Multi-spacecraft attitude cooperative tracking control method for transient performance enhancement

Abstract

The invention discloses a transient performance enhancement-oriented multi-spacecraft attitude cooperative tracking control method, which provides a fixed time controller through an inversion control strategy, realizes quick response of a multi-spacecraft attitude system, and ensures that a consistency error is converged to a sufficiently small domain within fixed time. A fuzzy weight updating law is designed, dependence on system model information is reduced, and adaptability and high robustness are achieved. According to the asymmetric fractional obstacle Lyapunov function, adherence of multiple spacecrafts to time-varying constraints is guaranteed, meanwhile, the problem that the control amplitude related to a large constraint boundary in a traditional logarithmic obstacle Lyapunov function is too large is solved, and therefore the proposed method can process constrained and unconstrained scenes. A saturation threshold event triggering strategy is designed, a multi-spacecraft system is allowed to select three different triggering strategies by adjusting parameters, the transmission frequency of control signals is flexibly changed, and control bus resources are reasonably distributed.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically a multi-spacecraft attitude cooperative tracking control method for enhancing transient performance. Background Technology

[0002] In recent decades, due to its increasing importance in aerospace engineering, attitude consensus control of multiple spacecraft has become a hot research area. This cooperative approach offers a promising solution for overcoming limitations related to the operating range and energy capacity of individual spacecraft, particularly for complex missions such as space telescope assembly, satellite surveillance, and complex maneuvers. As a key aspect of attitude consensus control, leader-tracking attitude consensus requires a group of spacecraft to converge to a given reference orbit through local communication. To date, researchers have proposed numerous studies on leader-tracking attitude consensus control for multiple spacecraft, such as iterative learning control, data-driven control, model predictive control, and adaptive fuzzy / neural network control. Notably, most of these control methods can only achieve asymptotic convergence of joint angle tracking errors, indicating that the errors require an infinite amount of time to gradually converge, making it difficult to meet the requirements of control tasks with strict convergence time requirements.

[0003] Convergence time is one of the key factors affecting system control performance. A shorter convergence time enables the system output to respond quickly, ultimately improving its control performance. To achieve the goal of fast response, finite-time control techniques are favored by researchers due to their fast convergence speed and good robustness to disturbances and parameter uncertainties. Compared with control methods that can only guarantee the asymptotic stability of the closed-loop system, finite-time control techniques can usually provide faster convergence speed and higher convergence accuracy. However, for finite-time control, the system's settling time is affected by the initial conditions. In some control tasks where the initial conditions cannot be arbitrarily set, the application of finite-time control techniques will be limited. For example, when the initial state of the spacecraft is far from the target position, the settling time of the error system will increase, and this defect will affect the spacecraft's global tracking performance. To overcome the limitations of finite-time control, the concept of fixed-time stability has been proposed. Its key advantage is that it ensures that the upper bound of the system's convergence time is independent of the initial system state. With this advantage, researchers have successfully applied fixed-time control to various nonlinear systems.

[0004] On the other hand, considering the transmission capacity of the spacecraft control bus, real-time data transmission will inevitably lead to congestion of the control bus and excessive energy consumption. To solve this problem, researchers have proposed the concept of time-triggered control. Time-triggered control is a control method based on a fixed sampling frequency. Its core is to sample the system state and update the control command according to a predetermined time interval. This method is widely used in industrial and automation systems because it is simple to operate and easy to implement. However, in time-triggered control, the sampling frequency has an important impact on system performance: (1) a higher sampling frequency can improve the system's response speed and accuracy, but it will increase the computation and communication burden; (2) a lower sampling frequency can reduce resource consumption, but it may lead to a decrease in control performance. To this end, researchers have further proposed the concept of event-triggered control. Event-triggered control refers to the fact that the signal in the control system is sampled and updated only under specific conditions. This feature allows the system to balance control performance and communication burden. Considering the rapid response of the system, a large control amplitude is required in the transient process. In this case, the control signal needs to be transmitted at a high frequency to ensure that the system is not subjected to excessive pulse input. When the system is in a steady state, the control amplitude is small, and the control signal only needs to be transmitted at a low frequency to save the transmission resources of the control bus. However, most current research on fixed-time event-triggered control employs a single event-triggered mechanism, which cannot flexibly adjust the transmission frequency of the control input. This may lead to the inefficient allocation of the spacecraft's limited control bus resources. Therefore, designing a suitable event-triggered strategy for multi-spacecraft systems to simultaneously achieve fixed-time stability is of great significance.

