A multi-missile space-time cooperative guidance method

Abstract

The application discloses a multi-missile time-space cooperative guidance method, which comprises the following steps: 1) establishing a guidance motion dynamics model of a missile intercepting a target in a three-dimensional space; 2) calculating a guidance time consistency error through information interaction among the missiles, and designing a line-of-sight direction acceleration control input as a control quantity for coordinating the attack time of the missiles; and 3) designing a bottom-layer missile guidance law, i.e. a line-of-sight normal control input, for controlling the missiles to intercept a maneuvering target at an expected line-of-sight angle. The application establishes a time-space cooperative guidance control of multiple missiles intercepting the same maneuvering target in the three-dimensional space based on a guidance time estimation method and a line-of-sight angle constraint, and can truly reflect the relative motion relationship among the multiple missiles and the target and the remaining time of the terminal guidance of the missiles.

Description

Technical Field

[0001] This invention relates to aircraft control technology, and more particularly to a multi-missile spatiotemporal coordinated guidance method. Background Technology

[0002] Unlike traditional guidance, in multi-missile cooperative guidance, the missiles can communicate and coordinate with each other during flight, exhibiting specific tactical motion patterns. This is especially true when engaging moving targets, placing higher demands on the performance of the cooperative guidance law. From a fundamental theoretical perspective, analysis of existing literature on multi-missile cooperative guidance technology reveals that current research, both domestically and internationally, is based on the following two guidance theories:

[0003] (1) Open-loop control method based on independent guidance. The essential characteristic of independent cooperative guidance is that the coordination information relies solely on its own state information, and the attack time or angle is pre-set for each missile to achieve coordinated attack by multiple missiles. However, in this guidance process, there is no dynamic information exchange between the missiles, and their respective state information cannot be perceived and utilized by other missiles. Therefore, this is an open-loop control method.

[0004] (2) Closed-loop control method based on cooperative guidance. Compared to the first method, the coordination information of each missile incorporates not only its own state information but also the state information of adjacent or all missiles participating in cooperative combat. This guidance method does not require pre-setting the guidance time. Instead, during the guidance process, missiles continuously exchange information with each other through a communication network and adjust their respective attack times according to the cooperative strategy, ultimately achieving consistency in attack time and possessing the basis for autonomous cooperation. However, the cooperative guidance model suffers from modeling errors and the instability of cooperative guidance due to external interference. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a multi-missile spatiotemporal coordinated guidance method to address the deficiencies in the prior art.

[0006] The technical solution adopted by this invention to solve its technical problem is: a multi-missile spatiotemporal cooperative guidance method, comprising the following steps:

[0007] 1) Establish a three-dimensional guidance motion dynamics model for missile interception targets;

[0008]

[0009]

[0010]

[0011] Where r is the relative distance between the missile and the target, qε Represents the angle of view, q β Represents the angle of deflection, a T =[a Tr ,a Tε ,a Tβ ] T Let a be the target acceleration vector projected onto the line-of-sight coordinate system in three directions. M =[a Mr ,a Mε ,a Mβ ] T Let be the missile acceleration vectors projected onto the line-of-sight coordinate system in three directions;

[0012] 2) Through information exchange between missiles, calculate the guidance time consistency error and design the control input a for line-of-sight acceleration. Mr It is used as a control quantity to coordinate the missile's strike time;

[0013] 2.1) Establish the state equations for the missile's three-dimensional cooperative terminal guidance model;

[0014]

[0015] Among them, t go The terminal guidance remaining time for a missile refers to the time required for the missile to hit its target at the current moment, as given by the formula... Estimate the state variables in the state equation as follows: Where, q εd ,q βd These represent the desired missile-target line-of-sight tilt angle and line-of-sight deflection angle during the terminal guidance phase, respectively; the subscript i indicates the i-th missile.

[0016]

[0017]

[0018]

[0019] a Mq For the acceleration input in the line-of-sight direction, a Mr The acceleration input is in the line-of-sight direction, and This represents the total interference in the line-of-sight direction. This represents the total interference caused by the target's acceleration and external disturbances along the line-of-sight direction.

