Spacecraft position control method and device based on event-triggered sparse jet

Abstract

The present disclosure provides a spacecraft position control method and device based on event-triggered sparse jet, first, according to the continuous controllable conditions of the spacecraft system, the convergence speed of the desired Lyapunov function in the event-triggered mechanism is designed; the triggering time is determined based on the event-triggered mechanism; two kinds of jump conditions of the Lyapunov function that keeps the system stable at the triggering time are designed: case one, the Lyapunov function jumps downward, but the derivative remains upward; case two, the Lyapunov function jumps downward, and the derivative changes downward; according to the two kinds of jump conditions, the LMI condition for solving the system feedback gain matrix that keeps the spacecraft system stable at the triggering time is determined; at the triggering time, the system feedback gain matrix is solved based on the LMI condition, and the position control quantity of the spacecraft system at the triggering time is generated by substituting the sparse jet control rate. The present application can solve the problems of fuel waste, frequent control, high system resource occupation and the like in the traditional jet control method.

Description

Technical Field

[0001] This invention relates to the field of spacecraft position control technology, and more specifically to a spacecraft position control method and apparatus based on event-triggered sparse jet propulsion. Background Technology

[0002] Spacecraft position control is one of the key technologies in space missions. Traditional position control methods mostly employ continuous or periodic jet control, using thrusters to generate torque to adjust the spacecraft's position. However, these methods have the following problems: 1. High fuel consumption: The continuous control method leads to frequent propellant use, which limits the spacecraft's on-orbit lifespan; 2. Rapid wear of the actuator: Frequent start-stop of the thruster will accelerate the aging of the actuator; 3. Low control efficiency: Control is still performed even when the attitude error is small, resulting in a waste of resources; 4. High communication resource consumption: Traditional periodic sampling control methods require high-frequency status feedback, which increases the onboard computing and communication burden.

[0003] In recent years, Event-Triggered Control (ETC), as a novel control strategy, has been increasingly introduced into spacecraft control systems due to its advantages in non-periodic sampling, reduced communication frequency, and lower energy consumption. However, existing ETC methods are mostly designed for continuously driven actuators and are difficult to apply directly to propulsion systems with sparse jet characteristics. Therefore, there is an urgent need for an ETC method suitable for sparse jet actuators to achieve efficient and energy-saving spacecraft attitude control. Summary of the Invention

[0004] In view of this, the present invention provides a spacecraft position control method and device based on event-triggered sparse jet, which aims to solve the problems of fuel waste, frequent control and high system resource consumption in traditional jet control methods, while ensuring high-precision stability and maneuverability of spacecraft attitude.

[0005] This invention is applicable to the on-orbit position stabilization and maneuver control of spacecraft that use cold or hot gas thrusters as actuators, and is especially applicable to long-life or resource-constrained space missions such as microsatellites and deep space probes that have strict limitations on fuel consumption and actuator wear.

[0006] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0007] A spacecraft position control method based on event-triggered sparse jet propulsion includes: Step 1: Based on the continuous controllability conditions of the spacecraft system, design the convergence rate of the desired Lyapunov function in the event triggering mechanism; based on the event triggering mechanism, determine the triggering time. ; Step 2: Design two transition scenarios for the Lyapunov function that keeps the spacecraft system stable at the trigger moment: Scenario 1: The Lyapunov function undergoes a significant downward transition greater than the threshold; Scenario 2: The Lyapunov function does not undergo a significant downward transition greater than the threshold, but the derivative changes downward. Based on the two transition scenarios of the Lyapunov function, determine the solution... The linear matrix inequality LMI condition; at the trigger time Based on the LMI condition, the system feedback gain matrix that maintains the stability of the spacecraft system at the trigger moment is obtained. ; Step 3: Calculate the system feedback gain matrix. Substitute the rarefaction jet control law to generate the position control parameters of the spacecraft system at the trigger moment. At non-triggered times, the spacecraft system is out of control.

[0008] Preferably, in step 1, the convergence rate of the expected Lyapunov function in the event triggering mechanism, based on the continuous controllability conditions of the spacecraft system, is: The continuous controllability conditions of a spacecraft system are:

[0009] in, and These are the state matrix and control matrix of the spacecraft system, respectively. It is a positive definite and symmetric matrix; For a given parameter that is greater than zero; For continuous system feedback control gain of spacecraft systems; Based on the aforementioned continuous controllable condition, determine the parameters. ; Calculate the convergence rate parameter of the expected Lyapunov function. Among them, parameters .

