Neural network satellite formation flight control method
By combining radial basis function neural network and adaptive sliding mode control technology, the problems of external interference and model uncertainty in satellite formation flying are solved, high-precision and robust trajectory tracking and collision avoidance are achieved, and the system stability and mission execution efficiency are improved.
Patent Information
- Application Number
- CN202510907464.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-02
- Publication Date
- 2025-10-17
AI Technical Summary
Satellite formation flying faces external interference and inherent model uncertainty, which leads to insufficient system stability and accuracy, making it difficult to achieve efficient and reliable trajectory tracking and collision avoidance.
Using radial basis function neural network and adaptive sliding mode control technology, the control law with adaptive update rate is designed through the approximation ability of neural network and the robustness of sliding mode control. Combined with Lyapunov stability analysis, the stability and precise tracking of the system under external interference and uncertainty are ensured.
It improves the accuracy and robustness of satellite formation flying, enhances the adaptability and stability of the system, reduces the risk of collision, reduces computational complexity and energy consumption, and improves mission execution efficiency and real-time response speed.
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Figure CN120793229A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of aerospace technology, and is directly applied to the field of aerospace, high-precision formation flight control of spacecraft. BACKGROUND
[0002] The patent discloses solves the problems of external interference and internal model uncertainty in the process of satellite formation flight, and proposes a high-precision satellite formation flight control technology. The method combines a radial basis function neural network and an adaptive sliding mode control technology, and through the approximation ability of the neural network and the robustness of the sliding mode control, the adaptability of the system to interference and the tolerance of uncertainty are improved. Meanwhile, the stability of the closed-loop system is enhanced through online adaptive adjustment of the neural network weight, so that the reliability and efficiency under unknown dynamics and interference conditions are ensured. With the help of Lyapunov stability analysis, the stability of the system is ensured. Finally, the simulation results verify the effectiveness of the proposed adaptive control strategy. SUMMARY
[0003] In order to effectively solve the problem of satellite collision, the present application provides a high-precision neural network satellite formation control method.
[0004] The technical scheme adopted by the present application to solve the technical problems is as follows:
[0005] The neural network satellite formation flight control method of the present application comprises the following steps:
[0006] Step one, establish a satellite formation flight relative kinematics model, that is, establish the relative motion equation of two rigid spacecraft, namely the tracking star and the target star;
[0007] Step two, design a neural network adaptive sliding mode controller, define an error equation, design a sliding mode surface, so as to obtain a control law. Since the neural network has excellent function approximation ability, it is used for modeling a nonlinear function in the case of uncertainty. Considering the satellite under the influence of model uncertainty and external interference, the proposed control law can realize accurate tracking of the target position in a limited time, and under the control, the closed-loop system is stable, the tracking error is gradually convergent to zero. Finally, an adaptive update rate is obtained.
[0008] Step three, establish a Lyapunov equation and judge its stability
[0009] As a preferred embodiment, the specific implementation process of step one is as follows:
[0010] The relative motion equation of two rigid spacecraft, namely the tracking star s and the target star d, is established. In order to establish the relative motion equation of two rigid spacecraft, namely the tracking s and the target star d, as follows, Figure 1As shown, we set the following coordinate system: X, Y, Z represent the inertial coordinate system with the earth as the center, which is a Cartesian right-hand coordinate system, whose axes are X, Y, Z respectively; d, represents a local vertical, local horizontal (LVLH) reference coordinate system fixed at the target spacecraft mass center, the LVLH coordinate system takes the target star as the origin, X d axis along the spacecraft radial direction, Z d axis perpendicular to the orbital plane and pointing to the angular momentum direction, Y d axis and X d , Z d axis constitute a right-hand rectangular coordinate system.
[0011] In the formation flying phase, the satellites are regarded as particles. Under the influence of external disturbances, the nonlinear differential equations of the relative motion of the two satellites in the earth inertial coordinate system are
[0012]
[0013] Where, the relative position vector of the spacecraft X1= [x, y, z] T , is m; x, y, z represent the positions on the x-axis, y-axis and z-axis respectively; [u x , u y , u z ] is the control acceleration increment, with the unit of m / s 2 ; d = [d x d y d z ] T is the external disturbance velocity, represent the velocities on the x-axis, y-axis and z-axis respectively; represent the accelerations on the x-axis, y-axis and z-axis respectively. θ is the dimension angle of the target star.
