Spacecraft attitude control method based on event triggering

Abstract

The invention discloses a spacecraft finite time sliding mode attitude control method based on dynamic threshold triggering, and the method comprises the steps: building an attitude tracking error model of a spacecraft through a quaternion-based kinematics and dynamics model; thirdly, designing a finite time nonsingular sliding mode surface, and performing approximate processing on concentrated disturbance in the system in combination with a fuzzy logic system to improve the anti-interference capability and the control precision of the system; finally, through a dynamic threshold triggering mechanism, a finite time attitude tracking controller is designed, control updating is triggered only when the state change of the system reaches a preset threshold, the communication and calculation burden is remarkably reduced, and it is ensured that the system converges within finite time and keeps stable. According to the method, a dynamic threshold triggering mechanism and a finite time sliding mode control technology are introduced, the control updating frequency is simplified, and the centralized disturbance is accurately processed by combining a fuzzy logic system, so that the control precision and stability of the system are improved, and a solid technical support is provided for spacecraft attitude control.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft attitude control, and relates to a spacecraft attitude control method, in particular to a finite-time sliding mode attitude control method for spacecraft based on dynamic threshold triggering. Background Technique

[0002] With the rapid development of space technology, the functions of modern spacecraft are becoming increasingly complex, posing higher requirements for their attitude control systems. Traditional attitude control methods mostly adopt periodic or continuous control strategies. Although they can meet basic requirements, they have problems such as high communication frequency, high energy consumption, and low resource utilization rate. As an emerging control strategy, event-triggered control can trigger control actions according to system state changes, reduce unnecessary operations, thereby effectively reducing the communication and computational burdens of the system and improving resource utilization efficiency. Although event-triggered control has shown significant advantages in fields such as robotics and network control systems, its application in spacecraft attitude control is still in the preliminary research stage, mainly focusing on theoretical discussions and simulation verification. Therefore, applying event-triggered control to spacecraft attitude tracking control has important research value, which can not only enrich existing control theories but also promote the development and application of spacecraft control technologies. Summary of the Invention

[0003] In order to overcome the limitations of traditional methods, improve resource utilization efficiency and control accuracy, and provide reliable support for the control of spacecraft attitude and the advancement of science and technology, the present invention provides an event-triggered spacecraft attitude control method. This method improves communication efficiency by designing a dynamic threshold triggering mechanism and combines a finite-time controller to ensure the tracking effect and stability of the system, providing solid technical support for the control of nonlinear systems.

[0004] The object of the present invention is achieved through the following technical solutions:

[0005] An event-triggered spacecraft attitude control method includes the following steps:

[0006] Step 1: Establish a spacecraft model based on quaternions, define attitude tracking error and angular velocity tracking error, and convert the spacecraft model into a tracking error model. The specific steps are as follows:

[0007] Step 1.1: Considering a rigid-body spacecraft with external disturbances, establish the kinematic and dynamic models of the spacecraft based on quaternions:

[0008]

[0009] where ω represents angular velocity, represents the quaternion, q0 is the scalar part, and q v is the vector part, and satisfies Let \(J\) be the moment of inertia of the spacecraft, \(\tau\) represent the control torque, \(d\) represent the external disturbance, \(I_3\) denote the \(3\times3\) identity matrix, and \([\omega × \) represent the cross product operator;

[0010] Step 1: Define the attitude tracking error between the system attitude and the desired attitude Let \(q \), \(q d0 \) be the scalar part and the vector part of \(q dv \) respectively, and \(q d \), \(q e0 \) be the scalar part and the vector part of \(q ev \) respectively. Define the angular velocity tracking error \(\omega e =\omega - C\omega e \), where \(\omega d \) is the desired angular velocity, and obtain the tracking error model: d where \(C\) represents the rotation matrix;

[0011]

[0012]

[0013] Step 2: Design the sliding surface \(S\) to ensure that when the sliding surface \(S = 0\), the attitude tracking error \(q ev \) can converge to the origin within a finite time. The specific steps are as follows:

[0014] Step 2.1: Define the sliding surface \(S\) as follows:

[0015]

