A cooperative guidance method for multiple aircraft

Abstract

This invention discloses a cooperative guidance method for multiple aircraft. This method employs an adaptive law to avoid the chattering phenomenon caused by the monotonically increasing adaptive parameters. At the same time, considering the specific terminal attack angle constraint of the intercepting target, an adaptive sliding mode guidance law based on fixed-time convergence non-singular terminal sliding mode is designed in the line-of-sight normal direction. While achieving the attack on the maneuvering target at a specific angle, the fixed convergence characteristic of the guidance system is guaranteed. Thus, this guidance law can efficiently achieve the cooperative attack on the maneuvering target by multiple aircraft at the desired angle, thereby completing this invention.

Description

Technical Field

[0001] This invention relates to a control method for multiple aircraft, and more specifically to a cooperative guidance method for multiple aircraft. Background Technology

[0002] With the rapid development of information and electronic technology, single aircraft are no longer able to effectively penetrate anti-missile defense systems to intercept and strike specific targets. The coordinated saturation attack mode of multiple aircraft swarms has become the main development direction for the future. The purpose of coordinated multi-aircraft attacks is to enable aircraft with different initial launch conditions to simultaneously hit the target, achieving a saturation attack. Depending on whether there is communication between the aircraft, the guidance law for coordinated attacks can be divided into closed-loop guidance laws that individually control the attack time of each aircraft, and open-loop guidance laws that distribute and adjust the attack time error among all missiles. Since open-loop coordinated guidance requires pre-determining the unified hit time of the missile swarm, it is often difficult to implement in engineering and lacks robustness to external disturbances. Therefore, it is necessary to study closed-loop coordinated guidance methods.

[0003] Thanks to the development of multi-agent consensus control theory, guidance laws for closed-loop systems based on different communication frameworks have been extensively studied in recent years. However, the design of specific guidance laws is extremely difficult, and there is currently no perfect method for synchronous hit control of multiple high-maneuverability aircraft.

[0004] Based on the above problems, the inventors have proposed a cooperative guidance method for multiple aircraft to address the shortcomings of existing research, so as to control multiple aircraft to hit the target simultaneously at a predetermined terminal angle. Summary of the Invention

[0005] To overcome the aforementioned problems, the inventors conducted intensive research and designed a cooperative guidance method for multiple aircraft. This method employs an adaptive law to avoid the chattering phenomenon caused by the monotonically increasing adaptive parameters. Simultaneously, considering the specific terminal attack angle constraint of the intercepting target, an adaptive sliding mode guidance law based on fixed-time convergence and non-singular terminal sliding mode is designed in the line-of-sight normal direction. While achieving the attack on the maneuvering target at a specific angle, the fixed convergence characteristic of the guidance system is guaranteed, thereby enabling the guidance law to efficiently achieve the cooperative attack on the maneuvering target by multiple aircraft at the desired angle, thus completing this invention.

[0006] Specifically, the purpose of this invention is to provide a cooperative guidance method for multiple aircraft, characterized in that, in this method, multiple aircraft each use the same guidance law to obtain an overload command, and control the aircraft to fly toward the target through the overload command, so that the multiple aircraft simultaneously hit the target at the desired angle.

[0007] The overload command includes an acceleration command in the direction of the missile-target line, an acceleration command in the pitch direction perpendicular to the direction of the missile-target line, and an acceleration command in the yaw direction perpendicular to the direction of the missile-target line.

[0008] Preferably, the guidance law obtains the overload command through the following equations (i), (ii), and (iii):

[0009]

[0010]

[0011]

[0012] Among them, a Mr,i This represents the acceleration command in the direction of the line connecting the target and the target of the i-th aircraft; a Mθ,i This represents the pitch acceleration command for the i-th aircraft; a Mφ,i This indicates the yaw acceleration command for the i-th aircraft.