[0014]
[0015] In the formula,
[0016]
[0017] As a preferred embodiment, the specific implementation process of step two is as follows:
[0018] First, define the error equation, which is the expectation of the relative position and velocity respectively; design the sliding mode surface to obtain the switching control rate;
[0019] Three hypothetical cases are proposed, Lyapunov functions are defined, and according to Lyapunov theorem, it can be proved that the system is globally asymptotically stable. Due to the excellent function approximation ability of neural network, it is often used to model nonlinear functions in dealing with uncertainty.
[0020] The error formula is:
[0021]
[0022] where X 1d X 2d are the desired relative position and velocity, respectively.
[0023] Substitute equation (2) into equation (1) to get The middle of equation (1) is:
[0024]
[0025] The sliding surface is designed as follows:
[0026]
[0027] where λ is a positive definite diagonal matrix, and the deviation on the sliding surface tends to zero when s→0.
[0028] The derivative of the sliding surface is:
[0029]
[0030] Let be equivalent to the switching control rate u sw =ρsgn(s) to get the controller:
[0031]
[0032] Assumption 1: The unknown system disturbance f has an upper bound ρ, such that ρ-|f|≥2ε, where ρ>0, 2ε>ε1+ε2, and ε is a very small positive number.
[0033] Define the Lyapunov function as:
[0034] V1=s T s≥0 (9)
[0035] Substitute equation (7) into the derivative of V1 to get:
[0036]
[0037] Substitute the control rate u into the above equation and get from assumption 1:
[0038]
[0039] Since ρ is the upper bound of the disturbance, we have s T (d-ρsgn(s))≤0, according to Lyapunov's theorem, it can be proved that the system is globally asymptotically stable.
[0040] Because of the excellent function approximation ability, neural networks are often used to model nonlinear functions in the presence of uncertainty. To better cope with uncertainty, we take
[0041] f = W *T h(x) + ε(x) (12)
[0042] where W *T ∈ R l×m is the ideal weight, l and m are the number of hidden layers and output layers, respectively, h(x) ∈ R l represents the activation function, and φ(x) is the radial basis function, then
[0043]
[0044] where h(x) = [hi(x) h2(x) · · · h n (x)], a i ∈ [a 11 … a 1l … a il ] represents the center of the neuron, and σ i ∈ R represents the width of the neuron.
[0045] Assumption 2: The neural network estimation error is bounded, i.e., ||ε|| ≤ ε * , and where ε * is a small positive quantity close to zero.
[0046] Assumption 3: The ideal weight W * is bounded and exists in a compact set.
[0047] ||W * || F ≤ W M (14)
[0048] where W M is a positive constant.
[0049] To reduce the chattering in the system, we decided to use RBF neural networks to approximate the nonlinear function and estimate the upper bound of the disturbance ρ, respectively.
[0050] From equations (12)-(13), we have
[0051] f(X) = W *T h(X) + ε1 (15)
[0052] ρ = w *T h(X) + ε2 (16)
[0053] where X represents the input of the neural network, W * and w* is the ideal weight of the neural network. Where h(X) is the radial basis function
[0054] Define the estimated variables of f(X) and d as follows:
[0055]
[0056] The designed neural network control rate is
[0057]
[0058] Theorem: Considering a satellite under the influence of model uncertainty and external interference, its motion equation is given by
[0059] (2) Description. The proposed control law (8) can achieve accurate tracking of the target position within a finite time, and under this control, the closed-loop system is stable and the tracking error converges to zero asymptotically. The adaptive update rate is as follows.