[0016] where \(q evi \) are the components of \(q ev \) in each direction, \(\lambda_1>0\), \(\lambda_2>0\), \(a>1\), and the function \(sig(\cdot)\) is defined as \(sig a (x)=[|x_1| a \cdot sgn(x_1),\cdots,|x n | a \cdot sgn(x n )] T \), \(x = [x_1,x_2,\cdots,x n T \) is an \(n -\)dimensional vector, and \(x i (i = 1,2,\cdots,n)\) is the \(i -\)th component of \(x\);

[0017] Step 2.2: Define the Lyapunov function and take its derivative:

[0018]

[0019] ​​Ensure that it can converge to the origin within a finite time when S = 0;

[0020] Step 3. For the lumped disturbance in the model, approximate it using a fuzzy logic system. The specific steps are as follows:

[0021] Step 3-1. Differentiate the sliding surface S in Step 2 to obtain the lumped disturbance Υ in the system:

[0022]

[0023] where, Γ = diag(Γ1, Γ2, Γ3), i = 1, 2, 3, is the lumped disturbance of the system, and ψ is an auxiliary variable;

[0024] Step 3-2. For the lumped disturbance Υ obtained in Step 3-1, approximate it using a fuzzy logic system:

[0025] Υ(S) = θ(S) T Φ(S)

[0026] where S is the input vector, Φ(S) is the fuzzy basis function, and θ(S) is the corresponding coordinate of Υ(S) under Φ(S);

[0027] Step 4. Design a dynamic event-triggering mechanism, and on this basis, design a finite-time attitude tracking controller for the spacecraft to ensure that the system can converge within a finite time. The specific steps are as follows:

[0028] Step 4-1. Assume that the k-th sampling point of the spacecraft state is t k , then the (k + 1)-th sampling point is t k+1 , define the measurement error e S = S(t) - S(t k ), e F = F(t) - F(t k ), S(t) and S(t k ) respectively represent the values of S at times t and t k , F(t) and F(t k ) respectively represent the values of F at times t and t k . The triggering condition for the dynamic threshold trigger is:

[0029] t k+1 = inf{t > t k || ||e S || 2 ≥α1||S|| 2 + γ1 + h1(t) or ||e F || 2≥α2||S|| 2 +γ2+h2(t)}

[0030] h1(0) = h 10 > 0

[0031] h2(0) = h 20 > 0

[0032] where α1, α2 ∈ (0, 1), γ1, γ2 ≥ 0, and H1(·), H2(·) are locally Lipchitz continuous k ∞ functions;

[0033] Step 4.2. On the basis of Step 4.1, design a finite-time controller τ:

[0034]

[0035] where are the estimated values of S, θ, and F respectively, and θ(t k ) represents the value of θ at time t k , and k > 0;

[0036] Step 4.3. Define a Lyapunov function V = V1 + V2:

[0037]

[0038] where is the error between the fuzzy weight and , and the update law of is:

[0039] t k ≤ t < t k+1

[0040] t = t k

[0041] where β > 0;

[0042] Step 5. Combine the event-triggering mechanism with the finite-time controller to form a closed-loop control structure of the system. In this closed-loop system, the finite-time controller ensures that the spacecraft tracks the target attitude, and the event-triggering mechanism obtains the actual control torque of the spacecraft to achieve stable control of the spacecraft attitude.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1. Through the combination of the dynamic threshold triggering mechanism and finite-time sliding mode control, the present invention not only significantly reduces the communication frequency and computational burden of the system, but also improves the resource utilization efficiency and control accuracy, overcoming the deficiencies of traditional periodic or continuous control strategies; by introducing the finite-time sliding mode control method, it ensures that the system can converge to the target attitude within a finite time, enhancing the dynamic response speed and anti-interference ability of the system; through the fuzzy logic system to approximately process the concentrated disturbance, it further improves the robustness and adaptability of the system, effectively coping with complex interference environments.