[0013] x 1,i x 2,i x 3,i x 4,i x 5,i x 6,i Each represents a control variable of the i-th aircraft;

[0014] θ L,i Indicates the line-of-sight tilt angle of the i-th aircraft;

[0015] Represents θ L,i The derivative of the line-of-sight tilt angular velocity of the i-th aircraft;

[0016] φ L,i This represents the line-of-sight deflection angle of the i-th aircraft;

[0017] φ L,i The derivative of , i.e., the line-of-sight deflection angular velocity of the i-th aircraft;

[0018] α1, β1, α2, β2, α3, and β3 each represent design parameters, and their values ​​are all greater than zero.

[0019] η ij This represents the communication relationship between the i-th and j-th aircraft.

[0020] t f,j This indicates the time when the j-th aircraft predicted a successful interception of the target at time t;

[0021] t f,iThis represents the time when the i-th aircraft predicts a successful interception of the target at time t;

[0022] Indicates the desired timing of the terminal attack;

[0023] m r n r p r q r m θ n θ p θ q θ p φ q φ Both represent design parameters;

[0024] β θ This represents a design parameter, and its value is greater than zero.

[0025] β φ This represents a design parameter, and its value is greater than zero.

[0026] s θ,i and s φ,i Each represents a sliding mode variable;

[0027] Υ r,i Indicates adaptive parameters;

[0028] Υ θ,i Indicates adaptive parameters;

[0029] Υ φ,i This represents the adaptive parameter.

[0030] Among them, the adaptive parameter Υ r,i Through the Calculate the points to obtain;

[0031] The We obtain it through the following formula (iv):

[0032]

[0033] in, ε r μ r Each represents a design parameter, and all values ​​are normal numbers.

[0034] Among them, the adaptive parameter Υ θ,i Through the Calculate the points to obtain;

[0035] The Obtained through the following formula (5):

[0036]

[0037] in, ε θ μ θ Each represents a design parameter, and all values ​​are normal numbers.

[0038] Among them, the adaptive parameter Υ φ,i Through the Calculate the points to obtain;

[0039] The Obtained through the following formula (VI):

[0040]

[0041] in, ε φ μ φ Each represents a design parameter, and all values ​​are normal numbers.

[0042] Wherein, sliding mode variable s θ,i We obtain it through the following formula (VII):

[0043]

[0044] Wherein, sliding mode variable s φ,i Obtained through the following formula (8):

[0045]

[0046] Wherein, the control variable x of the i-th aircraft 1,i x 2,i x 3,i x 4,i x 5,i x 6,i The specific value is obtained through the following formula (IX);

[0047]

[0048] Where, r i This represents the distance between the i-th aircraft and the target;

[0049] This represents the speed of the i-th aircraft relative to the target;

[0050] θ Lf,i This represents the expected terminal line-of-sight tilt angle of the i-th aircraft;

[0051] φ Lf,i Let represent the expected terminal line-of-sight deflection angle of the i-th aircraft.

[0052] The communication relationship between the i-th and j-th aircraft is a. ijObtained through the following formula (x);

[0053]

[0054] Where, when the i-th spacecraft and the j-th spacecraft can communicate with each other, (υ i ,υ j )∈ε,(υ j ,υ i )∈ε.

[0055] The beneficial effects of this invention include:

[0056] (1) According to the cooperative guidance method for multiple aircraft provided by the present invention, the method is based on the fixed-time convergence first-order consistency method, the fixed-time convergence non-singular terminal sliding mode and the adaptive sliding mode to design a multi-missile cooperative saturation strike guidance law, and can achieve simultaneous hits on targets by multiple aircraft.

[0057] (2) According to the multi-vehicle cooperative guidance method provided by the present invention, for maneuvering targets, precise guidance under time constraints of multiple missiles is realized based on distributed cluster cooperation, and combined with the fixed-time convergence theory, the global fixed-time convergence of the closed-loop system is guaranteed for the finite-time problem of cooperative guidance.