[0060]
[0061] Where, Θ 1, Θ2 is a positive definite symmetric matrix
[0062] As a preferred implementation method, the specific implementation process of step three is as follows:
[0063] Then the stability proof is performed:
[0064] Substitute equation (19) into have to
[0065]
[0066] In the formula
[0067] The estimated errors of f(X) and d are
[0068]
[0069] Define the Lyapunov function as
[0070]
[0071] Then take its derivative and we get:
[0072]
[0073] The present invention provides a neural network formation flight control method with significant beneficial effects. By introducing a neural network model, the method can effectively learn and approximate the complex nonlinear characteristics of the spacecraft system, thereby improving the position and trajectory tracking accuracy of the spacecraft during formation flight. At the same time, the neural network has self-learning and self-adaptive capabilities, and can maintain the stability and high-performance control effects of the system under adverse conditions such as external disturbances, system parameter uncertainty, and communication delay, thereby enhancing the robustness and adaptability of the system. In addition, by designing a suitable neural network structure and control strategy, the method realizes information sharing and collaborative control among multiple spacecraft, ensures the efficiency of formation flight, avoids collisions between spacecraft, reduces energy consumption, and prolongs the execution time of flight missions.
[0074] The present invention reduces the reliance on high-precision mathematical modeling, simplifies the complexity of the control algorithm through the online learning mechanism of the neural network, reduces the computational burden of the system, and is particularly suitable for resource-constrained flight control system platforms. In terms of real-time performance, the method utilizes the rapid response characteristics of the neural network to achieve rapid closed-loop feedback of the control system, shorten the error convergence time, and improve the system response speed. In addition, the neural network control strategy can be dynamically adjusted according to different flight mission objectives, adapt to multi-task requirements such as formation reorganization, path planning, obstacle avoidance, etc., and has flexible task switching capabilities. By optimizing the formation path and control strategy, the present invention further reduces system energy consumption and improves the economy and execution efficiency of the overall formation mission.
[0075] In summary, the present invention combines neural networks with flight formation control technology, which not only improves the system accuracy, robustness and real-time performance, but also overcomes the shortcomings of traditional control methods in nonlinear modeling, external disturbance suppression and complex calculations, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS
[0076] Figure 1 This is a simulation result diagram of a neural network satellite formation flight control method of the present invention.
[0077] Figure 2 This is a simulation result diagram of a neural network satellite formation flight control method of the present invention.
[0078] Figure 3 This is a simulation result diagram of a neural network satellite formation flight control method of the present invention.
[0079] Figure 4 This is a simulation result diagram of a neural network satellite formation flight control method of the present invention.
[0080] Figure 5 This is a simulation result diagram of a neural network satellite formation flight control method of the present invention.
[0081] Figure 6 A simulation result diagram of a neural network satellite formation flight control method of the present application.
[0082] Figure 7 A simulation result diagram of a neural network satellite formation flight control method of the present application.
[0083] Figure 8 A simulation result diagram of a neural network satellite formation flight control method of the present application.
[0084] Figure 8 A simulation result diagram of a neural network satellite formation flight control method of the present application.
[0085] Figure 9 A simulation result diagram of a neural network satellite formation flight control method of the present application.
[0086] Figure 10 A schematic diagram of relative motion of satellites of the present application.
[0087] Figure 11 A satellite formation trajectory tracking diagram.
[0088] Figure 12 A general flow chart of a neural network satellite formation flight control method of the present application DETAILED DESCRIPTION
[0089] The present application will be further described in detail below in combination with the drawings and examples.
[0090] A neural network satellite formation flight control method of the present application, firstly establishes a kinematic model, and secondly designs a neural network adaptive sliding mode control algorithm. Specifically, the following steps are included:
[0091] Step one, kinematic modeling
[0092] As shown in Figure 1 , two satellites d and s normally fly in orbit, at time t, satellite d intersects satellite s at a certain point in space, and the two satellites intersect. The position vector p of satellite d relative to satellite s is:
[0093] p = r1 - r2 (1)
[0094] Wherein, r1 is the geocentric vector of satellite d, with a unit of km; r2 is the geocentric vector of satellite s, with a unit of km.
