Missile maximum expected miss distance maneuver penetration method, system, medium and product

Abstract

The present invention discloses a maneuvering penetration method, system, medium and product for the maximum expected miss distance of a missile, which relates to the technical field of missile interception. The method includes obtaining the initial state information of the penetration missile and the interceptor missile; determining the terminal time based on the initial state information of the penetration missile and the interceptor missile; constructing a linear motion model of the engagement system based on the parameter uncertainty model; performing augmentation processing on the linear motion model of the engagement system to obtain an augmented linear engagement model; determining the optimal control command of the penetration missile based on the performance index function, the augmented state vector, the augmented linear engagement model and the terminal time; and controlling the penetration missile to perform penetration based on the optimal control command. The present invention can achieve penetration when the guidance coefficient of the interceptor missile is uncertain.

Description

Technical Field

[0001] The present invention relates to the technical field of missile interception, and in particular to a method, system, medium and product for maneuvering penetration with the maximum expected miss distance of a missile. Background Art

[0002] At present, a major threat faced by various missiles is the interceptor missiles launched by the interception system, which usually intercept the missiles in ways such as proportional navigation. Based on this requirement, it is necessary to design a penetration guidance law for the missile to perform maneuvering evasion. The existing research on various penetration strategies often relies on the so-called "complete information", that is, the interceptor missile can completely and real-time obtain various parameters required to generate the optimal penetration strategy, including the interception guidance law, flight control system parameters and guidance coefficients, etc. However, this is impossible to achieve in actual combat scenarios. Due to the lack of appropriate guidance rules and parameter identification schemes, the practicability of these target evasion guidance strategies is greatly reduced. Online identification of these parameters is a feasible approach. However, there are very few publicly available literatures on missile guidance laws and parameter identification. The parameter identification method represented by the Multiple Model Adaptive Estimator (MMAE) also has relatively high requirements for the computational load. Therefore, it is of great significance to design a penetration strategy considering dynamic uncertainties. Summary of the Invention

[0003] The purpose of the present invention is to provide a method, system, medium and product for maneuvering penetration with the maximum expected miss distance of a missile, which can achieve penetration when the guidance coefficient of the interceptor missile is uncertain.

[0004] To achieve the above purpose, the present invention provides the following solutions.

[0005] A method for maneuvering penetration with the maximum expected miss distance of a missile includes.

[0006] Obtain the initial state information of the penetration missile and the interceptor missile; the initial state information includes the included angle of the initial line of sight and the initial velocity; the initial line of sight is the straight line connecting the penetration missile and the interceptor missile at the initial moment.

[0007] Determine the termination time based on the initial state information of the penetration missile and the interceptor missile.

[0008] Construct a linear motion model of the engagement system based on the parameter uncertainty model.

[0009] Perform augmentation processing on the linear motion model of the engagement system to obtain an augmented linear engagement model.

[0010] Determine the optimal control command of the penetration missile based on the performance index function, augmented state vector, augmented linear engagement model and termination time.

[0011] Control the penetration bullet to penetrate based on the optimal control instruction.

[0012] A computer system includes: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement the steps of the missile maximum expected miss distance maneuvering penetration method described above.

[0013] A computer-readable storage medium has a computer program stored thereon, and when the computer program is executed by a processor, it implements the steps of the missile maximum expected miss distance maneuvering penetration method described above.

[0014] A computer program product includes a computer program, and when the computer program is executed by a processor, it implements the steps of the missile maximum expected miss distance maneuvering penetration method described above.

[0015] According to the specific embodiments provided by the present invention, the following technical effects of the present invention are disclosed.

[0016] The present invention discloses a missile maximum expected miss distance maneuvering penetration method, system, medium and product. The method includes obtaining the initial state information of the penetration bullet and the interceptor; determining the terminal time based on the initial state information of the penetration bullet and the interceptor; constructing a linear motion model of the engagement system based on a parameter uncertainty model; performing augmentation processing on the linear motion model of the engagement system to obtain an augmented linear engagement model; determining the optimal control instruction of the penetration bullet based on a performance index function, an augmented state vector, the augmented linear engagement model, and the terminal time; and controlling the penetration bullet to penetrate based on the optimal control instruction. The present invention can achieve penetration when the guidance coefficient of the interceptor is uncertain. Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0018] Figure 1 It is a schematic flowchart of the missile maximum expected miss distance maneuvering penetration method provided in Embodiment 1 of the present invention.

[0019] Figure 2 It is a schematic diagram of the mathematical expectation of the terminal miss distance generated by different total engagement times when the penetration bullet adopts the maximum miss distance expected maneuvering penetration strategy and the deterministic optimal maneuvering penetration strategy respectively.