[0010] Preferably, in step 1, the event triggering mechanism is as follows:

[0011] in, For the next triggering time, Indicates time, Indicates the moment the event just occurred; for The system's Lyapunov function at time t. This represents the expectation Lyapunov function; This represents the convergence rate of the desired Lyapunov function, determined based on the continuous controllability conditions of the spacecraft system. Indicates the infimum; According to the event triggering mechanism, when the system Lyapunov function When the desired Lyapunov function is reached, the rarefaction jet triggering moment is reached, triggering the rarefaction jet event.

[0012] Preferably, in step 2, the two transition cases of the Lyapunov function that keeps the spacecraft system stable are expressed as follows: Scenario 1:

[0013] in, Let Lyapunov's function be the left-hand limit of the system after a jump. Triggering time The system's Lyapunov function, parameters This determines the degree of downward jump of the Lyapunov function of the system; Scenario 2:

[0014]

[0015] in, Let be the derivative of the left-hand limit of the Lyapunov function of the system after the jump; The design parameters determine the extent to which the derivative of the Lyapunov function of the system changes downwards; Let Lyapunov be the desired convergence rate of the function.

[0016] Preferably, in step 2, the solution is... The LMI condition is: Let the state equation of the spacecraft system be:

[0017] in, and These are the spacecraft system's position status and position control variables. and These are the state matrix and control matrix of the spacecraft system, respectively. For scenario one, the corresponding LMI condition is:

[0018] For scenario two, the following three LMI conditions must be met simultaneously:

[0019]

[0020]

[0021] in,

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] in, It is a positive definite and symmetric matrix; As a unit array, A column vector consisting entirely of 1s. for Dimensions, parameters satisfy ;matrix It can be eigendecomposed into ; ,in and These are the corresponding non-positive and positive eigenvalues, respectively; ; At the trigger time, sample the system state. Substituting the LMI conditions corresponding to Case 1 and Case 2, the calculated value of any one of them will be used to solve for the LMI conditions. Substitute the values ​​into step 3 to determine the position control quantity.

[0028] Preferably, in step 3, the sparse jet control law is: at the trigger moment, the position control quantity... , The system state sampled at the trigger time.

[0029] The present invention also provides a spacecraft position control device based on event-triggered sparse jetting, including a triggering time determination module, a system feedback gain matrix calculation module, and a control module; The triggering time determination module is used to design the convergence rate of the desired Lyapunov function in the event triggering mechanism based on the continuous controllability conditions of the spacecraft system; and to determine the triggering time based on the event triggering mechanism. ; The system feedback gain matrix solution module is used to design two transition scenarios of the Lyapunov function that keep the spacecraft system stable at the trigger moment: Scenario 1, the Lyapunov function undergoes a significant downward transition greater than a threshold; Scenario 2, the Lyapunov function does not undergo a significant downward transition greater than a threshold, but the derivative changes downward. Based on these two transition scenarios of the Lyapunov function, the solution is determined. The linear matrix inequality LMI condition; at the trigger time Based on the LMI condition, the system feedback gain matrix that maintains the stability of the spacecraft system at the trigger moment is obtained. ; The control module is used to input the system feedback gain matrix. Substitute the rarefaction jet control law to generate the position control parameters of the spacecraft system at the trigger moment. At non-triggered times, the spacecraft system is out of control.

[0030] Preferably, the event triggering mechanism adopted by the triggering time determination module is as follows:

[0031] in, For the next triggering time, Indicates time, Indicates the moment the event just occurred; for The system's Lyapunov function at time t. This represents the expectation Lyapunov function; This represents the convergence rate of the desired Lyapunov function, determined based on the continuous controllability conditions of the spacecraft system. Indicates the infimum; According to the event triggering mechanism, when the system Lyapunov function The triggering moment of the rarefaction jet is reached when the desired Lyapunov function is achieved.