[0095] In the formation flight phase, the satellite is regarded as a particle. Under the influence of external disturbance, the nonlinear differential equation of the relative motion of the two satellites in the earth inertial coordinate system is
[0096]
[0097] where X1= [x, y, z] is the relative position vector of the spacecraft T , in m; x, y, z denote the position in x, y, and z axes, respectively; [u x , u y , u z ] T is the control acceleration increment in m / s 2 ; d = [d x d y d z ] T is the external disturbance velocity, denote the velocity in x, y, and z axes, respectively; denote the acceleration in x, y, and z axes, respectively. θ is the target star dimension angle.
[0098]
[0099] Then
[0100]
[0101] where u = [u x u y u z ] T , d = [d x d y d z ] T
[0102] Step two, neural network adaptive sliding mode control algorithm design
[0103] The goal of the tracking control problem in the system is to find a control law so that the state trajectory X tracks the desired reference trajectory X d . Assuming that all system parameters are fully known, the design of the ideal adaptive neural network sliding mode controller of the system can be described step by step as follows:
[0104] Define the tracking error as:
[0105] e = X1- X 1d (5)
[0106] The derivative of the tracking error is:
[0107]
[0108] Design the sliding surface as follows:
[0109]
[0110] where λ is a positive definite diagonal matrix, and when s→0, the error on the sliding surface tends to zero.
[0111] The derivative of the sliding surface is:
[0112]
[0113] Let is equivalent to the switching control rate u sw = ρsgn(s) can be obtained:
[0114]
[0115] Define the Lyapunov function as:
[0116] V1= s T s≥0 (10)
[0117] The derivative of V1is:
[0118]
[0119] Design the neural network control rate:
[0120]
[0121] Finally, the stability is proved:
[0122] Define the Lyapunov function as
[0123]
[0124] Then the derivative is:
[0125]
[0126] The adaptive rate is brought into equation (14), and the following equation can be obtained:
[0127]
[0128] According to assumption 1, ε1+ε2-2ε<0, so
[0129] According to the Lyapunov stability theorem, the SMC control algorithm based on neural network designed can guarantee that the satellite system is asymptotically stable, and the proof is complete.
[0130] The initial orbit parameters and control parameters are shown in Table 1 and Table 2.
[0131] Table 1 Satellite orbit parameters
[0132] Orbital parameters Parameter values for satellite d Parameter values for satellite s Semi-major axis 7256.14 km 7256.14 km Eccentricity 0.001 0.001 Orbital inclination 53° 53° Argument of perigee 120° 120° Longitude of ascending node 30° 30° Mean anomaly 5° 5.004°
[0133] The mass of satellite s is 60kg, which is in the same orbit plane as satellite d, and the two satellites fly in front and back. To achieve the lap flying of the two satellites, the lap parameters are shown in Table 2
[0134] Table 2 Control strategy parameters
[0135] Flyby parameters Parameter values Flyby radius 40m Flyby face angle Θ x ]]> 90° Flyby face angle Θ z ]]> 30° Initial phase angle 0° Flyby period 180s
[0136] The numerical simulation is carried out by using matlab, and the simulation time is 500s, and the simulation results are shown in Figs. 1-4 Figures 1-3 It can be seen that the satellite tracking trajectory
[0137] Under the RBFNN sliding mode control, the expected trajectory is tracked at 25s, and the tracking control in a shorter time is realized.
[0138] In Figures 4-9 , the RBFNN control strategy well realizes the trajectory tracking and rapid stability, and the error position and velocity curves of three axes (x, y, z) are shown, which indicates that even if the actuator loses part of effectiveness and is subjected to saturation limitation, the system still remains stable near 0. In order to reduce the chattering in the system, it is decided to use the RBF neural network to respectively approximate the nonlinear function and estimate the upper bound of disturbance. The block diagram of the control system is shown in Fig. 5. Figure 12
[0139] Figure 11 The results show that the actual trajectory of the satellite formation can completely track the expected trajectory. Therefore, the proposed neural network adaptive sliding mode control scheme is effective for tracking control under the influence of model uncertainty and external disturbance.
[0140] In summary, from the simulation effect, the designed neural network adaptive sliding mode control technology well realizes the formation flying control of the satellite, and proves that the algorithm is effective and feasible.