[0005] In practical applications, state constraints are crucial for ensuring the safety and transient response of spacecraft during space operations. Therefore, Lyapunov barriers have attracted considerable attention in the control community, becoming an effective method for solving state-constrained problems. However, most research on barrier Lyapunov functions uses logarithmic barrier Lyapunov functions. As the constraint boundary approaches infinity, the logarithmic barrier Lyapunov function approaches zero, causing the controller amplitude to significantly exceed the saturation limit of most practical control systems. This is especially important considering that the system state is not always constrained. It is worth noting that the logarithmic barrier Lyapunov is a transcendental function, which can lead to excessive online computational burdens in practical applications. Therefore, it is necessary to design a barrier Lyapunov function to handle constrained and unconstrained attitude control problems with lower online computational complexity. Summary of the Invention

[0006] The purpose of this invention is to provide a fixed-time event-triggered control method for multi-spacecraft attitude consistency with asymmetric time-varying constraints. Through an inversion control strategy, a fixed-time controller is systematically proposed, which enables rapid response of the multi-spacecraft attitude system, ensuring that the consistency error converges to a sufficiently small domain within a fixed time, and that the upper bound of the convergence time is independent of the initial state. To address spacecraft uncertainties, a fuzzy weight update law is designed, reducing dependence on system model information and exhibiting adaptability and strong robustness.

[0007] This invention is implemented as follows: a multi-spacecraft attitude consistency fixed-time event triggering control method with asymmetric time-varying constraints, defining the following symbols: It is a three-dimensional identity matrix; for a vector and a constant , for , for ; It is the set of all 3-dimensional vectors, where each vector has real numbers as its components. It is the set of all 3×3 matrix; To describe the directed topology of information interaction among multiple spacecraft, , , Let them represent the set of spacecraft, the set of edges, and the adjacency matrix, respectively. Indicates the first The spacecraft can receive the first Information about a spacecraft, otherwise ; , is a leader association matrix, where Indicates the first A spacecraft can receive information from the leader; otherwise... ; The proposed technical solution to address the above-mentioned technical problems is as follows: Using the attitude angle model of a spacecraft with external disturbances and model uncertainties, a consistent attitude error model is established, and the system state and sampling time are initialized. The process is as follows: Establish the first The attitude angle model of the spacecraft is as follows: (1) in, , , , , , , It is the set of all 3-dimensional vectors, where each vector has real numbers as its components. It is the set of all 3×3 matrix vectors, where each vector component is a real number; the relevant definitions are shown in Table 1 below. Table 1 Definitions of symbols in a spacecraft attitude angle model