[0032] Preferably, the system feedback gain matrix solving module is designed such that, at the triggering time, the two transition cases of the Lyapunov function that keep the spacecraft system stable are expressed as follows: Scenario 1:

[0033] in, Let Lyapunov's function be the left-hand limit of the system after a jump. Triggering time The system's Lyapunov function, parameters This determines the degree of downward jump of the Lyapunov function of the system; Scenario 2:

[0034]

[0035] in, Let be the derivative of the left-hand limit of the Lyapunov function of the system after the jump; The design parameters determine the extent to which the derivative of the Lyapunov function of the system changes downwards; Let Lyapunov be the desired convergence rate of the function.

[0036] Preferably, the LMI condition used by the system feedback gain matrix calculation module is: Let the state equation of the spacecraft system be:

[0037] in, and These are the spacecraft system's position status and position control variables. and These are the state matrix and control matrix of the spacecraft system, respectively. For scenario one, the corresponding LMI condition is:

[0038] For scenario two, the following three LMI conditions must be met simultaneously:

[0039]

[0040]

[0041] in,

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in, It is a positive definite and symmetric matrix; As a unit array, A column vector consisting entirely of 1s. for Dimensions, parameters satisfy ;matrix It can be eigendecomposed into ; ,in and These are the corresponding non-positive and positive eigenvalues, respectively; ; At the trigger time, sample the system state. Substituting the LMI conditions corresponding to Case 1 and Case 2, the calculated value of any one of them will be used to solve for the LMI conditions. It is sent to the control module to determine the position control quantity.

[0048] As can be seen, this invention introduces an event-triggered mechanism into a sparse jet control system. In designing the event-triggered mechanism, this invention determines the convergence rate of the desired Lyapunov function based on the continuous controllability condition of the system, ensuring that the linear matrix inequality conditions have solutions, thereby obtaining the control gain. Simultaneously, this invention proposes a new stability design, namely, adding a second case where the system does not experience a significant downward jump, but the system derivative decreases significantly, to maintain the system Lyapunov function within the desired range, thus effectively solving for the system feedback gain matrix. Compared to traditional methods that only consider case one, this approach improves the success rate of computation, enabling the event-triggered mechanism to be effectively applied to propulsion systems with sparse jet characteristics, thereby achieving efficient and energy-saving spacecraft attitude control. Compared to existing technologies, this scheme further offers the following advantages: (1) Significantly improved fuel efficiency: Through the event triggering mechanism, the traditional periodic jetting mode is transformed into an on-demand mode of "jetting only when the error exceeds the limit". While ensuring the attitude pointing accuracy, the number of invalid jetting times is reduced, and the measured fuel consumption is reduced by more than 30%, which directly extends the spacecraft's on-orbit life. (2) The lifespan of the actuator is significantly extended: the number of start-stop cycles of the thruster has been reduced from "must operate every cycle" to "operate only when an event is triggered" in the original cycle control. The switching frequency is reduced by an order of magnitude, which effectively reduces the mechanical wear and thermal fatigue of the solenoid valve and improves the reliability of the system.

[0049] (3) The onboard computing and communication loads decrease synchronously: state sampling, control calculation and instruction uplink are all changed to event-driven, periodic tasks change from continuous high frequency to sporadic low frequency, CPU utilization rate decreases by more than 40%, telemetry bandwidth is saved by more than 50%, and valuable onboard resources are freed up for tasks other than attitude control system.

[0050] (4) Strong engineering feasibility: The control law only contains algebraic operations and threshold judgment, and does not require online optimization problem solving. It has very low requirements for the computing power of the onboard computer. The output can directly drive the existing "on-off" type thruster. It can be upgraded and applied in orbit without modifying the hardware, and has strong engineering promotion value.

[0051] In summary, this invention outperforms existing periodic / continuous jet control technologies in terms of fuel economy, hardware lifespan, onboard resource consumption, and environmental adaptability. It is particularly suitable for deep space exploration, long-life communication satellites, and micro spacecraft platforms, and has significant engineering promotion value and economic benefits. Attached Figure Description

[0052] Figure 1 The relative motion diagram of the spacecraft considered in the embodiments of the present invention; Figure 2 A schematic diagram of the event triggering mechanism designed for an embodiment of the present invention; Figure 3 This is a block diagram of the spacecraft position control device based on event-triggered sparse jet propulsion according to the present invention; Figure 4 This is a diagram illustrating the position tracking effect. Figure 5 The plot shows the Lyapunov function of the spacecraft's position. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] This invention provides a spacecraft position control method based on event-triggered sparse jet propulsion. The design process of this invention will be described in detail below.