[0141] The above only describes the preferred embodiments of the present application, and it should be noted that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.
Claims
1. A high-precision satellite formation flight control technology method, characterized in that: The following steps are involved: Step 1: Establish a satellite kinematic model; Step 2: Design of Neural Network Adaptive Sliding Mode Controller Step 3: Prove stability.
2. The high-precision satellite formation flying control technology method according to claim 1, characterized in that: The specific implementation process of step one is as follows: Two satellites s and d are flying normally in orbit. At time t, satellite s and satellite d intersect at a certain point in space and the two satellites collide. The position vector ρ of satellite s relative to satellite d is: ρ=r1-r2 (1) Where r1 is the Earth's center radius of satellite s, in km; r2 is the Earth's center radius of satellite d, in km; During the formation flight phase, the satellites are regarded as point masses. Under the influence of external disturbances, the nonlinear differential equation of the relative motion of the two satellites in the Earth's inertial coordinate system is: Among them, the relative position vector of the spacecraft is X1=[x,y,z] T , The unit is m; x, y, z represent the positions on the x-axis, y-axis and z-axis respectively; [u x ,u y ,u z ] T To control the acceleration increment, the unit is m / s 2 ; d = [d x d y d z ] T is the external disturbance velocity, Represents the speed on the x-axis, y-axis and z-axis respectively; are the accelerations on the x-axis, y-axis, and z-axis respectively. θ is the target star latitude angle. Where, 3. According to claim 2, a method for controlling satellite formation flight based on a neural network is characterized in that: The specific implementation process of step 2 is as follows: First, design the controller and define the error formula as Among them, X 1d ,X 2d are the expectations of relative position and velocity, respectively. Substitute (3) into middle Design the sliding surface as follows: Where λ is a positive definite diagonal matrix. When s→0, the deviation on the sliding surface tends to zero. The derivative of the sliding surface is: make Equivalent to the switching control rate u sw =ρsgn(s) and the controller can be obtained 4. The method for controlling satellite formation flight based on a neural network according to claim 3, characterized in that: The specific implementation process of step three is as follows: Assumption 1: The unknown system disturbance f has an upper bound ρ such that ρ-|f|≥2ε, where ρ>0, 2ε>ε1+ε2, and ε is a very small positive number. Define the Lyapunov function: V1=s T s≥0 (10) Substituting formula (8) into the derivative of V1, we can get Substitute the control rate u into the above formula and from assumption 1 Since ρ is the upper bound of the perturbation, According to Lyapunov's theorem, it can be proved that the system is globally asymptotically stable. Since neural networks have excellent function approximation capabilities, they are often used to model nonlinear functions in the case of uncertainty. f=W *T h(x)+ε(x) (13) Where W *T ∈R l×m is the ideal weight, l and m are the number of hidden layers and output layers respectively, is the neural network estimation error, h(x)∈R l Represents the activation function, taking h(x) as the radial basis function, then Where h(x)=[h1(x)h2(x)···h n (x)],a i ∈[a 11 …a 1l a il ] represents the center of the neuron, σ i ∈R represents the width of the neuron. Assumption 2: The neural network estimation error is bounded, that is, ||ε||≤ε * , and where ε * is a small positive quantity close to zero. Assumption 3: Ideal weight W * is bounded and exists in a compact set. ||In * || F ≤W M (15) Where W M is a positive constant. In order to reduce the jitter in the system, we decided to use RBF neural network to approximate the nonlinear function f and estimate the upper bound of interference ρ. From formula (13)-(14), we can see that f(X)=W *T h(X)+ε1 (16) ρ=w *T h(X)+ε2 (17) Where X represents the input of the neural network, W * and w * are the ideal weights of the neural network. Define the estimated variables of f(X) and d as The designed neural network control rate is Theorem: Consider a satellite under model uncertainty and external disturbances, whose motion equation is described by Equation (3). The proposed control law (9) can accurately track the target position within a finite time. Under this control, the closed-loop system is stable and the tracking error converges to zero asymptotically. The adaptive update rate is as follows. Where Θ1 and Θ2 are both positive definite symmetric matrices.