[0020] Figure 3Schematic diagram of the variance of the terminal miss distance generated with respect to different total engagement times when using the maximum miss distance expected maneuver penetration strategy and the deterministic optimal maneuver penetration strategy for penetration against bullets Specific implementation manners

[0021] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0022] The object of the present invention is to provide a missile maximum expected miss distance maneuver penetration method, system, medium and product, aiming to achieve missile maximum expected miss distance maneuver penetration.

[0023] Based on the Polynomial Chaos Expansions (PCE) method for analyzing the propagation of dynamic uncertainties, the present invention regards the interceptor guidance coefficient as a random variable that does not require online identification, expands the original engagement scenario linear motion model with uncertainties into a group of high-dimensional deterministic linear systems, and uses the properties of orthogonal polynomials and optimal control theory to obtain an optimal penetration strategy in the statistical sense, which can maximize the expectation of the terminal miss distance. This optimal penetration strategy is obtained through numerical calculation by a method similar to fixed-point iteration, and has a small computational amount and a fast iteration speed. It can handle the maneuver penetration game engagement scenario with unknown interceptor parameters, and has high adaptability and reliability.

[0024] The object of the present invention is to propose a missile maximum expected miss distance maneuver penetration strategy based on the intrusive PCE method, which can be applied to the guidance system of penetration missiles. The maximum expected miss distance maneuver penetration strategy proposed by the present invention can give control instructions that maximize the expectation of the terminal miss distance of the penetration bullet in an engagement scenario where the guidance coefficient of the augmented proportional navigation (APN) interceptor used by the defense side is uncertain, so that the penetration bullet can complete the maneuver penetration task under the condition of incomplete prior information.

[0025] The maximum expected miss distance maneuver penetration strategy proposed by the present invention is applied to the computer of the missile guidance system. Without identifying the guidance parameters of the interceptor, it can maximize the expectation of the terminal miss distance of the penetration bullet, thus ensuring the success of the penetration task. The maximum expected miss distance maneuver penetration strategy proposed by the present invention has high adaptability, reliability and computational efficiency, and is applicable to missile guidance systems with high requirements for reliability and computational efficiency.

[0026] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] Embodiment 1

[0028] As Figure 1 shown, a method for maneuvering penetration of a missile with a maximum expected miss distance in this embodiment includes the following steps.

[0029] Step 101: Obtain the initial state information of the penetrating missile and the intercepting missile. The initial state information includes the angle between the initial line of sight and the initial velocity; the initial line of sight is the straight line connecting the penetrating missile and the intercepting missile at the initial moment.

[0030] Step 102: Determine the termination time based on the initial state information of the penetrating missile and the intercepting missile.

[0031] The penetrating missile obtains the initial velocity V M of the intercepting missile and the angle δ M0 between the initial velocity of the intercepting missile and the initial line of sight through a seeker or other observation means; obtain the initial relative distance ρ 0 between the penetrating missile and the intercepting missile; obtain the initial velocity V T of the penetrating missile and the angle δ T0 between the initial velocity of the penetrating missile and the initial line of sight through a navigation system.

[0032] Among them, the initial velocities V M , V T are both the rates of displacement change in the plane geodetic inertial coordinate system and are scalars; the plane geodetic inertial coordinate system is a well-known concept in the field of aerospace.

[0033] Among them, the initial line of sight refers to the straight line obtained by connecting the penetrating missile and the intercepting missile at the initial moment of the engagement.

[0034] For convenience, let k M = cosδ M0 , k T = cosδ T0 . According to the collision triangle hypothesis of the engagement scenario, the following formula is used to approximately calculate the termination time t f .

[0035] Based on the collision triangle hypothesis of the engagement scenario, the termination time is determined based on the initial state information of the penetrating missile and the intercepting missile, and the formula is as follows.

[0036]

[0037] Among them, t f represents the termination time, and the termination time refers to the predicted rendezvous time of the penetrating missile and the intercepting missile in the direction of the initial line of sight; ρ 0represents the initial relative distance between the penetration-proof missile and the interceptor missile; V M represents the initial velocity of the interceptor missile; V T represents the initial velocity of the penetration-proof missile; k M represents the cosine value of the angle between the initial velocity of the interceptor missile and the initial line of sight; k T represents the cosine value of the angle between the initial velocity of the penetration-proof missile and the initial line of sight.

[0038] Step 103: Construct a linear motion model of the engagement system based on the parameter uncertainty model.

[0039] Since the guidance coefficient of the APN interceptor missile is unknown, while the upper bound N u and the lower bound N l exist and are known, the parameter uncertainty model is as follows.

[0040] N′ = N 0 +N 1 ξ.

[0041] where N′ represents the true guidance coefficient of the interceptor missile, and the parameter the upper bound N of the guidance coefficient u and the lower bound N l are concepts existing in missile guidance-related literature. Generally speaking, N l = 3, N u = 6.