[0020] 2.2) By controlling the direction of the line of sight, input a Mri The design involves coordinating the remaining time of each missile to ensure that the remaining time of each missile is consistent, thereby achieving time coordination.

[0021] Let t be the current time, t goi (i = 1, 2, 3, ..., n) represents the remaining time of final guidance for the i-th missile. Therefore, the predicted guidance time for the i-th missile is:

[0022] t fi =t+t goi (5)

[0023] For t fi Differentiation yields a new state equation along the line of sight:

[0024]

[0025]

[0026] Among them, the state variables are q εi Represents the angle of view, q βi Represents the angle of deflection, a Tri To interfere with the target's acceleration in the line of sight, a Mri The missile acceleration input is the line-of-sight direction of the target; t goi Represents the remaining guidance time for the missile;

[0027] Design the following disturbance observer to estimate the target acceleration a. Tri ;

[0028]

[0029] In the formula:

[0030] z 1i The estimated value representing the relative velocity between the missile and the target.

[0031] z 2i This represents an estimate of the target acceleration along the line of sight.

[0032] z ki This represents an estimate of the derivative of the target acceleration along the line of sight. Where k = 3, ..., m+1;

[0033] parameters of the interference observer The selection rules are as follows:

[0034] (1)l k and Each value is l k =kl0-(k-1) and in It is a small value;

[0035] (2) Gain value κ k and It is a positive number and satisfies the polynomial y. m+1 +κ1y m +…+κ m y+κ m+1 and It is a Hurwitz polynomial;

[0036] (3) η is a positive constant and satisfies

[0037] The convergence time range of the disturbance observer can be given by the following inequality:

[0038]

[0039] Where τ = 1 - l0, For any Q h >0, symmetric matrix P h Satisfying the Lyapunov equation P h B h +B h T P h =-Q h , (h=1,2), matrix B h It is given by the following formula:

[0040]

[0041] Define the guidance time consistency error between missiles as:

[0042]

[0043] Based on the designed fixed-time disturbance observer and state equation, the control input command in the line-of-sight direction is designed as follows:

[0044]

[0045] in, This refers to the target acceleration interference along the line-of-sight direction observed by the interference observer. Where α > 0, β > 0, 0 < p < 1, q > 1.

[0046] 3) Design the underlying missile guidance law, namely the line-of-sight upward control input, to control each missile to intercept the maneuvering target at the desired line-of-sight angle, control the relative line-of-sight angle error between the missile and the target within the preset performance boundary, and enable multiple missiles to complete the attack on the target under the action of the guidance law.

[0047] A performance function with fixed-time convergence is selected, which allows the system state to achieve a predetermined tracking performance within a fixed time. Its expression is as follows:

[0048]

[0049]

[0050] Where ρ0 is a constant, representing the initial value of the performance function, ρ ∞ The constant T represents the preset upper bound of the steady-state error, and the decay rate of ρ(t) is the lower bound of the convergence rate of the tracking error e(t). f For ρ(t) to converge to ρ ∞ The maximum allowable convergence time, c, affects the convergence speed of the performance function, and its value satisfies 0 < ρ. ∞ <|e i (0)|<ρ0,0<T f <∞, c>1. Therefore, for a performance function that converges in a fixed time, it means that the tracking error will converge strictly within the performance envelope, and the performance function can converge to any expected tracking accuracy within a specified time.

[0051] Differentiating the performance function ρ(t) gives:

[0052]

[0053] in

[0054] The designed error function after transformation is as follows:

[0055]

[0056] Where k h >0, 0≤δ≤1, ρ(t) is a performance function that converges in a fixed time. This is because it satisfies the inequality 0<ρ ∞ <|e i Since (0)|<ρ0, h(0) exists, and the derivative of the error function h(t) is:

[0057]

[0058] To ensure the system tracking error meets the specified performance, it can be seen that since h(0) exists, it is only necessary to ensure that h(t) is bounded during the system convergence process. It is known that when h(t) is bounded, since |e(0)|<ρ(t), we have |e|≠ρ(t) and |e|≠δρ(t), which means that the system tracking error e will not exceed the preset convergence curve. Therefore, the state constraint problem of nonlinear system tracking control can be transformed into a boundedness problem of the error function h(t), and the controller below will be designed based on this principle.

