Multi-leader and multi-follower coordinated game guidance method and system with interception angle constraints

Abstract

The embodiment of the present invention discloses a collaborative game guidance method and system for multiple leader missiles and multiple follower missiles with interception angle constraints. The multiple leader missiles are modeled as a non-cooperative game guidance problem, and the influence of actuator failure and linearization error is considered. The game guidance law of the leader missile is designed by combining the function envelope idea and the near-optimal control principle. In the line of sight direction, the follower missile guidance law is designed based on the consistency theory and the preset time stability theory to ensure that the sliding mode surface converges within the preset time, thereby realizing a salvo attack of the missile group. At the same time, a finite-time super-helical sliding mode guidance law is designed in the line of sight normal direction to ensure the rapid convergence of the interception angle and effectively suppress the chattering of the sliding mode surface, thereby realizing all-round blockade and attack of the target. The guidance method disclosed by the present invention can achieve saturation attack on multiple targets through the master-slave collaboration of multiple missile groups. When facing interference from unknown factors, the leader missile can still achieve precise strike with a low miss rate, so that the robustness of the guidance system is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of collaborative guidance control, and relates to a collaborative game guidance method and system for multiple leader and follower missiles with interception angle constraints. Background Art

[0002] In recent years, the continuous upgrading of defense systems has significantly reduced the range of missile strikes. Traditional single missiles have difficulty effectively intercepting highly defensive targets. In contrast, collaborative guidance utilizes information exchange and data sharing between missiles to deliver a comprehensive, saturated strike on the target, optimizing interception time and angle, thereby maximizing damage. Therefore, the issue of collaborative guidance is of great practical significance.

[0003] Based on the different terminal constraints, cooperative guidance methods can be divided into temporal and spatial coordination. Temporal coordination achieves simultaneous target impacts by controlling the timing of impacts. This guidance method is also known as impact time control guidance (ITCG). Spatial coordination requires that each missile strike the target at the desired intercept angle, achieving spatial interdiction and enhancing the lethality. This guidance method is also known as impact angle constraint guidance (IACG). Based on their roles and performance, existing guidance methods can be divided into "master-slave" guidance and masterless distributed guidance. Compared with distributed guidance, master-slave cooperative guidance has significant advantages in alleviating decision conflicts, reducing communication load, and resolving information asymmetry. Based on the communication structure, existing guidance methods can be divided into explicit and implicit cooperative guidance. Explicit cooperation offers significant advantages over implicit cooperation in terms of information exchange and real-time performance, anti-interference and robustness, and mission flexibility.

[0004] Although the proposed guidance law for multi-missile coordinated guidance systems covers most strike mission scenarios, the construction and solution of guidance systems assume that the missiles operate in an ideal combat environment and ignore linearization deviations. However, in reality, missiles may be affected by unknown factors such as environmental interference, enemy electromagnetic interference, and false data injection attacks, which can prevent the missile's actuator from obtaining a true control strategy, potentially rendering the missile's guidance law ineffective and causing significant misses. Furthermore, in master-slave coordinated guidance systems, the issue of safe guidance primarily focuses on single-leader, multi-slave systems. Compared to coordinated guidance systems with multiple leaders, single-leader, multi-slave and implicit coordinated guidance systems exhibit poor robustness in the face of unknown interference factors, failing to meet the demands of combat in a real battlefield with these factors. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem in the prior art that the missile's execution unit cannot obtain a true control strategy due to the influence of unknown factors such as environmental interference, enemy electromagnetic interference, and false data injection attacks, which may cause the missile guidance law to fail and result in a large miss rate. The present invention provides a multi-leader and multi-follower missile collaborative game guidance method and system with interception angle constraints.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A multi-leader and multi-follower coordinated game guidance method with interception angle constraints comprises the following steps:

[0008] Establish a multi-leader-multi-slave coordinated game guidance model;

[0009] A leader guidance model is constructed based on a multi-leader-multi-follower collaborative game guidance model. Performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption are constructed. Upper bounds for each performance indicator are set. Based on the leader guidance model, each performance indicator, and its upper bound, a Nash equilibrium guidance law between leaders is derived.

[0010] Based on the multi-leader-multi-follower cooperative game guidance model, a leader-follower cooperative sliding mode guidance law is established in the line of sight direction;

[0011] Based on the multi-leader-multi-follower coordinated game guidance model, a finite-time super-helical sliding mode guidance law is established in the line-of-sight direction.