[0045] 2. The present invention not only proposes a new method based on dynamic threshold triggering and finite-time sliding mode control theoretically, but also has broad application prospects in the field of spacecraft attitude control, applicable to complex nonlinear systems such as satellite attitude control, deep space probes, and space stations that require high precision, low energy consumption, and high stability, providing new technical support for the development of spacecraft control technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the structural block diagram of the closed-loop control system;

[0047] Figure 2 is the response curve of the spacecraft attitude q v1 ;

[0048] Figure 3 is the response curve of the spacecraft attitude q v2 ;

[0049] Figure 4 is the response curve of the spacecraft attitude q v3 ;

[0050] Figure 5 is the response curve of the spacecraft attitude q0;

[0051] Figure 6 The response curve of the spacecraft angular velocity ω;

[0052] Figure 7 The response curve of the control torque τ;

[0053] Figure 8 is the distribution diagram of the trigger time and trigger event interval. DETAILED DESCRIPTION OF THE INVENTION

[0054] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0055] Aiming at the problems of high communication frequency, high energy consumption and low resource utilization rate in spacecraft attitude control, the present invention provides a finite-time sliding mode attitude control method for spacecraft based on dynamic threshold triggering. First, through the kinematic and dynamic models based on quaternions, an attitude tracking error model of the spacecraft is established. Then, a finite-time non-singular sliding mode surface is designed, and combined with a fuzzy logic system to approximately process the lumped disturbances in the system, improving the anti-interference ability and control accuracy of the system. Finally, through the dynamic threshold triggering mechanism, a finite-time attitude tracking controller is designed to trigger control updates only when the system state change reaches the preset threshold, significantly reducing the communication and computational burden, and ensuring that the system converges and remains stable within a finite time. By introducing the dynamic threshold triggering mechanism and the finite-time sliding mode control technology, the present invention simplifies the control update frequency, combines the fuzzy logic system to achieve precise processing of lumped disturbances, thereby improving the control accuracy and stability of the system, and providing solid technical support for spacecraft attitude control. The specific steps are as follows:

[0056] Step 1: Establish a spacecraft model based on quaternions, define the attitude tracking error and angular velocity tracking error, and convert the spacecraft model into a tracking error model. The specific steps are as follows:

[0057] Step 1.1: Consider a rigid spacecraft with external disturbances, and establish the kinematic and dynamic models of the spacecraft based on quaternions:

[0058]

[0059] where ω = [ω1, ω2, ω3] T represents the angular velocity, and ω i (i = 1, 2, 3) are the angular velocity components in three directions respectively, represents the quaternion, q0 is the scalar part, and q v is the vector part, and satisfies is the moment of inertia of the spacecraft, represents the control torque, represents the external disturbance, I3 represents the 3×3 identity matrix, and the cross product operator is defined as:

[0060]

[0061] Step 1.2: Define the attitude tracking error between the system attitude and the desired attitude q d0 , q dv are the scalar part and vector part of q d respectively, and q e0 , q ev are the scalar part and vector part of q eThe scalar part and the vector part. Define the angular velocity tracking error ω e = ω - Cω d , ω d is the desired angular velocity, and the tracking error model is obtained as follows:

[0062]

[0063] where the rotation matrix

[0064] Step 2: Design the sliding surface S to ensure that when the sliding surface S = 0, the attitude tracking error q ev can converge to the origin within a finite time. The specific steps are as follows:

[0065] Step 2-1: Define the sliding surface S as follows:

[0066]

[0067] where q evi is the component in each direction of q ev , λ1 > 0, λ2 > 0, a > 1, and the function sig(·) is defined as sig a (x) = [|x1| a ·sgn(x1), …, |x n | a ·sgn(x n )] T .

[0068] Step 2-2: Define the Lyapunov function and take its derivative:

[0069]

[0070] Ensure that it can converge to the origin within a finite time when S = 0;

[0071] Step 3: For the lumped disturbance in the model, approximate it using a fuzzy logic system. The specific steps are as follows:

[0072] Step 3-1: Take the derivative of the sliding surface S in Step 2 to obtain the lumped disturbance Υ in the system:

[0073]

[0074] where Γ = diag(Γ1, Γ2, Γ3), i = 1, 2, 3, is the lumped disturbance of the system, and the auxiliary variable ψ is defined as:

[0075]

[0076] Step 3-2: For the concentrated disturbance Υ obtained in Step 3-1, approximate it using a fuzzy logic system:

[0077] Υ(S) = θ(S) T Φ(S)

[0078] where k is the input vector, Φ(S) is the fuzzy basis function, and θ(S) is the corresponding coordinate of Υ(S) under Φ(S);