[0059] Since the guidance law in the line-of-sight direction is the local guidance law of each missile, and all members are equal, for ease of writing, the subscript 'i' is not considered, and a single missile is selected for the design of acceleration commands. Based on the model established above, the state variable e1 = q is defined. ε -q εd , e2 = q β -q βd , Where q εd and q βd These are the desired terminal line-of-sight tilt angle and line-of-sight deflection angle, respectively. Therefore, the guidance state equation for a single missile can be obtained as follows:

[0060]

[0061] Combining the missile guidance model and preset performance control, it can be seen that the guidance law based on preset performance mainly controls the relative line-of-sight angle error between the missile and the target within the preset performance boundary by designing the control input in the line-of-sight direction, enabling multiple missiles to complete their attack on the target under the action of the guidance law. Based on the previous analysis, the control objective can be expressed by the following inequality:

[0062]

[0063] The sliding surface is designed using the designed error transformation function as follows:

[0064]

[0065] Where k1>0, k2>0, λ1>0, λ2>0 are the parameters to be designed, and h1 and h2 are the error functions of the state variables e1 and e2 based on the design, respectively;

[0066] Differentiating with respect to the sliding surface, we get:

[0067]

[0068] Based on the sliding mode control method, the preset performance guidance law and adaptive law are designed as follows:

[0069]

[0070] u ε ,u β For equivalent control input:

[0071]

[0072] The adaptive law is:

[0073]

[0074] Where k3>0, k4>0, and μ≥1 are selected adaptive constants. To interfere with the upper boundary The estimated value.

[0075] The beneficial effects of this invention are:

[0076] 1. Based on the guidance time estimation method and line-of-sight angle constraint, this invention establishes a time-space coordinated guidance and control system for multiple missiles to intercept the same maneuvering target in three-dimensional space. It can truly reflect the relative motion relationship between each missile and the target, as well as the remaining time of the missile's terminal guidance.

[0077] 2. A fixed-time convergence interference observer was designed, which can make the remaining guidance time of multiple missiles tend to be consistent within a preset fixed time, ensuring that the flight control system has higher control accuracy, faster convergence speed and stronger robustness, and effectively enhancing the control performance of the system. Attached Figure Description

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0079] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0080] Figure 2 This is a schematic diagram of the three-dimensional strike relationship between missile targets according to an embodiment of the present invention;

[0081] Figure 3 This is a schematic diagram of the geometric relationship of the three-dimensional cooperative guidance model in an embodiment of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0083] like Figure 1 As shown, a multi-missile spatiotemporal cooperative guidance method includes the following steps:

[0084] 1) Establish a three-dimensional guidance motion dynamics model for missile interception targets;

[0085]

[0086]

[0087]

[0088] Where r is the relative distance between the missile and the target, qε Represents the angle of view, q β Represents the angle of deflection, a T =[a Tr ,a Tε ,a Tβ ] T Let a be the target acceleration vector projected onto the line-of-sight coordinate system in three directions. M =[a Mr ,a Mε ,a Mβ ] T Let be the missile acceleration vectors projected onto the line-of-sight coordinate system in three directions;

[0089] For the problem of missile striking a moving target in three-dimensional space, the geometric relationship between the missile and the target is as follows: Figure 2 As shown in the figure, the missile represents the missile's center of mass, the target represents the target's center of mass, Oxyz is the reference inertial coordinate system, Ox4y4z4 is the line-of-sight coordinate system, and the origin O is located at the missile's center of mass.

[0090] 2) Through information exchange between missiles, calculate the guidance time consistency error and design the control input a for line-of-sight acceleration. Mr It is used as a control quantity to coordinate the missile's strike time;

[0091] Considering a scenario where multiple missiles strike the same maneuvering target in three-dimensional space, the geometric relationship is illustrated in the diagram below. Figure 3 As shown;

[0092] Establish the state equations for a three-dimensional cooperative terminal guidance model of a missile;

[0093]

[0094] Among them, t go The terminal guidance remaining time for a missile refers to the time required for the missile to hit its target at the current moment, as given by the formula... Estimate the state variables in the state equation as follows: x3=[q ε -q εd ,q β -q βd ] T , Where, q εd ,q βd These represent the expected line-of-sight tilt angle and line-of-sight deflection angle during the terminal guidance phase, respectively.