[0012] The target strike mission is carried out based on the Nash equilibrium guidance law between the leader and the missile, the leader-follower cooperative sliding mode guidance law and the finite time super spiral sliding mode guidance law.

[0013] A further improvement of the present invention is:

[0014] The establishment of a multi-leader missile-multi-slave missile collaborative game guidance model includes the following steps:

[0015] Assuming that all missiles have ideal dynamics, the relative kinematic equation between the kth missile and the target can be described as:

[0016]

[0017] Where V k ,V T are the speeds of the missile k and the target, and the corresponding acceleration a k ,a T Perpendicular to the velocity direction; θ k ,γ k are the sight angle and track angle respectively; r k It is expressed as the relative distance between the lead projectile k and the target;

[0018]

[0019] Derivatives of formula (2) and formula (3) are taken, and then formula (4) is substituted into the equation to obtain:

[0020]

[0021] in, They represent the guidance strategies of the i-th follower missile and target in the k-th group of missiles in the line of sight direction and normal direction respectively.

[0022] The construction of the missile guidance model is as follows:

[0023]

[0024] Where, ΔB k =[-Δk k ,0] T , where ΔB k is the time-varying term caused by the linearization error and satisfies the constraint: ||ΔB k ||≤b, where b is a positive scalar.

[0025] The method of constructing the performance indicators of minimizing the zero control miss amount, minimizing the zero control angle deviation, and minimizing the energy consumption comprises the following steps:

[0026]

[0027] Where, t fk is the terminal time for missile k to intercept the target, and the weight matrix Q kN ≥0,Q k ≥0 is positive semidefinite, R k >0,R kj >0 is positive definite;

[0028] The upper bounds of the performance indicators are set as follows:

[0029]

[0030] Obtaining the Nash equilibrium guidance law between the missiles includes the following steps:

[0031] Obtaining optimal navigation gain using near-optimal control Guidance Law of the Leader-Missile Game Reaching Nash equilibrium Then the Nash equilibrium guidance law between the missiles is:

[0032]

[0033] Where, represents the optimal navigation gain, and Z represents the ammunition state.

[0034] The method of establishing a leader-follower cooperative sliding mode guidance law in the line of sight direction includes the following steps:

[0035]

[0036] Where, δ≥1 is a positive scalar, Sliding surface Preset time for convergence is the terminal time for missile i of group k to intercept the target, It can be regarded as interference caused by target maneuvering in the line of sight direction.

[0037] The finite-time super-helical sliding mode guidance law is established in the line-of-sight normal direction, comprising the following steps:

[0038]

[0039] Where, is the expected interception angle error of the i-th slave missile in the k-th group, l5>0,l6>0, It can be regarded as interference caused by target maneuvering in the line of sight direction.

[0040] A multi-leader and multi-follower coordinated game guidance system with interception angle constraints, comprising:

[0041] Guidance model construction module, used to establish a multi-leader-multi-slave coordinated game guidance model;

[0042] The leader guidance law construction module is used to build a leader guidance model based on the multi-leader-multi-follower coordinated game guidance model, establish performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption, set upper bounds for each performance indicator, and obtain the Nash equilibrium guidance law between the leaders based on the leader guidance model, each performance indicator, and the upper bounds of the performance indicators.

[0043] The follower guidance law construction module is used to establish a leader-follower collaborative sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model. It is also used to establish a finite-time super-helical sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model.

[0044] The mission execution module is used to execute target strike missions based on the Nash equilibrium guidance law between leader and missile, the leader-follower cooperative sliding mode guidance law, and the finite-time super-helical sliding mode guidance law.