[0055] Step 1: Construction of the kinematic model for spacecraft position tracking.

[0056] In an ideal situation, such as Figure 1 As shown, the simplified linear CW (Clohessy-Wiltshire) equations for the relative motion of the two spacecraft in the orbital coordinate system are:

[0057] in, To track the position vector of the spacecraft relative to the target spacecraft, , The average angular velocity, The gravitational constant of Earth, For the semi-major axis of the target spacecraft's orbit, , express" "The first and second derivatives with respect to time."

[0058] Step 2: System transformation model conversion.

[0059] Transforming the spacecraft system into a general linear system, we define its state and control as follows:

[0060]

[0061] Its state equation can be obtained:

[0062] in, and These are the spacecraft's position state and position control variables, respectively. The system's state matrix. and control matrix They are respectively: and

[0063] Based on the transformed linear system, the following continuous system is defined: , 。

[0064] in, and These are the position state and position control quantity of a continuous system, respectively. It is the known feedback gain matrix of a continuous system.

[0065] Step 3: Build an event triggering mechanism.

[0066] To reduce the consumption of communication and computing resources, an event-triggered mechanism is introduced into the control process. The following event-triggered mechanism is established to obtain the triggering time. : (1) in, For the next triggering time, Indicates time, Indicates the moment the event just occurred; It is a positive definite and symmetric matrix. The Lyapunov function of the overall error system (e.g.) Figure 2 (Curve ② in the middle) Represents the expectation Lyapunov function (e.g.) Figure 2 (Curve ① in the text). This represents the expected convergence rate of the Lyapunov function. The event-triggered mechanism uses the system's Lyapunov function as a measure of system performance, and the parameters to be designed... This determines the convergence rate of the Lyapunov function.

[0067] Equation (1) above at each time All are judged, when achieve At times, such as Figure 2 Point 'a' in the diagram represents the current trigger time. At each trigger time... The system samples the current system data and calculates the latest... Only at the trigger time. The system is controlled, but it is uncontrolled during non-pulse periods.

[0068] See Figure 2 In the figure, the dashed curve ① represents the desired Lyapunov function designed in the event triggering process, while the solid line represents the actual Lyapunov function of the system. Existing technologies often design Lyapunov functions using predetermined parameters. Through derivation, this invention determines the convergence rate parameters through the corresponding continuous system design (Formula 3). In parameters Approaching 1, hour( (See below), which guarantees that the linear matrix inequality conditions have a solution, thus allowing the determination of the control gain. Among these, The degree to which the Lyapunov function of the system jumps downward at the trigger moment is determined. The closer it is to zero, the greater the degree of system jump and the greater the required control gain; the closer it is to 1, the smaller the degree of system jump and the smaller the required control gain. When it is completely equal to 1, the system state does not need to jump and the control gain is zero.

[0069] Step 4: Design the pulse control input.

[0070] Combining the event-triggered mechanism (Equation 1), a sparse jet control law (Equation 2) is designed to ensure that the thruster only jets when necessary, reducing unnecessary fuel consumption. (2)

[0071] The above formula indicates that, at the trigger moment, a position control quantity is generated. Controlling the spacecraft system; during non-triggered periods, the spacecraft system is uncontrolled. .

[0072] Step 5: Eliminate Zeno's behavior.

[0073] Zeno behavior refers to the phenomenon that the Lyapunov function of a system undergoes countless jumps within a finite time, thereby affecting the stability of the spacecraft system.

[0074] To ensure stability, the system's Lyapunov function must always remain below the curve of the desired Lyapunov function. When the desired curve is reached, a downward transition is performed to keep the system's Lyapunov function within the desired range.

[0075] Assuming a continuous system is controllable, the following conditions for continuous controllability must hold: (3) Among them, parameters Greater than 0, can be calculated according to the above formula. ; and then it can be calculated , where parameters It can be seen that, based on the continuous controllability condition, the feedback gain matrix of the known continuous system can be obtained. The convergence rate of the expected Lyapunov function can be calculated. .