[0008] Define attitude tracking error Relative attitude error with adjacent spacecraft as follows (2) in Referring to the attitude angle, the direction cosine matrix is ​​defined as follows: , Then the angular velocity tracking error and relative angular velocity error for and ,in Reference attitude angular velocity; Define consistent attitude error for The consistent relative attitude error system can be obtained as follows: (3) in , , , , , From a practical engineering perspective, due to spacecraft mechanical limitations or mission space constraints, , , It is bounded; furthermore, external disturbances It is bounded. and It is about , A continuous function; therefore, it is possible and It is bounded; Step 2: Design the obstacle Lyapunov function, design a virtual controller using an inversion control strategy, design an event-triggered strategy, design a fixed-time continuous controller, and sample the fixed-time continuous controller according to the event-triggered strategy to obtain the control torque. The process is as follows: Define the Lyapunov function as for (4) in, , For time-varying boundaries, , ,variable Defined as , The error variable satisfies ; Differentiating (4), we get (5) in, This is a virtual error. for first derivative , , , , It is a virtual controller, and its expression is as follows: (6) (7) in, , , , , ; Substituting equation (6) into equation (5), we can obtain (8) Define Lyapunov functions for (9) in, , For time-varying boundaries, , ,variable Defined as , The error variable satisfies ; Differentiating equation (9), we get (10) in, , , , , It is the unknown uncertainty; This invention employs a fuzzy logic system to estimate uncertainty. , (11) in, It is the input quantity. To estimate the error, satisfy the following conditions: , It is an unknown positive constant. and These are the weight vector and basis function of the fuzzy logic system, respectively. Substituting (11) into (10), we get (12) in, , ; Design a continuous controller for (13) (14) in, , , , , , , , for The estimated value, Design weight estimate The update law is (15) in, , ; The event triggering strategy is designed as follows: (16) in, , It is a continuous controller The elements in It is a controller The elements in Let be the saturation threshold function, and its expression is: ,in, , ; In time period controller Keep as When event (16) is achieved, Start from Update: According to equation (16), substituting (13) into (12), we get (17) in, , , It is an unknown positive constant that satisfies , , Define the Lyapunov function as follows: for (18) Differentiating (18), we get (19) in, , , , ; For a constant ,when At that time, it can be concluded that (20) From equation (20), it can be concluded that the tracking error converges to a sufficiently small domain. Inside, satisfy (twenty one) Stabilization time satisfy Therefore, the system is stable over a fixed period of time.

[0009] The beneficial effects of this invention are as follows: An asymmetric fractional barrier Lyapunov function guarantees compliance with time-varying constraints for multiple spacecraft, while simultaneously solving the problem of excessively large control amplitudes related to large constraint boundaries in traditional logarithmic barrier Lyapunov functions. This allows the proposed method to handle both constrained and unconstrained scenarios. Furthermore, a saturation threshold event triggering strategy is designed. This strategy, by adjusting parameters, allows the multi-spacecraft system to select three different triggering strategies, enabling flexible changes in the transmission frequency of control signals and reasonable allocation of control bus resources. Compared to finite-time control, this invention designs a multi-spacecraft attitude consistency fixed-time event-triggered controller with asymmetric time-varying constraints, ensuring rapid response of the spacecraft system without violating state constraints. By constructing a weighted estimate update law, the dependence on system model information is reduced, eliminating the need for information on lumped uncertainties, including external disturbances, model uncertainties, and fuzzy approximation errors. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0011] Figure 1 The attitude angle tracking error diagrams for the three spacecraft are shown. Figure 2 The attitude angular velocity tracking error diagram for the three spacecraft; Figure 3 The consistency error and virtual error diagrams for spacecraft 1 are shown. Figure 4 The consistency error and virtual error diagrams for Spacecraft 2 are shown. Figure 5 The consistency error and virtual error diagrams for spacecraft 3 are shown. Figure 6 The diagram shows the trigger time intervals for control torque under different threshold parameters for three spacecraft. Figure 7 Control torque diagrams for fractional and logarithmic Lyapunov barrier functions; Figure 8 This is the control flowchart of the present invention. Detailed Implementation

[0012] 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 with reference to the accompanying drawings. 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.

[0013] The invention will now be further described with reference to the accompanying drawings.

[0014] Reference Figures 1-7 A method for triggering fixed-time event-driven control of attitude consistency among multiple spacecraft with asymmetric time-varying constraints, comprising the following steps: Step 1: Using the attitude angle model of the spacecraft with external disturbances and model uncertainties, establish a consistent attitude error model, and initialize the system state and sampling time. The process is as follows: Establish the first The attitude angle model of the spacecraft is as follows: (1) in, , , , , , , It is the set of all 3-dimensional vectors, where each vector has real numbers as its components. It is the set of all 3×3 matrix vectors, where each vector component is a real number; the relevant definitions are shown in Table 1 below. Table 1 Definitions of symbols in a spacecraft attitude angle model