[0045] A terminal device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0046] A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of any method described in the present invention.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention discloses a collaborative game guidance method for multiple leader and follower missiles with interception angle constraints. The method utilizes the concept of function envelope to obtain the upper bound of performance indicators and provides a Nash equilibrium guidance law between the leader and follower missiles through near-optimal control. Compared with the single-leader master-slave collaborative guidance system in the prior art, the method can flexibly adjust the coordination mode and attack strategy of the leader and follower missiles according to combat needs, thereby achieving saturation strikes on multiple targets. Furthermore, the optimal guidance strategy disclosed in the method can tolerate the uncertain effects caused by actuator failures and model errors in real environments. The leader missile can strike the target with a small miss margin and the desired interception angle. The near-optimal guidance law of the leader missile and the multi-leader missile architecture ensure the robustness of the entire guidance system. At the same time, a guidance law for the follower missiles along the line of sight is provided, ensuring that the remaining flight time of the missiles in the same group converges within a limited time, thereby achieving an effective salvo attack. The convergence time of the sliding mode surface can be flexibly preset according to different mission requirements, ensuring that the interception of the target is completed at the optimal time. By designing a finite-time super-helical sliding mode guidance law in the normal direction of the missile's line of sight, the vibration of the sliding mode surface is suppressed, ensuring that the missile can converge to the desired interception angle within a limited time, blockade the target in all directions in space, and complete a saturation strike on the target. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 A flow chart of the guidance method disclosed in the present invention;

[0051] Figure 2 Graph showing the simulation results of the method of the present invention. DETAILED DESCRIPTION

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0053] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0054] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0055] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0056] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0057] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0058] The present invention is described in further detail below with reference to the accompanying drawings:

[0059] See also Figure 1 The embodiment of the present invention discloses a collaborative game guidance method for multiple leader missiles and multiple follower missiles with interception angle constraints. The multiple leader missiles are modeled as a non-cooperative game guidance problem. Considering the influence of actuator failure and linearization error, the game guidance law of the leader missile is designed by combining the function envelope idea and the near-optimal control principle; in the line of sight direction, the follower missile guidance law is designed based on the consistency theory and the preset time stability theory to ensure that the sliding mode surface converges within the preset time, thereby realizing the salvo attack of the missile group; at the same time, a finite time super-helical sliding mode guidance law is designed in the line of sight normal direction to ensure the rapid convergence of the interception angle and effectively suppress the vibration of the sliding mode surface, thereby realizing the all-round blockade and attack of the target; the guidance method disclosed by the present invention can achieve saturation attack on multiple targets through the master-slave collaboration of multiple missile groups. When facing interference from unknown factors, the leader missile can still achieve precise strike with a low miss rate, so that the robustness of the guidance system is guaranteed.

[0060] The specific steps include:

[0061] Step 1: Based on the relative motion relationship between the missile and the target, a multi-leader-multi-follower coordinated game guidance model is established;

[0062] Specifically: for missiles using STT control, their three-dimensional spatial motion can be decomposed into two two-dimensional planes for analysis. Therefore, we establish a plane game guidance model based on the relative motion relationship between the missile and the target.

[0063] There are n groups of ammunition to attack high-defense targets, each group of ammunition contains 1 lead and m k (k=1,2,...,n) pieces from the missile For the kth bullet, is the i-th missile in the k-th missile group, T is the maneuvering target, z k The relative initial line of sight LOS between the missile k and the target k0 Assume that the communication topology between a group of missiles is undirected and connected, and the leader missile in a group does not need to receive the communication information of the follower missiles, but can instead transmit its own information to the follower missiles. To express the communication relationship between the lead bullet k and the follower bullet i, if the i-th follower bullet can receive the lead bullet information, then otherwise,

[0064] Assuming that all missiles have ideal dynamics, the relative kinematic equation between the kth missile and the target can be described as:

[0065]

[0066] Where V k ,V Tare the speeds of the missile k and the target, and the corresponding acceleration a k ,a T Perpendicular to the velocity direction; θ k ,γ k are the sight angle and track angle respectively; r k Expressed as the relative distance between the missile k and the target.

[0067] Similarly, the kinematic equation of the i-th follower projectile in the k-th group relative to the target can be expressed as

[0068]

[0069] By taking the derivative of formula (2) and formula (3), and then substituting formula (4), we can get

[0070]

[0071] The above formula decomposes the kinematic equation between the missile and the target into the direction along the line of sight and the direction normal to the line of sight, where They represent the guidance strategies of the i-th follower missile and target in the k-th group of missiles in the line of sight and normal direction respectively, which are expressed as

[0072]

[0073] The remaining time for the kth round to be collected can be estimated as:

[0074]

[0075] According to the collision time of the lead projectile, it can be calculated as t fk =t+t gok , where t is the time after the lead missile k is launched. Similarly, the remaining time of the follower missile can be expressed as

[0076] Step 2: Based on the multi-leader-multi-follower coordinated game guidance model, a leader guidance model is established that takes into account actuator failures and linearization error uncertainties. Performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption are established. The upper bounds of these performance indicators are obtained using the function envelope concept, and the Nash equilibrium guidance law between the leader and follower is derived using the near-optimal control principle.