[0095]

[0096]

[0097] For the acceleration input in the line-of-sight direction, a Mr The acceleration input is in the line-of-sight direction, and This represents the total interference in the line-of-sight direction.

[0098] This represents the total disturbance caused by the target's acceleration and external interference along the line-of-sight direction.

[0099] By controlling the direction of the line of sight, input a Mri The design coordinates the remaining time of each missile to ensure that the remaining time of each missile is consistent, thereby achieving time coordination.

[0100] Let t be the current time, t goi (i = 1, 2, 3, ..., n) represents the remaining time of final guidance for the i-th missile. Therefore, the predicted guidance time for the i-th missile is:

[0101] t fi =t+t goi (5)

[0102] It can be seen that to achieve simultaneous interception, the prediction guidance time t of all missiles needs to be guaranteed. fi The convergence to uniformity occurs before the missile hits the target. Therefore, for t... fi Differentiation yields a new state equation along the line of sight:

[0103]

[0104]

[0105] Among them, the state variables are q εi Represents the angle of view, q βi Represents the angle of deflection, a Tri To interfere with the target's acceleration in the line of sight, a Mri This is the missile acceleration input along the target's line of sight. goi This represents the remaining guidance time for the missile. For the above system, the following jamming observer is designed to estimate the target acceleration 'a'. Tri ;

[0106]

[0107] In the formula:

[0108] z 1i The estimated value representing the relative velocity between the missile and the target.

[0109] z 2i This represents an estimate of the target acceleration along the line of sight.

[0110] z ki This represents an estimate of the derivative of the target acceleration along the line of sight. k = 3, ..., m+1;

[0111] parameters of the interference observer The selection rules are as follows:

[0112] (1)l k and Each value is l k =kl0-(k-1) and in It is a small value;

[0113] (2) Gain value κ k and It is a positive number and satisfies the polynomial y. m+1 +κ1y m +…+κ m y+κ m+1 and It is a Hurwitz polynomial;

[0114] (3) η is a positive constant and satisfies

[0115] The convergence time range of the disturbance observer can be given by the following inequality:

[0116]

[0117] Where τ = 1 - l0, For any Q h >0, symmetric matrix P h Satisfying the Lyapunov equation P h B h +B h T P h =-Q h , (h=1,2), matrix B h It is given by the following formula:

[0118]

[0119] Next, in order to design the time coordination law for multiple missiles, the guidance time consistency error between missiles is defined as:

[0120]

[0121] Because t fi =t+tgoi Guidance timing consistency error can also be caused by get.

[0122] Based on the designed fixed-time disturbance observer and state equation, the control input command along the line of sight is designed as follows:

[0123]

[0124] in, This refers to the target acceleration interference along the line-of-sight direction observed by the interference observer. Where α > 0, β > 0, 0 < p < 1, q > 1.

[0125] 3) Design the underlying missile guidance law, namely the line-of-sight upward control input, to control each missile to intercept the maneuvering target at the desired line-of-sight angle;

[0126] A performance function with fixed-time convergence is selected, which allows the system state to achieve a predetermined tracking performance within a fixed time. Its expression is as follows:

[0127]

[0128]

[0129] Where ρ0 is a constant, representing the initial value of the performance function, ρ ∞ The constant T represents the preset upper bound of the steady-state error, and the decay rate of ρ(t) is the lower bound of the convergence rate of the tracking error e(t). f For ρ(t) to converge to ρ ∞ The maximum allowable convergence time, c, affects the convergence speed of the performance function, and its value satisfies 0 < ρ. ∞ <|e i (0)|<ρ0,0<T f <∞, c>1. Therefore, for a performance function that converges in a fixed time, it means that the tracking error will converge strictly within the performance envelope, and the performance function can converge to any expected tracking accuracy within a specified time.