[0015] Define attitude tracking error Relative attitude error with adjacent spacecraft as follows (2) in Referring to the attitude angle, the direction cosine matrix is ​​defined as follows: , Then the angular velocity tracking error and relative angular velocity error for and ,in Reference attitude angular velocity; Define consistent attitude error for The consistent relative attitude error system can be obtained as follows: (3) in , , , , , From a practical engineering perspective, due to spacecraft mechanical limitations or mission space constraints, , , It is bounded; furthermore, external disturbances It is bounded. and It is about , A continuous function; therefore, it is possible and It is bounded; Step 2: Design the obstacle Lyapunov function, design a virtual controller using an inversion control strategy, design an event-triggered strategy, design a fixed-time continuous controller, and sample the fixed-time continuous controller according to the event-triggered strategy to obtain the control torque. The process is as follows: Define the Lyapunov function as for (4) in, , For time-varying boundaries, , ,variable Defined as , The error variable satisfies ; Differentiating (4), we get (5) in, This is a virtual error. for first derivative , , , , It is a virtual controller, and its expression is as follows: (6) (7) in, , , , , ; Substituting equation (6) into equation (5), we can obtain (8) Define Lyapunov functions for (9) in, , For time-varying boundaries, , ,variable Defined as , The error variable satisfies ; Differentiating equation (9), we get (10) in, , , , , It is the unknown uncertainty; This invention employs a fuzzy logic system to estimate uncertainty. , (11) in, It is the input quantity. To estimate the error, satisfy the following conditions: , It is an unknown positive constant. and These are the weight vector and basis function of the fuzzy logic system, respectively. Substituting (11) into (10), we get (12) in, , ; Design a continuous controller for (13) (14) in, , , , , , , , for The estimated value, Design weight estimate The update law is (15) in, , ; The event triggering strategy is designed as follows: (16) in, , It is a continuous controller The elements in It is a controller The elements in Let be the saturation threshold function, and its expression is: ,in, , ; In time period controller Keep as When event (16) is achieved, Start from Update: According to equation (16), substituting (13) into (12), we get (17) in, , , It is an unknown positive constant that satisfies , , Define the Lyapunov function as follows: for (18) Differentiating (18), we get (19) in, , , , ; For a constant ,when At that time, it can be concluded that (20) From equation (20), it can be concluded that the tracking error converges to a sufficiently small domain. Inside, satisfy (twenty one) Stabilization time satisfy Therefore, the system is stable over a fixed period of time.

[0016] To verify the effectiveness of the proposed control method, this invention will use MATLAB to perform three simulations of attitude consistency control for uncertain spacecraft. First, given the... The parameters of the spacecraft's attitude system are: , , ; The desired angular velocity trajectory is , The constraint boundary is , , , The parameters for the virtual controller, continuous controller, adaptive update law, and event-triggered mechanism are as follows: , , , , , , , , , , , , .

[0017] The simulation results are shown in Figures 1-6. Figures 1 and 2 illustrate the tracking errors of the three spacecraft attitude angles, respectively. and angular velocity tracking error ,from Figure 1 and Figure 2 As can be seen, the attitude angles and angular velocities of the three spacecraft can quickly track the desired trajectory, demonstrating that the multi-spacecraft system can achieve rapid response. Figure 3-5 shows the consistency errors of the three spacecraft. and virtual error .from Figure 3-5 It can be seen that, due to the effect of the barrier Lyapunov function, the consistency error and virtual error of all spacecraft remain within the constraint boundaries, demonstrating the effectiveness of the invented fractional barrier Lyapunov function under strong constraints. Figure 6 shows the triggering time interval of the control torque for the three spacecraft. As can be seen from Figure 6, due to the selection of the threshold parameter... , , , , This results in different triggering effects for torque control in different dimensions, indicating that adjusting the parameters... and The proposed triggering strategy can be flexibly adjusted.