[0077] Before establishing the missile guidance model considering uncertainties, the method also includes: obtaining the missile guidance dynamics model after order reduction;

[0078] Assuming the engagement scenario is in the final guidance phase and the target's maneuvering is detectable to the lead missile, place the lead missile k and the target at the initial line of sight LOS. k0 The acceleration in the normal direction is denoted as a kN ,a TNAt the same time, the following relations are satisfied:

[0079]

[0080] While considering the miss distance between the lead and the target, we also need to consider how to hit the target at a specific interception angle, and define the interception angle error as e k =γ k +γ T -q k , where q k is the expected interception angle of missile k, so the state vector is selected The kinetic equation can be expressed as:

[0081]

[0082] Where:

[0083]

[0084] In order to simplify the solution process of the game problem, terminal projection is used for order reduction, and the conversion relationship is:

[0085]

[0086] Where, is a constant matrix used to select appropriate state variables; is a homogeneous equation The state transition matrix of Z k =[Z k1 ,Z k2 ] T is the new state variable after the terminal projection transformation. Its physical meaning is: the zero-control miss amount and zero-control intercept angle error of the k-th lead missile intercepting the target, which is:

[0087]

[0088] After deriving formula (14), the dynamic equation can be expressed as:

[0089]

[0090] The following is a guidance model that takes into account actuator failure and linearization error uncertainty:

[0091]

[0092] Where, ΔB k =[-Δk k ,0] T , where ΔB kis the time-varying term caused by the linearization error and satisfies the constraint: ||ΔB k ||≤b, b is a positive scalar, Δu k =ΔΩ k Z, where ΔΩ k is the perturbation of the missile navigation gain in the real environment, and it is assumed that where δ is a positive scalar.

[0093] The performance indicators for minimizing zero-control miss distance, minimizing zero-control angle deviation, and minimizing energy consumption are as follows:

[0094] For ease of description, we define the following symbols:

[0095]

[0096] During the game, the goal of the missile leader is to minimize the miss distance from the target and reduce the error from the desired intercept angle, while minimizing the energy consumption of the missile leader. Therefore, the quadratic performance index is selected as follows:

[0097]

[0098] Where, t fk is the terminal time for missile k to intercept the target, and the weight matrix Q kN ≥0,Q k ≥0 is positive semidefinite, R k >0,R kj >0 is positive definite.

[0099] Due to the existence of navigation gain perturbation ΔΩ k The control-dependent noise caused by the linearization error makes it impossible to accurately obtain the exact value of the performance index. Therefore, the idea of ​​function envelope is used to obtain the upper bound of the performance index, that is:

[0100]

[0101] The above is the Nash equilibrium guidance law between the missiles:

[0102]

[0103] Where, is a positive definite matrix. In real combat environments and subsequent simulations, only measurable or estimable quantities can be used, such as the missile-target line-of-sight angle and the remaining time. Therefore, the first equation in (15) needs to be approximated, and we can obtain:

[0104]

[0105] When the leading missile adopts the guidance strategy of formula (22), the final game result of multiple leading missiles will reach Nash equilibrium:

[0106]

[0107] Step 3: Based on the multi-leader-multi-follower coordinated game guidance model, a leader-follower coordinated sliding mode guidance law is designed in the line of sight direction by combining consistency theory and preset time stability theory. This ensures that the sliding mode surface converges within the preset time and the consistency error approaches zero, thus achieving a salvo attack by the missile group.

[0108] To achieve a saturation strike on the target in the "leader-follower" structure collaborative guidance problem, it means that the follower missile must quickly keep consistent with the remaining flight time of the leader missile. Therefore, the design goal of the line-of-sight guidance law of the i-th follower missile in the k-th group is to meet it within a finite time T.