[0130] Differentiating the performance function ρ(t) gives:

[0131]

[0132] in,

[0133] The designed error function after transformation is as follows:

[0134]

[0135] Where k h>0, 0≤δ≤1, ρ(t) is a performance function that converges in a fixed time. This is because it satisfies the inequality 0<ρ ∞ <|e i Since (0)|<ρ0, h(0) exists, and the derivative of the error function h(t) is:

[0136]

[0137] To ensure the system tracking error meets the specified performance, it can be seen that since h(0) exists, it is only necessary to ensure that h(t) is bounded during the system convergence process. It is known that when h(t) is bounded, since |e(0)|<ρ(t), we have |e|≠ρ(t) and |e|≠δρ(t), which means that the system tracking error e will not exceed the preset convergence curve. Therefore, the state constraint problem of nonlinear system tracking control can be transformed into a boundedness problem of the error function h(t), and the controller below will be designed based on this principle.

[0138] Since the guidance law in the line-of-sight direction is the local guidance law of each missile, and all members are equal, for ease of writing, the subscript 'i' is not considered, and a single missile is selected for the design of acceleration commands. Based on the model established above, the state variable e1 = q is defined. ε -q εd , e2 = q β -q βd , Where q εd and q βd These are the desired terminal line-of-sight tilt angle and line-of-sight deflection angle, respectively. Therefore, the guidance state equation for a single missile can be obtained as follows:

[0139]

[0140] Combining the missile guidance model and preset performance control, it can be seen that the guidance law based on preset performance mainly controls the relative line-of-sight angle error between the missile and the target within the preset performance boundary by designing the control input in the line-of-sight direction, enabling multiple missiles to complete their attack on the target under the action of the guidance law. Based on the previous analysis, the control objective can be expressed by the following inequality:

[0141]

[0142] The sliding surface is designed using the designed error transformation function as follows:

[0143]

[0144] Where k1>0, k2>0, λ1>0, λ2>0 are the parameters to be designed, and h1 and h2 are the error functions of the state variables e1 and e2 based on the design, respectively;

[0145] Differentiating with respect to the sliding surface, we get:

[0146]

[0147] Based on the sliding mode control method, the preset performance guidance law and adaptive law are designed as follows:

[0148]

[0149] u ε ,u β For equivalent control input:

[0150]

[0151] The adaptive law is:

[0152]

[0153] Where k3>0, k4>0, and μ≥1 are selected adaptive constants. To interfere with the upper boundary The estimated value.

[0154] Because of the presence of a sign function, the designed guidance law is not continuous, leading to chattering, a phenomenon that can negatively impact practical engineering applications. To address this problem, the boundary layer method is typically used, replacing the sign function with a continuous saturation function. The specific form of the saturation function is as follows:

[0155]

[0156] Where σ > 0.