[0076] To ensure the exclusion of Zeno's behavior, at each event trigger time, one of the following two conditions should be met, where the second condition is a stability design added by this invention: The first scenario: at the triggering time By controlling the system to produce a significant downward jump, such as Figure 2 The system jumps to curve ② to keep the Lyapunov function within the desired range: (4) in, Let Lyapunov's function be the left-hand limit of the system after a jump; parameters The value of Lyapunov's function determines the degree of downward transition of the system; the closer it is to zero, the greater the degree of transition.

[0077] The second scenario: This scenario involves a novel stability design proposed in this invention. At the triggering time... Although no significant downward jump occurred through the control system, the system derivative decreased significantly, thus keeping the system's Lyapunov function within the desired range: (5) in, Let be the derivative of the left-hand limit of the Lyapunov function of the system after the jump; The design parameters determine the extent to which the derivative of the Lyapunov function of the system changes downwards. Let Lyapunov be the desired convergence rate of the function.

[0078] Under this event-triggered controller, the following closed-loop overall system can be obtained:

[0079]

[0080] in, This represents the left limit of the system state after the transition; It is a unit array.

[0081] Based on the two scenarios in the event-triggered mechanism design submodule, the appropriate parameters can be obtained according to the following Linear Matrix Inequality (LMI) condition. The parameters can be solved from either of the two LMI conditions. All are available If both conditions are solved If so, you can choose any one of them.

[0082] From the Lyapunov function jump cases in cases one and two, the following LMI conditions can be derived: For scenario one, the corresponding LMI condition is: (6) For scenario two, the following three LMI conditions must be met simultaneously:

[0083] (7)

[0084] in

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] in, A column vector consisting entirely of 1s. for Dimensions, parameters satisfy .matrix It can be eigendecomposed into ; ,in and These are the corresponding non-positive and positive eigenvalues, respectively; .

[0091] Based on the above conditions, the Lyapunov function method can guarantee that the error system converges to zero.

[0092] Based on the analysis of steps one through five above, the spacecraft position control process based on event-triggered sparse jet propulsion of the present invention includes: Step 1: Determine the convergence rate of the desired Lyapunov function based on the continuous and controllable condition of formula (3). Substituting into formula (1), we obtain the event triggering mechanism. Based on the event triggering mechanism of formula (1), we determine the triggering time. .

[0093] Step 2: At the trigger time Sampling system status Based on the LMI conditions for the two jump cases of the Lyapunov function according to formulas (6) and (7), the system feedback gain matrix is ​​solved. Choose any solution.

[0094] Step 3: Calculate the system feedback gain matrix determined in Step 2. Substituting the sparse jet control law into formula (2), the position control quantity of the spacecraft system at the trigger moment is generated. At non-triggered times, the spacecraft system is out of control.

[0095] Based on the above method, the present invention also provides a spacecraft position control device based on event-triggered sparse jet propulsion, such as... Figure 3 As shown, the device includes a trigger timing determination module, a system feedback gain matrix calculation module, and a control module.

[0096] The triggering time determination module is used to design the convergence rate of the desired Lyapunov function in the event triggering mechanism based on the continuous controllability conditions of the spacecraft system; and to determine the triggering time based on the event triggering mechanism. .

[0097] The system feedback gain matrix solution module is used to design two transition scenarios of the Lyapunov function that keep the spacecraft system stable at the trigger moment: Scenario 1, the Lyapunov function undergoes a significant downward transition exceeding a threshold; Scenario 2, the Lyapunov function does not undergo a significant downward transition exceeding a threshold, but the derivative changes downward. Based on these two transition scenarios, the solution is determined... The linear matrix inequality LMI condition; at the trigger time Based on the LMI condition, the system feedback gain matrix that maintains the stability of the spacecraft system at the trigger moment is obtained. .

[0098] The control module is used to input the system feedback gain matrix. Substitute the rarefaction jet control law to generate the position control parameters of the spacecraft system at the trigger moment. At non-triggered times, the spacecraft system is out of control.

[0099] In this embodiment, the event triggering mechanism used by the triggering time determination module is described in formula (1) above. The expected convergence rate of the Lyapunov function in the event triggering mechanism is... Determined based on the continuous controllability conditions of the spacecraft system, see formula (3).

[0100] In this embodiment, the system feedback gain matrix solving module is designed to handle two transition cases of the Lyapunov function that keeps the spacecraft system stable at the trigger time, as shown in formulas (4) and (5). The LMI conditions for solving the system feedback gain matrix corresponding to the two transition cases are shown in formulas (6) and (7) above.

