Adaptive sliding mode multi-uav cooperative terminal guidance law design method based on super-twisting observer

Abstract

Aiming at the problem of multi-vehicle cooperative guidance law design with time and attack angle constraints, an adaptive sliding mode multi-vehicle cooperative terminal guidance law design method based on super-twisting observer is provided. On the basis of establishing the relative motion model of missile and target, the design of the guidance law is divided into the line-of-sight direction and the line-of-sight normal direction, the guidance command in the line-of-sight direction is designed based on the multi-agent consensus principle, the residual time of each vehicle can be converged, so as to realize the line-of-sight cooperative attack; the guidance command in the line-of-sight normal direction is designed based on the adaptive sliding mode method, the vehicle can attack the target at a given angle, so as to meet the angle constraint.

Description

Technical Field

[0001] This invention relates to the field of multi-vehicle systems, and more specifically, to an adaptive sliding mode multi-vehicle cooperative terminal guidance law design method based on a super-twisted observer. Background Technology

[0002] Modern warfare is increasingly complex, with more diverse missions and more intelligent and maneuverable targets. Some targets can even launch decoy flares to interfere with the interception of incoming missiles. In this context, the difficulty of missiles simultaneously identifying targets and performing high-precision attacks (interceptions) and detection missions has significantly increased. Under this trend, multi-vehicle cooperative warfare has become a research hotspot in recent years, and cooperative guidance is a key technology in this model. Multi-vehicle cooperative guidance involves multiple missiles cooperating with each other under the support of a communication network, integrating multiple missiles into an information-sharing, functionally complementary, and tactically coordinated combat group. Following a certain cooperative control strategy, the entire cooperative missile group achieves a specific attack or defense mission. During cooperative guidance, studying multiple constraints under terminal guidance can achieve more precise and efficient strikes. These multiple constraints mainly include attack time constraints and attack angle constraints. The time constraint under multiple constraints aims to ensure that missiles hit the target simultaneously to achieve a saturation attack effect and enhance penetration capability; the attack angle constraint under multiple constraints aims to achieve better strike results, requiring the missile to hit the target at a specific angle to fully utilize its destructive performance.

[0003] Sliding mode variable structure control can overcome system uncertainties, exhibits strong robustness to external disturbances and unmodeled dynamics, and boasts a simple structure and fast response speed, making it highly suitable for guidance law design. However, singularities and chattering phenomena often occur in sliding mode variable structure control design, which is detrimental to system control. Furthermore, sliding mode variable structure control design is often based on a fixed upper bound of disturbances, which is generally much larger than the actual disturbance, resulting in a high degree of conservatism in the system. Summary of the Invention

[0004] Technical problems to be solved

[0005] To address the problem of designing cooperative guidance laws for multiple aircraft under simultaneous constraints of time and attack angle, this invention provides an adaptive sliding mode cooperative terminal guidance law design method for multiple aircraft based on a super-torsion observer.

[0006] Technical solution

[0007] An adaptive sliding mode multi-vehicle cooperative terminal guidance law design method based on a super-torsion observer, characterized by the following steps:

[0008] Step 1: Divide the design of the guidance law into the line-of-sight direction and the line-of-sight normal direction;

[0009] Step 2: During the terminal guidance phase of the aircraft, define the remaining time t. go for Among them, R, These are the line-of-sight distance and its derivative, respectively;

[0010] Step 3: Transform the cooperative guidance law design problem into the design problem of line-of-sight direction and line-of-sight normal acceleration commands, and the line-of-sight direction guidance law. Guarantee the remaining time t go The convergence of the lines of sight enables coordinated attacks; the line-of-sight normal guidance law u i Guarantee to hit the target at the given angle;

[0011] Step 4: First, design the cooperative guidance law under the nominal condition, i.e., without considering target maneuvering.