[0157] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A multi-missile spatiotemporal coordinated guidance method, characterized in that, Includes the following steps: 1) Establish a three-dimensional guidance motion dynamics model for missile interception targets; ； ； ； in, The relative distance between the missile and the target. Represents the angle of view. Represents the angle of view. These are the target acceleration vectors projected onto the line-of-sight coordinate system in three directions. Let be the missile acceleration vectors projected onto the line-of-sight coordinate system in three directions; 2) Through information exchange between missiles, the guidance time consistency error is calculated, and the control input of line-of-sight acceleration is designed as a control quantity to coordinate the missile's strike time; 2.1) Establish the state equations for the three-dimensional cooperative terminal guidance model of the missile; in, The terminal guidance remaining time for a missile refers to the time required for the missile to hit its target at the current moment, as given by the formula... Estimate the state variables in the state equation as follows: , ,in, These represent the desired missile-target line-of-sight tilt angle and line-of-sight deflection angle during the terminal guidance phase, respectively; the subscript i indicates the i-th missile. ， ， ， Input the acceleration along the line-of-sight direction. The acceleration input is in the line-of-sight direction, and This represents the total interference in the line-of-sight direction. This represents the total interference caused by the target's acceleration and external disturbances along the line-of-sight direction. 2.2) By controlling the input of the line of sight direction The design involves coordinating the remaining time of each missile to ensure that the remaining time of each missile is consistent, thereby achieving time coordination. 3) Design the underlying missile guidance law, i.e. the line-of-sight upward control input, to control each missile to intercept the maneuvering target at the desired line-of-sight angle; The design error function is as follows: Among them, parameters , A performance function that converges in a fixed time. Error function The derivative is: Define state variables , , , ,in and Let these be the desired terminal line-of-sight tilt angle and line-of-sight deflection angle, respectively. Then, the guidance state equation for a single missile is: By designing the control input along the line-of-sight direction, the relative line-of-sight angle error between the missile and the target is controlled within a preset performance boundary, enabling multiple missiles to complete their attack on the target under the guidance law. The control objective constraint is expressed by the following inequality: ； The sliding surface is designed using the designed error transformation function as follows: in, For the design parameters of the sliding surface, These are the state variables based on the design. The error function; Differentiating with respect to the sliding surface, we get: Based on the sliding mode control method, the preset performance guidance law and adaptive law are designed as follows: Equivalent control inputs for line-of-sight tilt angle and line-of-sight deflection angle: ； The adaptive law is: in, , The selected adaptive constant, To interfere with the upper boundary The estimated value.

2. The multi-missile spatiotemporal coordinated guidance method according to claim 1, characterized in that, In step 2.2), the control input for the line-of-sight direction. The design will be carried out as follows: make For the current moment, , i=1,2,3…,n; is the th The remaining time of the final guidance of the missile, then the... The predicted guidance time for each missile is: right Differentiation yields a new state equation along the line of sight: Among them, the state variables are , Represents the angle of view. Represents the angle of view. Acceleration interference for targets in the line of sight of the projectile. The missile's acceleration input is the direction of the target's line of sight; Represents the remaining guidance time for the missile; Design the following disturbance observer to estimate the target acceleration. ; In the formula: The estimated value representing the relative velocity between the missile and the target. ; This represents an estimate of the target acceleration along the line of sight. ; This represents an estimate of the derivative of the target acceleration along the line of sight. ,in, ; Define the guidance time consistency error between missiles as: Based on the designed fixed-time disturbance observer and state equation, the control input command in the line-of-sight direction is designed as follows: in, To interfere with the target acceleration interference along the line of sight observed by the interference observer, in the formula... , .

3. The multi-missile spatiotemporal coordinated guidance method according to claim 2, characterized in that, In step 2.2), the parameters of the interference observer k=1,2,…m+1; the selection rules are as follows: (1) and The values ​​are respectively and ,in , , It is a small value; (2) Gain value and It is a positive number and satisfies the polynomial. and It is a Hurwitz polynomial; (3) It is a positive constant and satisfies ;i=1,2,3…,n.

4. The multi-missile spatiotemporal coordinated guidance method according to claim 2, characterized in that, In step 2.2), the convergence time range of the interference observer is as follows: in, , , , For any symmetric matrix Satisfying the Lyapunov equation h=1,2, matrix It is given by the following formula: Define the guidance time consistency error between missiles as: Based on the designed fixed-time disturbance observer and state equation, the control input command in the line-of-sight direction is designed as follows: in, The interference is the target acceleration interference along the line of sight observed by the interference observer; where , .

5. The multi-missile spatiotemporal coordinated guidance method according to claim 1, characterized in that, In step 3), the performance function is designed as follows: in, The constant represents the initial value of the performance function; The constant represents the preset upper bound of the steady-state error; The decay rate is the tracking error Lower bound on convergence rate; constant for converged to The maximum allowable convergence time, The convergence speed of the performance function is affected, and its value satisfies... , ; For performance functions Differentiation yields: in, .

6. The multi-missile spatiotemporal coordinated guidance method according to claim 1, characterized in that, In step 3), a continuous saturation function is used to replace the sign function in the preset performance guidance law. The specific form of the saturation function is as follows: in, .

7. An electronic device, characterized in that, include: One or more processors; as well as Storage device for storing one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors perform the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 6.

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