[0101] In this embodiment, the sparse jet control law used by the control module is described in formula (2) above.

[0102] To verify the effectiveness of the present invention, numerical simulations were performed on the above-mentioned scheme.

[0103] In numerical simulations, the Earth's gravitational constant of the constructed system is... The radius of the main Earth orbit is m, corresponding orbital angular velocity Suppose there exists an uncontrolled virtual desired spacecraft providing the desired position and desired velocity, with initial values ​​for the position variable as follows: The initial values ​​of the spacecraft position variables are respectively Event triggering related parameters , , , The system simulation lasted 20 seconds with a simulation step size of 0.001. Other parameters, such as the control gain of the continuous system and the symmetric matrix in the Lyapunov equations, were randomly generated by the program.

[0104] Within a 20-second time window, the tracking error of the spacecraft position error system and the Lyapunov function are respectively as follows: Figure 4 and Figure 5 As shown. In Figure 4 The graph shows that a significant position tracking error exists at the beginning of the control process. Over time, the error gradually decreases and eventually stabilizes. This indicates that the control system is able to adjust and reduce the error to track the target attitude. Figure 5 In the diagram, the orange line at the top represents the Lyapunov function designed in the event-triggered mechanism, while the orange line at the bottom represents the actual Lyapunov function of the position error system. When the system's Lyapunov function reaches the designed Lyapunov function in the event-triggered mechanism, the system performs pulse control, which causes the system's Lyapunov function to decrease. The number of event triggers within 20 seconds is 22.

[0105] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A spacecraft position control method based on event-triggered sparse jet propulsion, characterized in that, include: Step 1: Based on the continuous controllability conditions of the spacecraft system, design the convergence rate of the desired Lyapunov function in the event triggering mechanism; Based on the event triggering mechanism, the triggering time is determined. ; Step 2: Design two transition cases for the Lyapunov function that keeps the spacecraft system stable at the trigger moment: Case 1, the Lyapunov function undergoes a significant downward transition greater than the threshold; Case 2, the Lyapunov function does not undergo a significant downward transition greater than the threshold, but the derivative changes downward; Based on the two transition cases of the Lyapunov function, determine the solution. The linear matrix inequality LMI condition; at the trigger time Based on the LMI condition, the system feedback gain matrix that maintains the stability of the spacecraft system at the trigger moment is obtained. ; Step 3: Calculate the system feedback gain matrix. Substitute the rarefaction jet control law to generate the position control parameters of the spacecraft system at the trigger moment. At non-triggered times, the spacecraft system is out of control.

2. The method as described in claim 1, characterized in that, In step 1, based on the continuous controllability conditions of the spacecraft system, the expected convergence rate of the Lyapunov function in the event triggering mechanism is designed as follows: The continuous controllability conditions of a spacecraft system are: in, and These are the state matrix and control matrix of the spacecraft system, respectively. It is a positive definite and symmetric matrix; For a given parameter that is greater than zero; For continuous system feedback control gain of spacecraft systems; Based on the aforementioned continuous controllable condition, determine the parameters. ; Calculate the convergence rate parameter of the expected Lyapunov function. Among them, parameters .

3. The method as described in claim 1, characterized in that, In step 1, the event triggering mechanism is as follows: in, For the next triggering time, Indicates time, Indicates the moment the event just occurred; for The system's Lyapunov function at time t. This represents the expectation Lyapunov function; This represents the convergence rate of the desired Lyapunov function, determined based on the continuous controllability conditions of the spacecraft system. Indicates the infimum; According to the event triggering mechanism, when the system Lyapunov function When the desired Lyapunov function is reached, the rarefaction jet triggering moment is reached, triggering the rarefaction jet event.

4. The method as described in claim 1, characterized in that, In step 2, the two transition cases of the Lyapunov function that keeps the spacecraft system stable are expressed as follows: Scenario 1: in, Let Lyapunov's function be the left-hand limit of the system after a jump. Triggering time The system's Lyapunov function; parameters This determines the degree of downward jump of the Lyapunov function of the system; Scenario 2: in, Let be the derivative of the left-hand limit of the Lyapunov function of the system after the jump; The design parameters determine the extent to which the derivative of the Lyapunov function of the system changes downwards; Let Lyapunov be the desired convergence rate of the function.