[0042] where ξ is a continuous random variable subject to a standard uniform distribution, with a probability density function of f(x) = 1 / 2 and a value range of [-1, 1]. ξ is a well-known concept in probability statistics.

[0043] Construct the state vector at time t as where d(t) is the distance of the penetration-proof missile relative to the interceptor missile in the normal direction of the initial line of sight at time t; is the velocity of the penetration-proof missile relative to the interceptor missile in the normal direction of the initial line of sight at time t, which is also the first derivative of d(t) with respect to time; y M , y T are the internal dynamics of the flight control systems of the interceptor missile and the penetration-proof missile respectively, which are well-known concepts in the field of missile guidance; is a 4-dimensional real vector space, which is a well-known concept in linear algebra.

[0044] For simplicity of analysis, approximate the flight control systems of the interceptor missile and the penetration-proof missile as first-order linear models. τ M is the time constant of the interceptor missile and can be obtained by online estimation using methods such as the Kalman filter; τ T is the time constant of the penetration-proof missile; therefore, τ M and τ T are both known.

[0045] Among them, the first-order linear model and the Kalman filter are both well-known concepts in control science.

[0046] Considering that the intercept missile adopts the APN guidance law, the linear motion model of the engagement system is as follows.

[0047]

[0048] Among them, represents the first-order derivative of the state vector at time t with respect to time; A E (t go ) represents the time-varying system matrix; y(t) represents the state vector at time t; b E (t go ) represents the input matrix; represents the projection of the anti-ballistic missile control command on the initial line-of-sight normal direction.

[0049] Among them

[0050] is the control command of the anti-ballistic missile control command on the initial line-of-sight normal direction; u T is the anti-ballistic missile control command, perpendicular to the velocity direction. The parameter t go = t f -t is called the time-to-go or remaining flight time, where t is the current moment of the engagement scenario.

[0051] The model is a linear time-varying differential equation set, which is a common modeling method in control science, where represents the first-order derivative of the state vector y(t) with respect to time.

[0052] Step 104: Augment the linear motion model of the engagement system to obtain an augmented linear engagement model.

[0053] Based on the intrusive PCE method and the orthogonal polynomial projection rule, take the PCE model truncation order as P + 1 = 3, and establish a high-dimensional augmented linear system with a dimension of (P + 1) × 4 = 12; P represents the retained order of the chaos polynomial.

[0054] Denote as the jth trajectory of the mth original state variable, then:

[0055] Φ i' (ξ) is the i'th order Legendre polynomial, which is a well-known concept in mathematics: the zero-order Legendre polynomial Φ 0 (ξ) = 1; the first-order Legendre polynomial Φ 1$\varPhi^{(0)}(\xi)=\xi$; Second-order Legendre polynomial $\varPhi$ 2 $^{(1)}(\xi)=(3\xi$ 2 $-1) / 2$.

[0056] The intrusive PCE method is used to augment the linear motion model of the engagement system to obtain an augmented linear engagement model, and the formula is as follows.

[0057]

[0058] where represents the first-order derivative of the augmented state vector with respect to time at time $t$; represents the augmented time-varying system matrix; represents the augmented input matrix; $Y(t)$ represents the augmented state vector at time $t$; represents the projection of the anti-bullet control command on the initial line-of-sight normal direction.

[0059] where $Y(t)$ is a new state combination obtained by performing chaotic polynomial expansion on each state in $y(t)$, is the augmented time-varying system matrix, is a 12-by-12 real matrix space, is the augmented input matrix, is a 12-dimensional real vector space, denoted as $c$ 1 is the first variable, $c$ 2 is the second variable, $c$ 3 is the third variable, $c$ 4 is the fourth variable.

[0060]

[0061]

[0062]

[0063] where

[0064] The intrusive PCE method is a well-known technique in uncertainty analysis, $0$ represents a 3-by-3 zero matrix, $I$ represents a 3-by-3 identity matrix, and $\Delta$ represents an intermediate variable.

[0065] Step 105: Determine the optimal control command of the anti-bullet based on the performance index function, the augmented state vector, the augmented linear engagement model, and the termination time.

[0066] For the uncertain maneuver penetration game scenario, the concerned index is the expectation of the terminal miss distance \(d(t f ) = |y 1 (t f )|\), and the performance index function \(J\) is to be simplified as follows. E As follows.

[0067]

[0068] Among them, denotes taking the expectation with respect to ; denotes the square of the first element in the state vector at the terminal time; denotes the \(i\)-th element in the augmented state vector at the terminal time.

[0069] Using the properties of orthogonal polynomials, the performance index function can be simplified as follows.

[0070]

[0071] Among them, denotes taking the expectation of the square of the Legendre polynomial, and the calculation method is a well-known technique in probability and statistics; the miss distance is a well-known concept in the field of missile guidance.