[0058] (3) According to the cooperative guidance method for multiple aircraft provided by the present invention, the proposed adaptive sliding mode relaxes the requirements for target maneuver information, avoids the design of the observer, and simplifies the form of the guidance law;

[0059] (4) According to the cooperative guidance method for multiple aircraft provided by the present invention, a non-singular terminal sliding surface with fixed time convergence is adopted to realize terminal angle constraint, which provides a basis for improving the damage capability of aircraft. Attached Figure Description

[0060] Figure 1 The communication topology diagram in Example 1 is shown;

[0061] Figure 2-1 The flight trajectory diagram in Example 1 is shown;

[0062] Figure 2-2 The graph showing the change in the relative distance between the projectile and the target in Example 1 is shown.

[0063] Figure 2-3 The graph shows the change in the remaining flight time of the aircraft in Example 1;

[0064] Figure 2-4 The diagram shows the overload curve of the aircraft in the line-of-sight direction in Embodiment 1;

[0065] Figure 2-5The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 1;

[0066] Figure 2-6 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 1;

[0067] Figure 2-7 The graph showing the change in the tilt angle of the bullet's line of sight in Example 1 is shown.

[0068] Figure 2-8 The graph shows the variation curve of the bullet-eye line of sight deflection in Example 1;

[0069] Figure 3-1 The flight trajectory diagram in Example 1 is shown;

[0070] Figure 3-2 The graph showing the change in the relative distance between the projectile and the target in Example 1 is shown.

[0071] Figure 3-3 The graph shows the change in the remaining flight time of the aircraft in Example 1;

[0072] Figure 3-4 The diagram shows the overload curve of the aircraft in the line-of-sight direction in Embodiment 1;

[0073] Figure 3-5 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 1;

[0074] Figure 3-6 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 1;

[0075] Figure 3-7 The graph showing the change in the tilt angle of the bullet's line of sight in Example 1 is shown.

[0076] Figure 3-8 The graph shows the variation curve of the bullet-eye line of sight deflection in Example 1;

[0077] Figure 4-1 The flight trajectory diagram in Example 2 is shown;

[0078] Figure 4-2 The graph showing the change in the relative distance between the projectile and the target in Example 2 is shown.

[0079] Figure 4-3 The graph shows the change in the remaining flight time of the aircraft in Example 2;

[0080] Figure 4-4 The diagram shows the overload curve of the aircraft in the line-of-sight direction in Embodiment 2;

[0081] Figure 4-5 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 2;

[0082] Figure 4-6 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 2;

[0083] Figure 4-7 The graph showing the change in the tilt angle of the bullet's line of sight in Example 2 is shown.

[0084] Figure 4-8 The graph showing the change in the bullet-eye line-of-sight angle in Example 2 is shown.

[0085] Figure 5-1 The flight trajectory diagram in Example 2 is shown;

[0086] Figure 5-2 The graph showing the change in the relative distance between the projectile and the target in Example 2 is shown.

[0087] Figure 5-3 The graph shows the change in the remaining flight time of the aircraft in Example 2;

[0088] Figure 5-4 The diagram shows the overload curve of the aircraft in the line-of-sight direction in Embodiment 2;

[0089] Figure 5-5 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 2;

[0090] Figure 5-6 The diagram shows the overload curve of the aircraft in the line-of-sight normal direction in Embodiment 2;

[0091] Figure 5-7 The graph showing the change in the tilt angle of the bullet's line of sight in Example 2 is shown.

[0092] Figure 5-8 The graph shows the change in the bullet-eye line-of-sight angle in Example 2. Detailed Implementation

[0093] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0094] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0095] According to the present invention, a cooperative guidance method for multiple aircraft is provided, in which multiple aircraft each use the same guidance law to obtain an overload command, and control the aircraft to fly toward the target through the overload command, so that the multiple aircraft simultaneously hit the target at the desired angle.

[0096] In a preferred embodiment, the overload command includes an acceleration command in the direction of the missile-target line, a pitch acceleration command perpendicular to the direction of the missile-target line, and a yaw acceleration command perpendicular to the direction of the missile-target line.