[0109]

[0110] According to the relative motion relationship between the missile and the target, select the state variable Define the state equation of the elastic body:

[0111]

[0112] From formula (26), we can see that in order to achieve simultaneous hits on the target, the remaining flight time of the follower missile must be controlled so that it converges quickly to the leading missile. Therefore, by differentiating the remaining flight time, we can obtain:

[0113]

[0114] The goal of this embodiment is to achieve consistency in the remaining flight time of the follower bullet and the same group leader bullet, that is, The remaining flight time of the missile can be approximately expressed as Further Therefore, the consistency convergence of the remaining flight time can be transformed into The consistency convergence problem of , through formula (27) is:

[0115]

[0116] Where, It can be regarded as the interference caused by the maneuvering of the target in the line of sight direction. The following fixed-time interference observer is designed to estimate it:

[0117]

[0118] Where, It can converge to the true value of the target maneuver interference in a limited time

[0119] According to the multi-agent consensus theory, consider the following integral sliding surface:

[0120]

[0121] Where, is the consistency error of the remaining flight time of the i-th slave missile in the k-th group, and we have:

[0122]

[0123] According to the sliding surface, formula (30), and the preset time convergence theory, the remaining time cooperative guidance law from the missile line of sight is designed as follows:

[0124]

[0125] Where δ≥1 is a positive scalar, Sliding surface The preset time for convergence. The remaining flight time of the follower missile can converge to the same group of lead missiles within a limited time, and the convergence time meets

[0126] Step 4: Based on the multi-leader-multi-slave coordinated game guidance model, a finite-time super-helical sliding mode guidance law is designed in the normal direction of the slave missile's line of sight to ensure rapid convergence of the interception angle and achieve all-round blockade and strike of the target;

[0127] In order for the missile to intercept the target at the desired angle, the designed line-of-sight normal guidance law should satisfy the following conditions within a finite time T′:

[0128]

[0129] Where, is the expected interception angle of the i-th follower missile in the k-th group. The expected interception angle error of the i-th follower missile in the k-th group is defined as Considering the interception angle subsystem in the normal direction of the line of sight, the dynamic equation is:

[0130]

[0131] In order to make the state of the above subsystem converge to zero within a finite time, the following sliding surface is designed:

[0132]

[0133] The parameters satisfy 0<ζ<1,

[0134] According to the sliding surface (35) and the preset time convergence theory, the guidance law of the kth group i in the normal direction of the missile line of sight is designed as

[0135]

[0136] Where, l5>0, l6>0, It can be regarded as the interference caused by the maneuvering of the target in the line of sight, and the following fixed-time interference observer is used to estimate it:

[0137]

[0138] Where, It can converge to the true value of the target maneuver interference in a limited time

[0139] Able to The time converges to zero, and the line of sight angle of the missile converges to the desired line of sight angle. Therefore, for the system (34), under the control of the line of sight normal guidance law (36)-(37), there is a fixed time convergence upper bound that satisfies

[0140] See also Figure 2 , Figure 2 Graph showing simulation results of the method of the present invention;

[0141] Figure 2 The simulation scenario shown is that there are two groups of missiles to attack high-defense stationary targets. Each lead missile contains three follower missiles to form a missile group. The lead missile and the follower missile can hit the target at different interception angles, and the follower missile can realize a salvo attack with the lead missile.

[0142] The present invention discloses a multi-leader-multi-slave cooperative game guidance method with interception angle constraint, which uses the idea of ​​function envelope to obtain the upper bound of performance indicators and gives the Nash equilibrium guidance law between the leader missiles through near-optimal control. Compared with the single-leader-slave cooperative guidance system in the prior art, the multi-leader-multi-slave cooperative guidance system disclosed by the present invention has the following advantages: on the one hand, the multi-leader-multi-slave cooperative guidance system can flexibly adjust the coordination mode and attack strategy of the leader missile and the follower missile according to combat needs to achieve saturation strikes on multiple targets; on the other hand, when faced with unknown interference in the real environment, the leader missile cannot obtain accurate guidance law, resulting in an increase in the miss rate, which will in turn lead to a high degree of information loss on the leader missile. The guidance law of the follower missile, which is dependent on the degree of missile control, fails. The near-optimal guidance strategy designed by the present invention can tolerate the uncertain effects of actuator failures and model errors in real environments. The leader missile can hit the target with a small miss and the desired interception angle. The near-optimal guidance law of the leader missile and the multi-leader missile architecture ensure the robustness of the entire guidance system. At the same time, the remaining time is used as a consensus variable. Based on the consistency theory and the preset time sliding mode control principle, a guidance law for the follower missile along the line of sight is given, ensuring that the remaining flight time of the missiles in the same group can converge within a finite time, realizing an effective salvo attack. The convergence time of the sliding mode surface can be flexibly preset according to different mission requirements to ensure that the target is intercepted at the optimal time. By designing a finite time super-helical sliding mode guidance law in the normal direction of the follower missile's line of sight, the chattering of the sliding mode surface is suppressed, ensuring that the follower missile can converge to the desired interception angle within a finite time, and comprehensively blockade the target in space, completing a saturation strike on the target.