[0079] Step 4: Design a dynamic event-triggering mechanism, and on this basis, design a finite-time attitude tracking controller for the spacecraft to ensure that the system can converge within a finite time. The specific steps are as follows:

[0080] Step 4-1: Assume that the k-th sampling point of the spacecraft state is t k , then the (k + 1)-th sampling point is t k+1 , define the measurement error e S = S(t) - S(t k ), e F = F(t) - F(t k ), S(t) and S(t k ) respectively represent the values of S at times t and t k , F(t) and F(t k ) respectively represent the values of F at times t and t k . The triggering condition for dynamic threshold triggering is:

[0081] t k+1 = inf{t > t k || |e S || 2 ≥ α1||S|| 2 + γ1 + h1(t) or ||e F || 2 ≥ α2||S|| 2 + γ2 + h2(t)}

[0082] h1(0) = h 10 > 0

[0083] h2(0) = h 20 > 0 where α1, α2 ∈ (0, 1), γ1, γ2 ≥ 0, H1(·), H2(·) are locally Lipchitz continuous k ∞ functions;

[0084] Step 4-2: On the basis of Step 4-1, design a finite-time controller τ c :

[0085]

[0086] Among them, are the estimated values of S, θ, and F respectively, and θ(t k ) represents the value of θ at time t k , where k > 0;

[0087] Step Four: Define the Lyapunov function V = V1 + V2:

[0088]

[0089] Among them, is the error between the fuzzy weight and . By designing , it is ensured that the system can converge within a finite time. The update law of

[0090] t k ≤ t < t k+1

[0091] t = t k

[0092] Among them β > 0;

[0093] Step Five: Combine the event-triggered mechanism with the finite-time controller to form the closed-loop control structure of the system. In this closed-loop system, the finite-time controller ensures that the spacecraft tracks the target attitude, and the event-triggered mechanism obtains the actual control torque of the spacecraft to achieve stable control of the spacecraft attitude.

[0094] Example:

[0095] For a rigid spacecraft with external disturbances and uncertainties, consider the following model:

[0096]

[0097] Among them, the disturbance d, the angular velocity ω of the spacecraft, and the angular acceleration are bounded.

[0098] Define the attitude tracking error between the system attitude and the desired attitude as Among them Define the angular velocity tracking error ω e = ω - Cω d , where ω d is the desired angular velocity, and the rotation matrix Obtain the error tracking model:

[0099]

[0100] Establish the following non-singular terminal sliding mode variable:

[0101]

[0102] where λ1>0, λ2>0, a>1, sig a (x) = [|x1| a ·sgn(x1), …, |x n | a ·sgn(x n )] T . When S i = 0, equation (3) is equivalent to the following conventional terminal sliding mode variable:

[0103]

[0104] where the parameter satisfies the following relationship:

[0105]

[0106] and When S i = 0, there is:

[0107]

[0108] Select the following Lyapunov function:

[0109]

[0110] Take the derivative of it to get:

[0111]

[0112] where, So q evi and can converge to the origin in finite time.

[0113] The derivative of the sliding mode surface S is:

[0114]

[0115] where, substituting (2) into the above formula gives:

[0116]

[0117] where, Γ = diag(Γ1, Γ2, Γ3), i = 1, 2, 3, To avoid the singularity problem, an auxiliary variable ψ is introduced to set the non-singular terminal sliding mode variable S. Equation (8) can be rewritten as:

[0118]

[0119] where is the lumped uncertainty, and the auxiliary variable ψ is given by:

[0120]

[0121] The lumped uncertainty Υ is approximated by a fuzzy logic system:

[0122]

[0123] where S is the input vector, Φ(S) is the fuzzy basis function, ||Φ(S)|| ≤ Φ N , is the estimated value of θ, and δ is the approximation error bounded by δ N , i.e., ||δ|| < δ N , and δ N is a small positive constant. Φ(S) satisfies the Lipchitz continuity condition:

[0124]

[0125] where l is a known positive constant.