[0097] Preferably, the guidance law obtains the overload command through the following equations (i), (ii), and (iii):

[0098]

[0099]

[0100]

[0101] Among them, a Mr,i This represents the acceleration command in the direction of the line connecting the target and the target of the i-th aircraft; a Mθ,i This represents the pitch acceleration command for the i-th aircraft; a Mφ,i This indicates the yaw acceleration command for the i-th aircraft.

[0102] x 1,i x 2,i x 3,i x 4,i x 5,i x 6,i Each represents a control variable of the i-th aircraft;

[0103] θ L,i This represents the line-of-sight tilt angle of the i-th aircraft; it is obtained through real-time detection and calculation using the gyroscope on the aircraft, GPS satellites, and the onboard computer.

[0104] Represents θ L,i The derivative of the line-of-sight tilt angular velocity of the i-th aircraft;

[0105] φ L,i This represents the line-of-sight deflection angle of the i-th aircraft; it is obtained through real-time detection and calculation using the gyroscope on the aircraft, GPS satellites, and the onboard computer.

[0106] φ L,i The derivative of , i.e., the line-of-sight deflection angular velocity of the i-th aircraft;

[0107] α1, β1, α2, β2, α3, and β3 all represent design parameters that are greater than zero; preferably, α1, β1, α2, β2, α3, and β3 all have a value of 10.

[0108] η ij This represents the communication relationship between the i-th and j-th aircraft.

[0109] t f,j This indicates the time when the j-th aircraft predicted a successful interception of the target at time t;

[0110] t f,i This represents the time when the i-th aircraft predicts a successful interception of the target at time t;

[0111] Indicates the desired timing of the terminal attack;

[0112] m r n r p r q r m r n θ p θ q θ p φ q φ Both represent design parameters, where m r >n r p r >q r m θ >n θ p θ >q θ p φ >q φ Preferably, m r m r The value is 9 for all n; preferably, n r n θ The value is 7; preferably, p r p θ p φ The value of q is 3; preferably, q r q θ q φ All values ​​are 5;

[0113] β θ This represents a design parameter that is greater than zero; preferably, the value is 2.

[0114] β φ This represents a design parameter that is greater than zero; preferably, the value is 2.

[0115] s θ,i and s φ,i Each represents a sliding mode variable;

[0116] Υ r,i Indicates adaptive parameters;

[0117] Υ θ,i Indicates adaptive parameters;

[0118] Υ φ,iThis represents the adaptive parameter.

[0119] In this application, the remaining flight time t is introduced. go As a coordinating variable,

[0120]

[0121] Furthermore, t f,j =t+t go,i ;

[0122] In a preferred embodiment, the adaptive parameter Y r,i Through the Calculate the points to obtain;

[0123] The We obtain it through the following formula (iv):

[0124]

[0125] in, ε r μ r Each represents a design parameter, and all values ​​are positive integers. Preferably... The value is 0.2, μ r The value is 0.1, ε r The value is ε r =0.001Y i (t), Υ i (t) represents the adaptive gain, which takes a value between 0 and 1, such as 0.1.

[0126] In a preferred embodiment, the adaptive parameter Y θ,i Through the Calculate the points to obtain;

[0127] The Obtained through the following formula (5):

[0128]

[0129] in, ε θ μ θ Each represents a design parameter, and all values ​​are positive integers. Preferably... The value is 0.2, μ θ The value is 0.1, ε θ The value is ε θ =0.001Y i (t).

[0130] In a preferred embodiment, the adaptive parameter Y φ,i Through the Calculate the points to obtain;

[0131] The Obtained through the following formula (VI):

[0132]

[0133] in, ε φ μ φ Each represents a design parameter, and all values ​​are positive integers. Preferably... The value is 0.2, μ φ The value is 0.1, ε φ The value is ε φ =0.001Y i (t).