[0143] The embodiment of the present invention discloses a multi-leader and multi-follower coordinated game guidance system with interception angle constraints, comprising:

[0144] Guidance model construction module, used to establish a multi-leader-multi-slave coordinated game guidance model;

[0145] The leader guidance law construction module is used to build a leader guidance model based on the multi-leader-multi-follower coordinated game guidance model, establish performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption, set upper bounds for each performance indicator, and obtain the Nash equilibrium guidance law between the leaders based on the leader guidance model, each performance indicator, and the upper bounds of the performance indicators.

[0146] The follower guidance law construction module is used to establish a leader-follower collaborative sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model. It is also used to establish a finite-time super-helical sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model.

[0147] The mission execution module is used to execute target strike missions based on the Nash equilibrium guidance law between leader and missile, the leader-follower cooperative sliding mode guidance law, and the finite-time super-helical sliding mode guidance law.

[0148] A schematic diagram of a terminal device provided in one embodiment of the present invention. The terminal device in this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of each of the aforementioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in each of the aforementioned device embodiments are implemented.

[0149] The computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to accomplish the present invention.

[0150] The terminal device may be a computing device such as a desktop computer, a notebook computer, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0151] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0152] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0153] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0154] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A multi-leader and multi-follower coordinated game guidance method with interception angle constraints, characterized in that: The following steps are involved: Establish a multi-leader-multi-slave coordinated game guidance model; A leader guidance model is constructed based on a multi-leader-multi-follower collaborative game guidance model. Performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption are constructed. Upper bounds for each performance indicator are set. Based on the leader guidance model, each performance indicator, and its upper bound, a Nash equilibrium guidance law between leaders is derived. Based on the multi-leader-multi-follower cooperative game guidance model, a leader-follower cooperative sliding mode guidance law is established in the line of sight direction; Based on the multi-leader-multi-follower coordinated game guidance model, a finite-time super-helical sliding mode guidance law is established in the line-of-sight direction. The target strike mission is carried out based on the Nash equilibrium guidance law between the leader and the missile, the leader-follower cooperative sliding mode guidance law and the finite time super spiral sliding mode guidance law; The establishment of a multi-leader missile-multi-slave missile collaborative game guidance model includes the following steps: Assuming that all missiles have ideal dynamics, the relative kinematic equation between the kth missile and the target can be described as: Where V k ,V T are the speeds of the missile k and the target, and the corresponding acceleration a k ,a T Perpendicular to the velocity direction; θ k ,γ k are the sight angle and track angle respectively; r k It is expressed as the relative distance between the lead projectile k and the target; Derivatives of formula (2) and formula (3) are taken, and then formula (4) is substituted into the equation to obtain: in, They represent the guidance strategies of the i-th follower missile and target in the k-th missile group in the line of sight and normal direction respectively, where Respectively expressed as: The construction of the missile guidance model is as follows: Obtain the reduced-order dynamics model of the missile: The missile and the target are in the initial line of sight LOS k0 The acceleration in the normal direction is denoted as a kN ,a TN , satisfying the following relationship: Define the intercept angle error as e k =γ k +γ T -q k , where q k is the expected interception angle of missile k, and the state vector is selected The kinetic equation is expressed as: Where: Use terminal projection to perform order reduction processing, and the conversion relationship is: Where, is a constant matrix used to select appropriate state variables; is a homogeneous equation The state transition matrix of Z k =[Z k1 ,Z k2 ] T is the new state variable after the terminal projection transformation. Its physical meaning is: the zero-control miss amount and zero-control intercept angle error of the k-th lead missile interception target, which is: After deriving formula (14), the dynamic equation can be expressed as: Get the missile guidance model: Where, ΔB k =[-Δk k ,0] T , where ΔB k is the time-varying term caused by the linearization error and satisfies the constraint: ||ΔB k ||≤b, b is a positive scalar, Δu k =ΔΩ k Z, where ΔΩ k is the perturbation of the missile navigation gain in the real environment, and it is assumed that Where δ is a positive scalar; The method of constructing the performance indicators of minimizing the zero control miss amount, minimizing the zero control angle deviation, and minimizing the energy consumption