[0018] To demonstrate the superiority of the fractional-barrier Lyapunov function in the unconstrained case, a comparison was made between the invented fractional-barrier Lyapunov function and the traditional logarithmic-barrier Lyapunov function. In the comparative simulation, an excessively large constraint boundary was selected. This is in an approximately unconstrained state. The corresponding simulation results are as follows: Figure 7 As shown in Figure 7, the norms of the control torques for the three spacecraft under different obstacle Lyapunov functions are illustrated. Figure 7It is evident that the norm of the control torque using the fractional barrier Lyapunov function is significantly smaller than that using the logarithmic barrier Lyapunov function. This indicates that the invented fractional barrier Lyapunov function has a significant advantage over the traditional logarithmic barrier Lyapunov function when dealing with large constraint boundaries.

[0019] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. 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 multi-spacecraft cooperative tracking control method for transient performance enhancement, characterized in that, The steps are as follows: Step 1: Establish a consistent attitude error model through the attitude angle model of a spacecraft with external disturbance and model uncertainty, initialize the system state, and sample time, and the process is as follows: The attitude angle model of the first spacecraft is as follows （1） wherein , , , , , , is the set of all 3-dimensional vectors, where each vector has real components, is the set of all 3x3-dimensional matrices, where each vector has real components; Definitions of the symbols in the spacecraft attitude angle model: is the attitude angle; is the attitude angular velocity; is the Jacobian matrix; is the inertia matrix; is the known part of is the uncertain part of is the bounded external disturbance; is the control torque;​ Defining pose tracking error and relative attitude error with neighboring spacecraft As follows （2） wherein Referring to the orientation angle, the direction cosine matrix is defined as , , the angular velocity tracking error and the relative angular velocity error is and where is the reference attitude angular velocity; Defining a consistent pose error For A consistent relative pose error system is obtained as follows （3） wherein , , , , ， Step 2, design barrier Lyapunov function, design virtual controller by using inversion control strategy, design event-triggered strategy, design fixed-time continuous controller, sample the fixed-time continuous controller according to the event-triggered strategy to obtain the control torque The process is as follows: The Lyapunov function is defined as is （4） wherein , is a time-varying boundary, , , a variable is defined as , , the error variable satisfies ; Differentiate (4) to obtain （5） wherein is a virtual error, is a first derivative , , , , is a virtual controller, whose expression is as follows （6） （7） wherein , , , , ; Substitute equation (6) into equation (5) to obtain （8） Defining Lyapunov function is （9） wherein , is a time-varying boundary, , , variable is defined as , , the error variable satisfies ; Differentiate equation (9) to obtain （10） wherein , , , , is an unknown uncertainty; Designing a continuous controller To （13） ； （14） wherein , , , , , , , is an estimate of ; Design an event-triggered strategy as （16） wherein , is an element in a continuous controller , is an element in a controller , is a saturation threshold function expressed as wherein , ; In a time period , the controller is kept as , when the event (16) is reached, the update is started by .

2. The multi-spacecraft cooperative tracking control method for transient performance enhancement according to claim 1, wherein, Using a fuzzy logic system to estimate uncertainty , （11） wherein is an input quantity, is an estimation error, satisfying , is an unknown constant, and are a weight vector and a base function of the fuzzy logic system, respectively; Substitute equation (11) into equation (10) to obtain （12） wherein , .

3. The multi-spacecraft cooperative tracking control method for transient performance enhancement according to claim 1, wherein, Designing weight estimate values The update law is （15） wherein , .

4. The multi-spacecraft cooperative tracking control method for transient performance enhancement according to claim 1, wherein, According to equation (16), substitute equation (13) into equation (12) to obtain （17） wherein , , is an unknown positive constant satisfying , , ; define the Lyapunov function as is （18） Differentiate equation (18) to obtain （19） wherein , , , ; for a constant When it follows that, （20） From equation (20), it can be concluded that the tracking error converges to a sufficiently small region where the following equation is satisfied （21） settling time satisfies Thus, the system is fixed-time stable.

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