[0012] Let t be the current time, t goi Let be the remaining time for the i-th aircraft to intercept the target, i = 1, 2, ..., n; then at time t, the predicted time for the i-th aircraft to intercept the target is t_i. fi =t+t goi And because of t goj -t goi =t fj -t fi Therefore, t is guaranteed fi The convergence of consensus can guarantee t goi To reach consensus; for t fi Differentiation yields: Where d ri It is the upper bound of the unknown bounded perturbation, and The next design objective is to achieve this through design. Thus guaranteeing t fi Towards uniformity; the integral sliding surface is selected as t fi (0) is t fi The initial value of c ij For coefficients;

[0013] The guidance law and cooperative guidance law designed based on the integral sliding mode control method in the line-of-sight direction are as follows:

[0014] Among them l i >0, 0<δ i <1, adaptive parameter ω i The update law is as follows:

[0015] In the formula, 0 < k 1i <1,k2i >0,k 3i >0,γ 0i >0, γ i >0, T0 is the time constant, whose value can be chosen as a sufficiently small positive constant, and sign() is the sign function, then we have The system state t can be guaranteed fi The signals can converge to a uniform state within a finite time. To mitigate chattering caused by the sign function in sliding mode guidance, a sigmoid function is introduced to replace the sign function. The sigmoid function can be expressed as follows: Where a > 0, is a constant;

[0016] The cooperative guidance algorithm for the line-of-sight normal direction is designed based on the fast non-singular sliding mode control method as follows:

[0017]

[0018] k4=(k 41 ,k 42 ), and k1>0, k2>0, k3>0 41 >0, k 42 >0, ε>0, μ>0, M is an estimate of k. i Let B be the system matrix for the i-th aircraft. i Let x be the input matrix for the i-th aircraft. 1i x 2i The line-of-sight angle error is given by λ1 and λ2, which are constants and have λ1 > λ2 and 1 < λ2 < 2. α = diag(α1, α2) and β = diag(β1, β2) are the parameters to be designed.

[0019] Step 5: Further, the uncertainty caused by the target maneuver is treated as a disturbance and estimated based on the super-twisted observer; for equation... The upper bound of the unknown bounded perturbation d in ri Assume the actual disturbance is D. ri Design auxiliary variable y ri for:

[0020] in Define t fi and y ri The error between them is e ri =t fi -y ri The perturbation observer is designed in the form of in p ri All are positive constants and satisfy the following conditions:

[0021] p ri ≥2, in

[0022] The designed observer can guarantee the error e ri and It converges to 0 in a finite time, thus estimating the actual perturbation, i.e., y. i →t fi ,

[0023] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium 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 cause the one or more processors to implement the method described above.

[0024] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0025] Beneficial effects

[0026] This invention, based on an adaptive sliding mode method and a super-twisted observer, designs a cooperative guidance law for situations where time and attack angle constraints coexist. Given a model of the relative motion between the projectile and the target, the guidance law is designed in two directions: line-of-sight (LOS) and line-of-sight normal (LOS). A LOS guidance command is designed based on the multi-agent consensus principle to ensure that the remaining time of each aircraft converges, thus achieving cooperative attack. A LOS guidance command is designed based on the adaptive sliding mode method to ensure that the aircraft can attack the target at a given angle, thus satisfying the angle constraint. Furthermore, target maneuvers are treated as interference, and the super-twisted observer estimates and compensates for them to achieve attack on maneuvering targets. Attached Figure Description

[0027] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0028] Figure 1 This is a schematic diagram of the ballistic trajectory.

[0029] Figure 2 This is a diagram showing the remaining time.

[0030] Figure 3 Line-of-sight angular velocity Response curve.

[0031] Figure 4 Angular velocity of line of sight Response curve.

[0032] Figure 5 The line-of-sight angle θ L Response curve.

[0033] Figure 6 The line-of-sight angle φ L Response curve.

[0034] Figure 7 The acceleration command a is given in the direction of the line of sight. LM Response curve.

[0035] Figure 8 The line-of-sight normal acceleration command a YM .