[0134] In a preferred embodiment, the sliding mode variable s θ,i We obtain it through the following formula (VII):

[0135]

[0136] In a preferred embodiment, the sliding mode variable s φ,i Obtained through the following formula (8):

[0137]

[0138] In a preferred embodiment, the control variable x of the i-th aircraft 1,i x 2,i x 3,i x 4,i x 5,i x 6,i The specific value is obtained through the following formula (IX);

[0139]

[0140] Where, r i This represents the distance between the i-th aircraft and the target; it is obtained through the seeker on the aircraft.

[0141] This indicates that the speed of the i-th aircraft relative to the target is obtained through the seeker on the aircraft;

[0142] θ Lf,i This represents the expected terminal line-of-sight tilt angle of the i-th aircraft;

[0143] φ Lf,i Let represent the expected terminal line-of-sight deflection angle of the i-th aircraft.

[0144] In a preferred embodiment, the communication relationship between the i-th aircraft and the j-th aircraft is a ij Obtained through the following formula (x);

[0145]

[0146] Where, when the i-th spacecraft and the j-th spacecraft can communicate with each other, (υ i ,υ j )∈ε,(υ j ,υ i )∈ε.

[0147] Example 1

[0148] Configure the communication topology between the four aircraft as follows: Figure 1 As shown, the specific adjacency matrix can be represented as:

[0149]

[0150] All four aircraft use the same guidance law to obtain overload commands, and use these overload commands to control the aircraft to fly toward the target. Ultimately, multiple aircraft hit the target at the desired angle simultaneously.

[0151] The guidance law obtains the overload command through the following equations (i), (ii), and (iii):

[0152]

[0153]

[0154]

[0155] We obtain it through the following formula (iv):

[0156]

[0157] Obtained through the following formula (5):

[0158]

[0159] Obtained through the following formula (VI):

[0160]

[0161] Sliding mode variable s θ,i We obtain it through the following formula (VII):

[0162]

[0163] Sliding mode variable sφ,i Obtained through the following formula (8):

[0164]

[0165] The control variable x of the i-th aircraft 1,i x 2,i x 3,i x 4,i x 5,i x 6,i The specific value is obtained through the following formula (IX);

[0166]

[0167] The design parameters are taken as follows:

[0168] The values ​​of α1, β1, α2, β2, α3, and β3 are all 10; β θ and β φ The value is 2;

[0169] m r m r The value of n is 9; r n θ The value of p is 7. r p θ p φ The value of q is always 3; r q θ q φ All values ​​are 5;

[0170] and All values ​​are 0.2, μ r μ θ and μ φ The value is 0.1, ε r ε θ and ε φ All values ​​are 0.001Y i (t);

[0171] The initial conditions for the four aircraft are shown in Table 1 below:

[0172] Table 1 Initial Conditions

[0173]

[0174] The initial conditions for the objective are shown in Table 2 below:

[0175] Table 2 Initial conditions of the target

[0176]

[0177] The target is a stationary target.

[0178] Set terminal time The value is 30s; the simulation yields relevant information about the aircraft, such as... Figure 2-1 , Figure 2-2 , Figure 2-3 , Figure 2-4 , Figure 2-5 , Figure 2-6 , Figure 2-7 and Figure 2-8 As shown;

[0179] Set terminal time The value is 40s; the simulation yields relevant information about the aircraft, such as... Figure 3-1 , Figure 3-2 , Figure 3-3 , Figure 3-4 , Figure 3-5 , Figure 3-6 , Figure 3-7 and Figure 3-8 As shown.

[0180] Figure 2-1 and Figure 3-1 The flight trajectories of four aircraft under the designed guidance law are shown. The figure shows that the designed guidance law can accurately hit the target. Since the remaining flight time of the four aircraft is different at the initial moment, in order to make the remaining flight time consistent, the aircraft need to adjust their flight trajectory to adjust the remaining flight time. Therefore, in the initial stage, the curvature of the flight trajectory increases.

