system parameters under different loads, a Markov model is used to establish the dynamic equations of the space manipulator system. A two-layer hidden Markov process is used to characterize the mode switching relationship between the space manipulator system and the safety controller mode when the actuator is subjected to a false data injection attack. Utilizing the measurement output information of the space manipulator, a novel safety output feedback sliding mode controller is designed, which ensures both the stochastic stability of the sliding mode of the space manipulator and safe and stable operation under false data injection attacks. A parameterized design method for the sliding surface gain is presented, reducing the implementation difficulty and control cost. Furthermore, designing the controller based solely on the system's output signal effectively expands the application scope of this invention.

[0156] Example 2

[0157] Based on Embodiment 1, Embodiment 2 of the present invention also provides a safe sliding mode control system for a space robotic arm under network attack scenarios, including:

[0158] The model building module is used to consider the output shaft inertia and system parameter mutations under different loads, establish the dynamic equations of the space manipulator system, and then consider the case where the actuator of the manipulator is subjected to false data injection attack, update the dynamic equations of the space manipulator system to obtain the stochastic model of the space manipulator under false data injection attack.

[0159] The modal relationship acquisition module is used to characterize the modal switching relationship between a space robotic arm system subjected to a false data injection attack and a safety controller using a two-layer hidden Markov process.

[0160] The sliding surface design module is used for designing sliding surfaces based on the measurement output of a space robot and a two-layer hidden Markov process.

[0161] The controller design module is used to design a safety output feedback sliding mode controller based on the modal switching relationship and the sliding surface. The parameters of the safety output feedback sliding mode controller are continuously adjusted so that the state of the space robot driven by the safety output feedback sliding mode controller reaches the sliding surface within a finite time and can resist false data injection attacks.

[0162] Specifically, the model building module is also used for:

[0163] The expression for the stochastic model of the space robotic arm is:

[0164]

[0165] Where x1(t) = Ω, x3(t) = ε, Let x(t) be the four components of the system state vector, Ω be the joint angle of the inertial axis of the space manipulator, ε be the joint angle of the output axis of the space manipulator, u(t) be the control input, and A be the joint angle of the output axis of the space manipulator. r B and C are both system parameter matrices, y(t) is the measurement output, and u a (y(t), t) represents the injection of attack signals using fake data.

[0166] More specifically, the modal relationship acquisition module is also used for:

[0167] Define a Markov random process {α} t} represents three different working modes of the space robot, r∈{1,2,3} represents the three different working modes, and a Markov random process {β} is defined. t} represents the mode of the safety sliding mode controller / sliding surface, {β t The modal switching} takes values ​​in the finite set S2 = {1, 2, ..., n2}, where n2 > 0 is a positive integer, representing the estimated number of modes, and satisfies the following mode switching relation.

[0168] Prob{β t =k|α t =r|}=π rk ,

[0169] Where k is a stochastic process {β} t The value of π is taken in set S2. rk It is a conditional probability and satisfies

[0170] Due to β t It takes values ​​within S2, therefore β t+Δt =l∈S2,Prob{β t+Δt =l|α t+Δt =q}=π ql , where π ql Let α be the working mode of the robotic arm t+Δt =q when safety sliding mode controller / sliding surface mode β t+Δt = conditional probability of l, β t+Δt For the mode of the safety sliding mode controller / sliding surface at time t+Δt, β t+Δt =l represents the mode β of the safety sliding mode controller / sliding surface at time t+Δt. t+Δt The value of α is l. t+Δt Let α be the working mode of the robotic arm at time t+Δt, and let q be the working mode α of the robotic arm at time t+Δt. t+Δt The value of is q.

[0171] More specifically, the sliding surface design module is also used for:

[0172] Based on the measured output signal y(t) and the two-layer hidden Markov process, the sliding surface is designed as follows:

[0173] s(β t ,t)=K(β) t )y(t),β t ∈S2,

[0174] Wherein, K(β) t ) represents the sliding surface gain.