[0036] Figure 9 The line-of-sight normal acceleration command a ZM . Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] To address the singularity and chattering phenomena in sliding mode variable structure control, this invention designs a better-performing adaptive law, which can improve the convergence speed of sliding mode and reduce chattering caused by the sign function in sliding mode guidance. To address the high conservatism of sliding mode variable structure control when facing highly maneuvering targets, this invention combines the advantage of the super-torsion observer, which can compensate for disturbances within a finite time, to reduce the system's conservatism. For multi-aircraft cooperative attack problems with time and angle constraints, this invention divides the aircraft's motion into the line-of-sight direction and the line-of-sight normal direction. Based on the integral sliding mode method, a guidance law in the line-of-sight direction is designed to ensure the aircraft hits the target. Furthermore, considering the target's highly maneuvering motion, a super-torsion observer is designed to compensate for generalized disturbances, thereby achieving effective tracking of highly maneuvering targets. Based on fast non-singular sliding mode, a guidance command in the line-of-sight normal direction is designed to ensure that the aircraft can complete the cooperative attack at a specified angle.

[0039] This embodiment provides an adaptive sliding mode multi-vehicle cooperative terminal guidance law design method based on a super-twisted observer. Based on establishing a missile-target relative motion model, the guidance law design is divided into line-of-sight (LOS) and line-of-sight normal (LOS) directions. Guidance commands for the LOS direction are designed based on the multi-agent consensus principle, ensuring that the remaining time of each vehicle converges, thus enabling LOS cooperative attack. Guidance commands for the LOS normal direction are designed based on an adaptive sliding mode method, ensuring that the vehicle can attack the target at a given angle, thereby satisfying the angle constraint. Finally, simulations verify the effectiveness of the method. The method includes the following steps:

[0040] Step 1: The design of the guidance law is divided into the line-of-sight direction and the line-of-sight normal direction.

[0041] Step 2: During the terminal guidance phase of the aircraft, define the remaining time t. go for R, These are the line-of-sight distance and its derivative, respectively;

[0042] Step 3: Transform the cooperative guidance law design problem into the design problem of line-of-sight direction and line-of-sight normal acceleration commands. Guarantee the remaining time t go The convergence of the line of sight, thus enabling a coordinated attack; line-of-sight normal u i Guarantee to hit the target at a given angle.

[0043] Step 4: First, design the cooperative guidance law under the nominal case (ignoring target maneuvering). Let t be the current time, t goi (i = 1, 2, ..., n) represents the remaining time for the i-th missile to intercept the target. Therefore, at time t, the predicted time for the i-th missile to intercept the target is t_i. fi =t+t goi And because of t goj -t goi =t fj -t fi Therefore, t is guaranteed fi The convergence of consensus can guarantee t goi Agree on the agreement. For t fi Differentiation yields: Where d ri It is the upper bound of the unknown bounded perturbation, and The next design objective is to achieve this through design. Thus guaranteeing t fi Towards uniformity. The integral sliding surface is selected as... t fi (0) is t fi The initial value of c ij The coefficient is used. Based on the integral sliding mode control method, the guidance law and cooperative guidance law in the line-of-sight direction are designed as follows:

[0044] Among them l i >0, 0<δ i <1, adaptive parameter ω i The update law is as follows:

[0045] In the formula, 0 < k 1i <1,k 2i >0,k 3i >0,γ 0i >0, γ i >0, T0 is the time constant, whose value can be chosen as a sufficiently small positive constant, and sign() is the sign function, then we have The system state t can be guaranteed fi They can converge to a uniform state within a finite time. To mitigate the chattering phenomenon caused by the sign function in sliding mode guidance, a sigmoid function is introduced to replace the sign function. The sigmoid function can be expressed as: Where a > 0, is a constant;

[0046] The cooperative guidance algorithm for the line-of-sight normal direction is designed based on the fast non-singular sliding mode control method as follows:

[0047]

[0048] k4=(k 41 ,k 42 ), and k1>0, k2>0, k3>0 41 >0, k 42 >0, ε>0, μ>0, M is an estimate of k. i Let B be the system matrix for the i-th missile. i Let x be the input matrix for the i-th missile. 1i x 2i Let λ1 and λ2 be constants, and let λ1 > λ2 and 1 < λ2 < 2. Let α = diag(α1, α2) and β = diag(β1, β2) be the parameters to be designed.