[0181] Figure 2-2 and Figure 3-2 The curves showing the relative distance between the missile and the target for the four aircraft are presented. As can be seen from the figure, the relative distance between the four aircraft can converge at the desired terminal time, meaning that all aircraft can hit the target at the desired time.

[0182] Figure 2-3 and Figure 3-3 The remaining flight time curves for the four aircraft are presented respectively. It can be seen that under the action of the designed guidance law, the remaining flight time will quickly converge to a uniform state. In addition, due to the effect of the expected terminal attack time error term in Equation (I), the designed guidance law can control the aircraft to strike the target at the expected terminal attack time.

[0183] Figure 2-4 , 2-5 2-6 and Figure 3-4 , 3-5 Figures 3-6 show the overload curves for the four aircraft in three directions. Figure 2-4 and Figure 3-4It can be seen that the overload command diverged at the attack terminal, which is a strange phenomenon caused by the relative distance between the missile and the target approaching zero. Considering the actual length and damage radius of the aircraft and the target, the phenomenon of terminal overload command divergence will not occur in actual applications.

[0184] Depend on Figure 2-5 , 2-6 and Figure 3-5 , 3-6 It can be seen that, under the influence of the desired angle error, the overload in the line-of-sight normal exhibits saturation in the initial guidance stage, fully utilizing the aircraft's overload capacity. The designed guidance law ensures rapid convergence of the missile-target line-of-sight angle error and the missile-target line-of-sight angular velocity. This guarantees that the aircraft attacks the target using a parallel approach strategy, which helps increase the control margin for offsetting external disturbances.

[0185] Figure 2-7 , 2-8 and Figure 3-7 , 3-8 The curves showing the changes in the missile's line-of-sight tilt angle and line-of-sight deflection angle are presented respectively. As can be seen from the figure, the designed guidance law can quickly and accurately control the aircraft to attack the target at the desired angle, which provides an important foundation for increasing the warhead's destructive effectiveness and meeting special operational requirements.

[0186] Example 2

[0187] The same aircraft and control method as in Example 1 are selected, as well as the same initial target position as in Example 1, but the target is a maneuvering target, and the target's velocity component along the inertial coordinate system is V. T =[100,0,0] T Its acceleration command is:

[0188]

[0189] Set terminal time The value is 30s; the simulation yields relevant information about the aircraft, such as... Figure 4-1 , Figure 4-2 , Figure 4-3 , Figure 4-4 , Figure 4-5 , Figure 4-6 , Figure 4-7 and Figure 4-8 As shown;

[0190] Set terminal time The value is 40s; the simulation yields relevant information about the aircraft, such as... Figure 5-1 , Figure 5-2 , Figure 5-3 , Figure 5-4 , Figure 5-5 , Figure 5-6 , Figure 5-7 and Figure 5-8 As shown.

[0191] Figure 4-1 and Figure 5-1 The flight trajectory curves of the aircraft under different time constraints are given. It can be seen that the designed guidance law can control four aircraft to accurately intercept maneuvering targets, which verifies the robustness of the designed guidance law to maneuvering targets.

[0192] Figure 4-2 and Figure 5-2 The curves showing the change in the relative distance between the four aircraft and the target are presented respectively. The designed guidance law ensures that the relative distance between the missile and the target converges at the desired moment.

[0193] Combination Figure 4-3 and Figure 5-3 The remaining flight time shows that even when engaging maneuvering targets, the designed guidance law can still ensure that all four aircraft intercept the target at the expected terminal moment, further proving the effectiveness of the designed guidance law.

[0194] Figure 4-4 , 4-5 4-6 and Figure 5-4 , 5-5 Figures 5-6 describe the overload curves of the aircraft in three directions. The target's maneuvering will cause the relative relationship between the missile and the target to change over time. In order to ensure that the missile attacks the target with a parallel approach strategy, the guidance system needs to compensate for the changes caused by the target's maneuvering in real time. Therefore, compared with attacking stationary targets, the overload curve of maneuvering targets shows a different trend.