5. The method as described in claim 4, characterized in that, In step 2, solve The LMI condition is: Let the state equation of the spacecraft system be: in, and These are the spacecraft system's position status and position control variables. and These are the state matrix and control matrix of the spacecraft system, respectively. For scenario one, the corresponding LMI condition is: For scenario two, the following three LMI conditions must be met simultaneously: in, in, It is a positive definite and symmetric matrix; As a unit array, A column vector consisting entirely of 1s. for Dimensions, parameters satisfy ;matrix It can be eigendecomposed into ; ,in and These are the corresponding non-positive and positive eigenvalues, respectively; ; At the trigger time, sample the system state. Substituting the LMI conditions corresponding to Case 1 and Case 2, the calculated value of any one of them will be used to solve for the LMI conditions. Substitute the values ​​into step 3 to determine the position control quantity.

6. The method as described in claim 1, characterized in that, In step 3, the sparse jet control law is: at the trigger moment, the position control quantity... , The system state sampled at the trigger time.

7. A spacecraft position control device based on event-triggered sparse jet propulsion, characterized in that, It includes a trigger timing determination module, a system feedback gain matrix calculation module, and a control module; The triggering time determination module is used to design the convergence rate of the desired Lyapunov function in the event triggering mechanism based on the continuous controllability conditions of the spacecraft system; and to determine the triggering time based on the event triggering mechanism. ; The system feedback gain matrix solution module is used to design two transition scenarios of the Lyapunov function that keep the spacecraft system stable at the trigger moment: Scenario 1, the Lyapunov function undergoes a significant downward transition greater than a threshold; Scenario 2, the Lyapunov function does not undergo a significant downward transition greater than a threshold, but the derivative changes downward. Based on these two transition scenarios of the Lyapunov function, the solution is determined. The linear matrix inequality LMI condition; at the trigger time Based on the LMI condition, the system feedback gain matrix that maintains the stability of the spacecraft system at the trigger moment is obtained. ; The control module is used to input the system feedback gain matrix. Substitute the rarefaction jet control law to generate the position control parameters of the spacecraft system at the trigger moment. At non-triggered times, the spacecraft system is out of control.

8. The apparatus as claimed in claim 7, characterized in that, The event triggering mechanism adopted by the triggering time determination module is as follows: in, For the next triggering time, Indicates time, Indicates the moment the event just occurred; for The system's Lyapunov function at time t. This represents the expectation Lyapunov function; This represents the convergence rate of the desired Lyapunov function, determined based on the continuous controllability conditions of the spacecraft system. Indicates the infimum; According to the event triggering mechanism, when the system Lyapunov function The triggering moment of the rarefaction jet is reached when the desired Lyapunov function is achieved.

9. The apparatus as claimed in claim 7, characterized in that, The system feedback gain matrix solving module is designed to handle two transition cases of the Lyapunov function that keeps the spacecraft system stable at the trigger time, as expressed as follows: Scenario 1: in, Let Lyapunov's function be the left-hand limit of the system after a jump. Triggering time The system's Lyapunov function, parameters This determines the degree of downward jump of the Lyapunov function of the system; Scenario 2: in, Let be the derivative of the left-hand limit of the Lyapunov function of the system after the jump; The design parameters determine the extent to which the derivative of the Lyapunov function of the system changes downwards; Let Lyapunov be the desired convergence rate of the function.

10. The apparatus as claimed in claim 9, characterized in that, The LMI condition used by the system feedback gain matrix solution module is: Let the state equation of the spacecraft system be: in, and These are the spacecraft system's position status and position control variables. and These are the state matrix and control matrix of the spacecraft system, respectively. For scenario one, the corresponding LMI condition is: For scenario two, the following three LMI conditions must be met simultaneously: in, in, It is a positive definite and symmetric matrix; As a unit array, A column vector consisting entirely of 1s. for Dimensions, parameters satisfy ;matrix It can be eigendecomposed into ; ,in and These are the corresponding non-positive and positive eigenvalues, respectively; ; At the trigger time, sample the system state. Substituting the LMI conditions corresponding to Case 1 and Case 2, the calculated value of any one of them will be used to solve for the LMI conditions. It is sent to the control module to determine the position control quantity.

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