[0049] Step 5: Further, the uncertainty caused by the target maneuver is treated as a disturbance and estimated based on the super-twisted observer. For equation... The upper bound of the unknown bounded perturbation d in ri Assume the actual disturbance is D. ri Design auxiliary variable y ri for:

[0050] in Define tfi and y ri The error between them is e ri =t fi -y ri The perturbation observer is designed in the form of in p ri All are positive constants and satisfy the following conditions:

[0051] p ri ≥2, in

[0052] The designed observer can guarantee the error e ri and It converges to 0 in a finite time, thus estimating the actual perturbation, i.e., y. i →t fi ,

[0053] The guidance law in the line-of-sight direction shown in step 4 can guarantee that the sliding surface converges in a finite time, that is, the remaining time of multiple aircraft tends to be consistent in a finite time. For the system with interference and the first derivative of the interference being bounded, there exists a constant d. ri and m ri , so that |D ri |≤d ri , Among them, D ri For interference, define

[0054]

[0055]

[0056] Define Lyapunov functions as

[0057]

[0058] Differentiating with respect to V1, we get

[0059]

[0060] As can be seen from the above formula, Since δ is bounded, we can obtain ω. i and γ i Bounded; according to the Russell invariant principle, it can be obtained that within a finite time t0,

[0061] For t > t0, we can obtain

[0062]

[0063] Define the Lyapunov function V2 as follows:

[0064]

[0065] Taking the derivative with respect to V2, we get

[0066]

[0067] In summary, the sliding surface can converge within a finite time.

[0068] For the kinematic equations of the line-of-sight normal direction in a multi-aircraft attack, if the guidance law in the line-of-sight normal direction satisfies step 4, then the sliding surface converges to the following region in a finite time:

[0069] |s j |≤ε j =min{ε 1j ,ε 2j} (2)

[0070]

[0071] Among them, s j Let ξ represent the j-th component of the sliding surface, and let ξ be a positive constant; x 1i and x 2i Converging to the following region:

[0072]

[0073] In the formula, x 1i(j) and x 2i(j) x represents 1i and x 2i The j-th component.

[0074] The following considers the scenario where three aircraft attack a maneuvering target simultaneously. The initial parameters of the aircraft are shown in Table 1.

[0075] Table 1 Initial parameters of the aircraft

[0076]

[0077] The target's initial position is (0,0,0)m, and the target's initial velocity components in the first target line-of-sight coordinate system are (75,279.9,77.65)m / s.

[0078] Guidance law in line of sight The parameters selected in the following way are: l i =15,δ i =0.5 and k 1i =0.9,k2i =0.01,k 3i =1.2,γ 0i =0.3, T0=0.05.

[0079] Guidance law of line of sight upward u 1i The parameters in (i = 1, 2, 3) are selected as follows: k i =1,α i =2,c i =0.7, p i =5, η i =1, r i =0.5, β1=0.08, β1=0.03, β1=0.05, a i =0.8, γ 0i =3.5, γ 00i =4.2,γ 1i =0.1 and γ 2i =0.99.

[0080] Figure 1 The trajectory of the bullet is given. Figure 2 The remaining time for the three spacecraft is given. As can be seen from the graph, the remaining time for the three spacecraft eventually becomes the same. Figure 3 and Figure 4 The graph shows the change of line-of-sight angle over time. As can be seen from the graph, the line-of-sight angular rate of the three aircraft converges to zero within a finite time. Figure 5 and Figure 6 A graph showing the change of line-of-sight angle over time is provided. It can be seen from the graph that all three aircraft converged to the desired line-of-sight angle. Figure 7 , Figure 8 and Figure 9 The acceleration command for the aircraft is given, which is an acceleration command in the line-of-sight normal direction. It can be seen that the acceleration command in the line-of-sight normal direction exhibits a saturation phenomenon in the first five seconds after the start of terminal guidance. This is because an attack needs to be carried out at a specified angle. The guidance law in the line-of-sight normal direction needs to ensure that the line-of-sight angle converges to the desired value. However, the saturation value is within a reasonable range, and the saturation phenomenon converges quickly.