[0126] Define the measurement error e S = S(t) - S(t k ), e F = F(t) - F(t k ), and design the following dynamic threshold trigger condition:

[0127] t k+1 = inf{t > t k |||e S || 2 ≥ α1||S|| 2 + γ1 + h1(t) or ||e F || 2 ≥ α2||S|| 2 + γ2 + g2(t)}

[0128] g1(0) = g 10 > 0

[0129] h2(0) = g20 >0 (13)

[0130] Controller τ c is designed to be:

[0131]

[0132] where the update law of is:

[0133]

[0134] Stability proof:

[0135] Choose the following Lyapunov function:

[0136] V = V1 + V2 (16)

[0137] where

[0138] Case 1: When t k ≤ t < t k+1 , take the derivative of V1 and substitute τ = τ c to get:

[0139]

[0140] where, Γ min and Γ max are the minimum and maximum eigenvalues of Γ respectively. Obviously, Γ min and Γ max are both positive. According to Young's inequality, we have:

[0141]

[0142] where l1 is a positive real number. Substitute Eqs. (12), (18), (19), (20) into Eq. (17) to get:

[0143]

[0144] When t k ≤ t < t k+1 , ||e S || 2 < α1||S|| 2 + γ1 + h1, ||e F || 2 < α2||S|| 2 + γ2 + h2. So we have

[0145]

[0146] To make the system stable, the selection of k, α1, and α2 should satisfy:

[0147]

[0148] When t k ≤ t < t k+1 From the triggering mechanism (15), and At this time, the derivative of V2:

[0149]

[0150] Case 2: When t = t k Take the first-order differences of V1 and V2:

[0151]

[0152] When t = t k At this time, So, ΔV1 = 0. Substitute Equation (15) into Equation (26):

[0153]

[0154]

[0155] Note that So, for Equation (27):

[0156]

[0157] To make the system stable, the selected κ should satisfy κ - 2κ 2 < 0, that is The structural block diagram of the entire closed-loop control system is as Figure 1 shown.

[0158] The spacecraft inertia matrix J = [20 1.2 0.9; 1.2 17 1.4; 0.9 1.4 15] kg·m 2 , the external disturbance d = [1 + 2sin(0.005t); -1 - 5cos(0.005t); 2 - 4cos(0.005t)] × 10 -3 N·m, the desired trajectory q d = [1, 0, 0, 0] T , ω d = [0, 0, 0] T , the initial state q(0) = [0.6698, -0.5158, 0.4716, 0.2508] T , ω(0) = [0, 0, 0] T。The sliding mode surface parameters are λ1 = 1, λ2 = 1, a = 2.5; the controller parameters are k = 1, κ = 0.3, β = 1, α1 = 0.5, α2 = 0.1, γ1 = 0.001, γ2 = 0.0001, h 10 = 0.1, h 20 = 0.1. In addition, the sampling time is 0.05 s, and the control torque is saturated, with the maximum control torque limited to 10 N·m.

[0159] According to the proposed triggering mechanism (13) and controllers (14), (15), the simulation results are as Figures 2 - 8 shown. Figures 2 - 6 They are respectively the curves of the spacecraft attitude q v , q0 and the angular velocity ω. Through Figures 2 - 6 , it can be seen that in the presence of disturbances, the spacecraft attitudes q v , q0 and the angular velocity ω quickly converge to the desired trajectories, showing good tracking characteristics. Figure 7 The control torque curve shows that the control torque is limited within 10 N·m and its magnitude changes dynamically with the triggering signal. Figure 8 The triggering time and triggering interval diagram shows that the triggering interval is between 0.05 s and 0.75 s, and a total of 73 triggers occur within 20 s, saving 81.8% of the computing resources. Considering Figures 2 - 8 the simulation results, the proposed finite-time sliding mode attitude control method for spacecraft based on dynamic threshold triggering can effectively achieve stable control of the spacecraft attitude in a complex disturbance environment, improving the control accuracy and dynamic response speed of the system. The simulation results show that the dynamic threshold triggering mechanism effectively reduces the communication frequency and computing burden of the system, verifying the effectiveness of the present invention in improving the resource utilization efficiency.