[0195] Figure 4-7 , 4-8 and Figure 5-7 , 5-8 The curves showing the change in the line-of-sight angle of the missile and the target are presented. It can be seen that when the designed guidance law is applied to attacking maneuvering targets, the angle error can still be quickly converged, enabling the attack on the target at a specific angle.

[0196] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A cooperative guidance method for multiple aircraft, characterized in that, In this method, multiple aircraft each use the same guidance law to obtain overload commands, and use these overload commands to control the aircraft to fly toward the target. Ultimately, multiple aircraft simultaneously hit the target at the desired angle. The overload commands include acceleration commands in the direction of the missile-target line, pitch acceleration commands perpendicular to the direction of the missile-target line, and yaw acceleration commands perpendicular to the direction of the missile-target line. The guidance law obtains the overload command through the following equations (i), (ii), and (iii): Among them, a Mr,i This represents the acceleration command in the direction of the line connecting the target and the target of the i-th aircraft; a Mθ,i This represents the pitch acceleration command for the i-th aircraft; a Mφ,i This indicates the yaw acceleration command for the i-th aircraft. x 1,i x 2,i x 3,i x 4,i x 5,i x 6,i Each represents a control variable of the i-th aircraft; θ L,i Indicates the line-of-sight tilt angle of the i-th aircraft; Represents θ L,i The derivative of the line-of-sight tilt angular velocity of the i-th aircraft; φ L,i This represents the line-of-sight deflection angle of the i-th aircraft; φ L,i The derivative of , i.e., the line-of-sight deflection angular velocity of the i-th aircraft; α1, β1, α2, β2, α3, and β3 each represent design parameters, and their values ​​are all greater than zero. η ij This represents the communication relationship between the i-th and j-th aircraft. t f,j This indicates the time when the j-th aircraft predicted a successful interception of the target at time t; t f,i This indicates the time when the i-th aircraft predicts a successful interception of the target at time t; Indicates the desired timing of the terminal attack; m r n r p r q r m θ n θ p θ q θ p φ q φ Both represent design parameters; β θ This represents a design parameter, and its value is greater than zero. β φ This represents a design parameter, and its value is greater than zero. s θ,i and s φ,i Each represents a sliding mode variable; Υ r,i Indicates adaptive parameters; Υ θ,i Indicates adaptive parameters; Υ φ,i This represents the adaptive parameter.

2. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, Adaptive parameter Υ r,i Through the Calculate the points to obtain; The Obtained through the following formula (iv): in, ε r μ r Each represents a design parameter, and all values ​​are normal numbers.

3. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, Adaptive parameter Υ θ,i Through the Calculate the points required; The Obtained through the following formula (5): in, ε θ μ θ Each represents a design parameter, and all values ​​are normal numbers.

4. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, Adaptive parameter Υ φ,i Through the Calculate the points to obtain; The Obtained through the following formula (VI): in, ε φ μ φ Each represents a design parameter, and all values ​​are normal numbers.

5. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, Sliding mode variable s θ,i We obtain it through the following formula (VII):

6. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, Sliding mode variable s φ,i Obtained through the following formula (8):

7. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, The control variable x of the i-th aircraft 1,i x 2,i x 3,i x 4,i x 5,i x 6,i The specific value is obtained through the following formula (IX); Where, r i This represents the distance between the i-th aircraft and the target; This represents the speed of the i-th aircraft relative to the target; θ Lf,i This represents the expected terminal line-of-sight tilt angle of the i-th aircraft; φ Lf,i Let represent the expected terminal line-of-sight deflection angle of the i-th aircraft.

8. The cooperative guidance method for multiple aircraft according to claim 1, characterized in that, The communication relationship between the i-th and j-th aircraft is η ij Obtained through the following formula (x); Where, when the i-th spacecraft and the j-th spacecraft can communicate with each other, (υ i ,υ j )∈ε,(υ j ,υ i )∈ε.

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