[0175] More specifically, the controller design module is also used for:

[0176] The inertial axis joint angle and output axis joint angle of the space robotic arm are both bounded physical quantities. For a given upper bound δ>0, a bounded sliding mode region is introduced:

[0177]

[0178] Where Ξ represents the bounded sliding mode region. n x 3D space

[0179] Design a sliding mode controller with safety output feedback in the following form:

[0180]

[0181] Where S1 is the set of modal values ​​and S1 = {1, 2, 3}, n1 is the number of working modes of the robotic arm and n1 = 3, λ rq K represents the probability rate of mode transition from r to q of the spatial robotic arm system from time t to t+Δt. l Let f(y(t), t) be the gain of the sliding surface at time t+Δt, f(y(t), t) be a known bounded function, γ>0 be a given scalar; sgn(s(β) t ,t)) is the sliding surface s(β) t The sign function of t), and the variable K k Let ν be the gain of the sliding surface at time t, and ν be a known constant.

[0182] More specifically, the controller design module is also used for:

[0183] By adjusting parameter γ, the safety output feedback sliding mode controller can drive the spatial robotic arm originating from the sliding mode region to reach the sliding surface within a preset time, and can resist spoofed data injection attacks. a The adverse effects of (y(t), t).

[0184] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A safe sliding mode control method for a space robotic arm under network attack conditions, characterized in that, Includes the following steps: Step 1: Consider the output shaft inertia and system parameter mutations under different loads, establish the dynamic equation of the space manipulator system, and then consider the case where the actuator of the manipulator is attacked by false data injection, update the dynamic equation of the space manipulator system to obtain the stochastic model of the space manipulator attacked by false data injection. Step 2: Use a two-layer hidden Markov process to characterize the modal switching relationship between the space robotic arm system and the safety controller under a false data injection attack; Step 3: Design the sliding mode surface based on the measurement output of the space robot and the two-layer hidden Markov process; Step four: Based on the modal switching relationship and sliding surface, design a safety output feedback sliding mode controller, and continuously adjust the parameters of the safety output feedback sliding mode controller so that the state of the space robot driven by the safety output feedback sliding mode controller reaches the sliding surface within a preset time, and can resist false data injection attacks; Step four includes: The inertial axis joint angle and output axis joint angle of the space robotic arm are both bounded physical quantities, given an upper bound. Introduce a bounded sliding mode region: in, Indicates a bounded sliding mode region. n x 3D space Represents the system state vector; Design a sliding mode controller with safety output feedback in the following form: in, To control the input, , These are all system parameter matrices. For sliding surface gain, For sliding surface, For the set of modal values ​​and , The number of working modes of the robotic arm and =3, Represents from t to The probability rate of mode transition from r to q in the time-space robotic arm system. In time Gain of the sliding surface at time step Given a bounded function, For a given scalar; For sliding surface The sign function, and the variable , In order to be in Gain of the sliding surface at time step It is the system parameter matrix. For a known constant, This represents three different working modes. It is a positive integer. For the working mode of the robotic arm Mode of the sliding mode controller / sliding surface The conditional probability, In time The mode of the safety sliding mode controller / sliding surface at any given time. In time Moment-based safety sliding mode controller / sliding surface mode The value is , In time The working modes of the robotic arm at any given time. In time Working modes of the robotic arm at any time The value of is q.

2. The safe sliding mode control method for a space robotic arm under network attack conditions according to claim 1, characterized in that, Step one includes: The expression for the stochastic model of the space robotic arm is: in, , , , The system state vector The four components, The joint angle of the inertial axis of the space robotic arm. The output axis joint angle of the space robotic arm. For measurement output, Injecting attack signals into fake data.

3. The safe sliding mode control method for a space robotic arm under network attack conditions according to claim 2, characterized in that, Step two includes: Define Markov random processes These represent three different working modes of a space robotic arm. Define a Markov random process to represent three different operating modes. For the modes of the safety sliding mode controller / sliding surface, In finite sets The inner value is taken, where A positive integer, representing the estimated number of modes, satisfying the following mode switching relationship. in, For random processes in the set Take the value from the middle. It is a conditional probability and satisfies ,because exist Therefore, we have ,but .