comprises the following steps: Define the following symbols: Get performance indicators: Where, t fk is the terminal time for missile k to intercept the target, and the weight matrix Q kN ≥0,Q k ≥0 is positive semidefinite, R k >0,R kj >0 is positive definite; The upper bounds of the performance indicators are set as follows: Obtaining the Nash equilibrium guidance law between the missiles includes the following steps: Obtaining optimal navigation gain using near-optimal control Guidance Law of the Leader-Missile Game Reaching Nash equilibrium Then the Nash equilibrium guidance law between the missiles is: Where, represents the optimal navigation gain, and Z represents the state of the missile; is a positive definite matrix; The method of establishing a leader-follower cooperative sliding mode guidance law in the line of sight direction includes the following steps: The design goal of the line-of-sight guidance law for the i-th slave missile in the k-th group is to satisfy the following conditions within a finite time T: According to the relative motion relationship between the missile and the target, select the state variable Define the state equation of the elastic body: According to formula (26), the remaining flight time can be differentiated: In order to achieve the same remaining flight time between the follower and the lead missile of the same group, The remaining flight time of the missile is approximately expressed as Further Therefore, the consistency convergence of the remaining flight time can be transformed into The consistency convergence problem of , through formula (27) is: Where, To estimate the interference caused by the target maneuvering in the line of sight, the following fixed-time interference observer is designed: Where, It can converge to the true value of the target maneuver interference in a limited time According to the multi-agent consensus theory, consider the following integral sliding surface: Where, is the consistency error of the remaining flight time of the i-th slave missile in the k-th group, and we have: According to formula (30) and the preset time convergence theory, the remaining time cooperative guidance law from the missile line of sight direction is designed as: Where, δ≥1 is a positive scalar, Sliding surface Preset time for convergence is the terminal time for missile i of group k to intercept the target, It can be regarded as the interference caused by the maneuvering of the target in the line of sight. The remaining flight time of the follower missile can converge to the same group of lead missiles within a limited time, and the convergence time satisfies The finite-time super-helical sliding mode guidance law is established in the line-of-sight normal direction, comprising the following steps: In order for the missile to intercept the target at the desired angle, the line-of-sight normal guidance law must satisfy the following in a finite time T′: Where, is the expected interception angle of the i-th follower missile in the k-th group; the expected interception angle error of the i-th follower missile in the k-th group is defined as Considering the interception angle subsystem in the normal direction of the line of sight, the dynamic equation is: In order to make the state of the above subsystem converge to zero within a finite time, the following sliding surface is designed: The parameters satisfy 0<ζ<1, The guidance law of the i-th group in the normal direction from the missile line of sight is: Where, is the expected interception angle error of the i-th slave missile in the k-th group, 0<ζ<1, l5>0,l6>0, It can be regarded as interference caused by target maneuvering in the line of sight direction; Design the following fixed-time disturbance observer to estimate it: Where, It can converge to the true value of the target maneuver interference in a limited time Able to time converges to zero, and thus makes the line of sight angle of the missile converge to the desired line of sight angle; therefore, for system (34), under the control of the line of sight normal guidance law (36)-(37), there is a fixed time convergence upper bound that satisfies 2. A multi-leader and multi-slave coordinated game guidance system with interception angle constraints according to the method of claim 1, characterized in that: include: Guidance model construction module, used to establish a multi-leader-multi-slave coordinated game guidance model; The leader guidance law construction module is used to build a leader guidance model based on the multi-leader-multi-follower coordinated game guidance model, establish performance indicators for minimizing zero-control miss, minimizing zero-control angle deviation, and minimizing energy consumption, set upper bounds for each performance indicator, and obtain the Nash equilibrium guidance law between the leaders based on the leader guidance model, each performance indicator, and the upper bounds of the performance indicators. The follower guidance law construction module is used to establish a leader-follower collaborative sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model. It is also used to establish a finite-time super-helical sliding mode guidance law in the line of sight direction based on the multi-leader-multi-follower collaborative game guidance model. The mission execution module is used to execute target strike missions based on the Nash equilibrium guidance law between leader and missile, the leader-follower cooperative sliding mode guidance law, and the finite-time super-helical sliding mode guidance law.

3. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to claim 1 are implemented.

4. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

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