Claims

1. An event-triggered spacecraft attitude control method, characterized in that The method includes the following steps: Step 1: Establish a spacecraft model based on quaternions, define the attitude tracking error and the angular velocity tracking error, and convert the spacecraft model into a tracking error model. Step 2: Design the sliding surface S to ensure that when the sliding surface S = 0, the attitude tracking error q ev can converge to the origin within a finite time; Step 3: For the lumped disturbance in the model, approximate it using a fuzzy logic system. The specific steps are as follows: Step 3-1: Differentiate the sliding surface S in Step 2 to obtain the lumped disturbance Υ in the system: wherein, Γ = diag(Γ1, Γ2, Γ3), i = 1, 2, 3, is the concentrated disturbance of the system, and ψ is the auxiliary variable; Step 3-2: For the lumped disturbance Υ obtained in Step 3-1, approximate it using a fuzzy logic system: Υ(S) = θ(S ) TΦ(S) where S is the input vector, Φ(S) is the fuzzy basis function, and θ(S) is the corresponding coordinate of Υ(S) under Φ(S); Step 4: Design a dynamic event-triggering mechanism. On this basis, design a finite-time attitude tracking controller for the spacecraft to ensure that the system can converge within a finite time. The specific steps are as follows: Step 4-1. Assume that the k-th sampling point of the spacecraft state is t k , then the (k + 1)-th sampling point is t k+1 . Define the measurement error e S = S(t) - S(t k ), e F = F(t) - F(t k ). S(t) and S(t k ) represent the values of S at times t and t k respectively, and F(t) and F(t k ) represent the values of F at times t and t k respectively. The triggering condition for dynamic threshold triggering is as follows: t k+1 = inf{t > t k |||e S || 2 ≥ α1||S|| 2 + γ1 + h1(t) or ||e F || 2 ≥ α2||S|| 2 + γ2 + h2(t)} where α1, α2 ∈ (0, 1), γ1, γ2 ≥ 0, and H1(·), H2(·) are locally Lipschitz continuous k ∞ functions; Step 4-2: On the basis of Step 4-1, design a finite-time controller τ: Among them, are the estimated values of S, θ, and F respectively, and θ(t k ) represents the value of θ at t k moment, where k > 0; Step 4-3: Define the Lyapunov function V = V1 + V2: Among them, is the error between the fuzzy weight and , and 's update law is: wherein β > 0; Step 5: Combine the event-triggering mechanism with the finite-time controller to form a closed-loop control structure of the system. In this closed-loop system, the finite-time controller ensures that the spacecraft tracks the target attitude, and the event-triggering mechanism obtains the actual control torque of the spacecraft to achieve stable control of the spacecraft attitude.

2. The event-triggered spacecraft attitude control method according to claim 1, wherein The specific steps of Step 1 are as follows: Step 1-1: Consider a rigid-body spacecraft with external disturbances, and establish a kinematic and dynamic model of the spacecraft based on quaternions: where ω represents the angular velocity, represents a quaternion, q0 is the scalar part, and q v is the vector part, J is the moment of inertia of the spacecraft, τ represents the control torque, d represents the external disturbance, I3 represents the 3×3 identity matrix, and [ω × represents the cross product operator; Steps 1 and 2: Define the system attitude and the desired attitude The attitude tracking error between q d0 , q dv are the scalar part and the vector part of q d respectively, q e0 , q ev are the scalar part and the vector part of q e respectively. Define the angular velocity tracking error ω e = ω - Cω d , ω d is the desired angular velocity, and obtain the tracking error model: where c represents the rotation matrix.

3. The event-triggered spacecraft attitude control method according to claim 2, wherein In the above step 1, the cross product operator is defined as: where ω i are the angular velocity components in three directions respectively, and i = 1, 2, 3.

4. The method for spacecraft attitude control based on event triggering according to claim 2, wherein In the above step 1-1, 5. The event-triggered spacecraft attitude control method according to claim 2, wherein The specific steps of Step 2 are as follows: Step 2-1: Define the sliding surface s as follows: where q evi is the component of q ev in each direction, λ1 > 0, λ2 > 0, a > 1; Step 22: Define the Lyapunov function And take the derivative of it: Ensure that it can converge to the origin within a finite time when S = 0.

6. The event-triggered spacecraft attitude control method according to claim 5, wherein In the second step, the function sig(·) is defined as sig a (x) = [|x1| a ·sgn(x1), …, |x n | a ·sgn(x n )] T , where x = [x1, x2, …, x n T is an n-dimensional vector, and x n is the nth component of x.​ 7. The method for spacecraft attitude control based on event triggering according to claim 1, characterized in that In Step 3-1, the auxiliary variable ψ is defined as:

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