4. The safe sliding mode control method for a space robotic arm under network attack conditions according to claim 3, characterized in that, Step three includes: Based on the measured output signal And a double-layer hidden Markov process, the sliding surface is designed as follows: in, This represents the gain of the sliding surface.

5. The safe sliding mode control method for a space robotic arm under network attack conditions according to claim 1, characterized in that, Step four also includes: By adjusting the parameters This enables the safety output feedback sliding mode controller to drive the state of the space robot arm originating from the sliding mode region to reach the sliding surface within a preset time, and it can resist spoofed data injection attacks. The adverse effects.

6. A safety sliding mode control system for a space robotic arm under network attack conditions, characterized in that, include: The model building module is used to consider the output shaft inertia and system parameter mutations under different loads, establish the dynamic equations of the space manipulator system, and then consider the case where the actuator of the manipulator is subjected to false data injection attack, update the dynamic equations of the space manipulator system to obtain the stochastic model of the space manipulator under false data injection attack. The modal relationship acquisition module is used to characterize the modal switching relationship between a space robotic arm system subjected to a false data injection attack and a safety controller using a two-layer hidden Markov process. The sliding surface design module is used for designing sliding surfaces based on the measurement output of a space robot and a two-layer hidden Markov process. The controller design module is used to design a safety output feedback sliding mode controller based on mode switching relationships and sliding surfaces. It continuously adjusts the parameters of the safety output feedback sliding mode controller to ensure that the state of the space robotic arm driven by the controller reaches the sliding surface within a preset time, and to resist spoofed data injection attacks. The controller design module is also used for: The inertial axis joint angle and output axis joint angle of the space robotic arm are both bounded physical quantities, given an upper bound. Introduce a bounded sliding mode region: in, Indicates a bounded sliding mode region. n x 3D space Represents the system state vector; Design a sliding mode controller with safety output feedback in the following form: in, To control the input, , These are all system parameter matrices. For sliding surface gain, For sliding surface, For the set of modal values ​​and , The number of working modes of the robotic arm and =3, Represents from t to The probability rate of mode transition from r to q in the time-space robotic arm system. In time Gain of the sliding surface at time step Given a bounded function, For a given scalar; For sliding surface The sign function, and the variable , In order to be in Gain of the sliding surface at time step It is the system parameter matrix. For a known constant, This represents three different working modes. It is a positive integer. For the working mode of the robotic arm Mode of the sliding mode controller / sliding surface The conditional probability, In time The mode of the safety sliding mode controller / sliding surface at any given time. In time Moment-based safety sliding mode controller / sliding surface mode The value is , In time The working modes of the robotic arm at any given time. In time Working modes of the robotic arm at any time The value of is q.

7. The safety sliding mode control system for a space robotic arm under network attack conditions according to claim 6, characterized in that, The model building module is also used for: The expression for the stochastic model of the space robotic arm is: in, , , , The system state vector The four components, The joint angle of the inertial axis of the space robotic arm. The output axis joint angle of the space robotic arm. For measurement output, Injecting attack signals into fake data.

8. The safety sliding mode control system for a space robotic arm under network attack conditions according to claim 7, characterized in that, The modal relationship acquisition module is also used for: Define Markov random processes These represent three different working modes of a space robotic arm. Define a Markov random process to represent three different operating modes. For the modes of the safety sliding mode controller / sliding surface, In finite sets The inner value is taken, where A positive integer, representing the estimated number of modes, satisfying the following mode switching relationship. in, For random processes in the set Take the value from the middle. It is a conditional probability and satisfies ,because exist Therefore, we have ,but .

9. The safety sliding mode control system for a space robotic arm under network attack conditions according to claim 8, characterized in that, The sliding surface design module is also used for: Based on the measured output signal And a double-layer hidden Markov process, the sliding surface is designed as follows: in, This represents the gain of the sliding surface.

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