[0081] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for designing an adaptive sliding mode multi-vehicle cooperative terminal guidance law based on a super-twisted observer, characterized in that, To address the simultaneous constraints of time and attack angle, based on a given missile-target relative motion model, the guidance law is designed in two directions: line-of-sight (LOS) and line-of-sight normal (LOS). A LOS guidance command is designed based on the multi-agent consensus principle to ensure the remaining time of each aircraft converges, thus achieving coordinated attack. A LOS guidance command is designed based on an adaptive sliding mode method to ensure the aircraft attacks the target at a given angle. Target maneuvers are treated as interference, and an over-twisting observer is used to estimate and compensate for them, enabling attack on maneuvering targets. The steps are as follows: Step 1: Divide the design of the guidance law into the line-of-sight direction and the line-of-sight normal direction; Step 2: Define the remaining time during the terminal guidance phase of the aircraft. for ;in , These are the line-of-sight distance and its derivative, respectively; Step 3: Transform the cooperative guidance law design problem into the design problem of line-of-sight direction and line-of-sight normal acceleration commands, and the line-of-sight direction guidance law. Guarantee remaining time The convergence of these convergences enables coordinated attacks. Line-of-sight normal guidance law Guarantee to hit the target at the given angle; Step 4: First, design the cooperative guidance law under the nominal condition, i.e., without considering target maneuvering. make For the current moment, For the first The remaining time for each aircraft to intercept the target. ;but At that moment, the The predicted time for the aircraft to intercept the target is And because Therefore, guarantee Convergence can guarantee To reach an agreement; Differentiation yields: ,in It is the upper bound of the unknown bounded perturbation, and The next design objective is to achieve this through design. Thus ensuring Towards consensus; Select the integral sliding surface as , , for initial value, For coefficients; The guidance law and cooperative guidance law designed based on the integral sliding mode control method in the line-of-sight direction are as follows: ,in , Adaptive parameters The update law is as follows: , , In the formula, , Let be the time constant, whose value can be chosen as a sufficiently small positive constant, and let sign() be the sign function. Then we have: This can ensure the system status The signals can converge to a uniform state within a finite time. To mitigate chattering caused by the sign function in sliding mode guidance, a sigmoid function is introduced to replace the sign function. The sigmoid function can be expressed as follows: ,in , is a constant; The cooperative guidance law for the line-of-sight normal direction is designed based on the fast non-singular sliding mode control method as follows: ， , And there are , , , , , , for k The estimate, For the first The system matrix of each aircraft For the first One aircraft input matrix, , This is the line-of-sight angle error. , It is a constant and has , , and These are the parameters to be designed; Step 5: Further, the uncertainty caused by the target maneuver is treated as a disturbance and estimated based on the super-twisted observer; for equation... Unknown bounded perturbation upper bound Assuming the actual disturbance is Design auxiliary variables for: ,in ,definition and The error between them is The perturbation observer is designed in the form of ,in , , , , All are positive constants and satisfy the following conditions: , , , , ,in , The designed observer can guarantee the error and It converges to 0 within a finite time, thus estimating the actual disturbance, i.e. , ; The guidance law in the line-of-sight direction shown in step 4 can guarantee that the sliding surface converges in a finite time, that is, the remaining time of multiple aircraft tends to be consistent in a finite time. For the system with interference and the first derivative of the interference being bounded, there exists a constant. and , making , ,in, For interference, define Define Lyapunov functions as right Differentiation yields As can be seen from the above formula, and Bounded, therefore, we can obtain and Bounded; according to the Russell invariant principle, it can be obtained that it is possible to achieve this in a finite time. Inside, against ,get Define Lyapunov functions V 2 is right Differentiation yields In summary, the sliding surface can converge in a finite amount of time; For the kinematic equations of the line-of-sight normal direction in a multi-aircraft attack, if the guidance law in the line-of-sight normal direction satisfies step 4, then the sliding surface converges to the following region in a finite time: in, The first sliding surface Each component, and It is a positive number; and Converging to the following region: In the formula, and express and The Each component.

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium 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 cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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