[0072] Based on the performance index function, the augmented state vector, and the augmented linear engagement model, an optimal control problem model is constructed as follows.

[0073]

[0074]

[0075]

[0076] Based on the terminal time, the augmented state transition matrix is calculated, and the first derivative of the remaining flight time \(t go and the initial conditions are as follows.

[0077]

[0078] \(\varPhi E (t go = 0) = \varPhi E (t f , t f ) = I

[0079] Using the standard 4th-order Runge-Kutta method, numerically integrate \(\varPhi go = 0\) backward from \(t E (t f , t)\) to \(t go = tf , the state transition matrix at any time t can be obtained.

[0080] Among them, the properties of the augmented state transition matrix are well-known concepts in linear systems, and the standard fourth-order Runge-Kutta method is a well-known technique in numerical analysis.

[0081] Based on the augmented state transition matrix and the augmented state vector, the zero-control miss vector is determined, and the formula is as follows.

[0082] Z E (t) = D E Φ E (t f , t)Y(t), 0 ≤ t ≤ t f .

[0083] Among them, the matrix Φ E (t f , t), Y(t) are the augmented state transition matrix and the augmented state vector at time t respectively, is a real matrix space of P + 1 rows and 4(P + 1) columns.

[0084] Based on the zero-control miss vector, the performance index function is transformed to obtain the transformed performance index function, and the formula is as follows.

[0085]

[0086] Among them, is a positive definite diagonal matrix, is the expectation of the square of the zero-order Legendre polynomial, is the expectation of the square of the first-order Legendre polynomial, is the expectation of the square of the second-order Legendre polynomial.

[0087] The first derivative of Z(t) with respect to time is as follows.

[0088]

[0089] In addition, a time-varying switching vector function is defined

[0090] According to the minimum principle, the optimal control problem model is processed based on the transformed augmented linear engagement model, and the control command model formula in the normal direction of the initial line of sight of the anti-projectile is as follows.

[0091]

[0092] Among them, the minimum principle is a well-known concept in optimal control theory.

[0093] Let Construct the control input for the k-th iteration. Let the value of k be 1, and the formula is as follows.

[0094]

[0095] Based on the zero-effort miss vector at the initial moment, the augmented state transition matrix, and the control input for the k-th iteration, calculate the terminal zero-effort miss vector for the k-th iteration. The formula is as follows.

[0096]

[0097] Where, Z E (0) = D E Φ E (t f , 0)Y(0) is determined by the initial moment, and Y(0) is determined by the following formula.

[0098]

[0099] Where, d(0) represents the distance of the target projectile relative to the interceptor in the initial line-of-sight normal direction at the initial moment, which is determined by observation equipment such as the navigation system and the seeker head; represents the velocity of the target projectile relative to the interceptor in the initial line-of-sight normal direction at the initial moment,

[0100] Input the terminal zero-effort miss vector for the k-th iteration into the control command model in the initial line-of-sight normal direction of the target projectile to obtain the control input for the (k + 1)-th iteration.

[0101] Judge whether the terminal zero-effort miss vector for the k-th iteration meets the preset condition to obtain the first judgment result.

[0102] The preset condition is ||[Z E (t f )] (k) - [Z E (t f )] (k-1) || < ε.

[0103] ||·|| represents the two-norm operator of the vector, which is a well-known concept in matrix theory; ε is a pre-set positive scalar used to judge the convergence of the iteration.

[0104] If the first judgment result is yes, then take the control input for the (k + 1)-th iteration as the optimal control input, and calculate the optimal control command for the target projectile based on the optimal control input.

[0105] Calculate the optimal control command for the target projectile based on the optimal control input using the optimal control command formula. The formula is as follows.

[0106]

[0107] Among them, (u T ) * represents the optimal control command of the anti - penetration bullet; represents the optimal control input; k T represents the cosine value of the included angle between the initial velocity of the anti - penetration bullet and the initial line of sight.

[0108] If the first judgment result is negative, then increase the value of k by 1, and return to the step of calculating the terminal zero - control miss vector at the k - th iteration, the augmented state transition matrix, and the control input at the k - th iteration from the zero - control miss vector, the augmented state transition matrix, and the control input at the initial time.

[0109] Among them, maximize represents maximizing; J E represents the performance index function; J' E represents the transformed performance index function; Y(t f ) represents the augmented state vector at the termination time; t f represents the termination time; subject to represents the constraint set; represents the first - order derivative of the augmented state vector at time t with respect to time; represents the augmented time - varying system matrix; represents the augmented input matrix; Y(t) represents the augmented state vector at time t; represents the control command of the anti - penetration bullet in the normal direction of the initial line of sight; represents the maximum value of the control command of the anti - penetration bullet in the normal direction of the initial line of sight, which is determined by the missile design performance and is known; k T represents the cosine value of the included angle between the initial velocity of the anti - penetration bullet and the initial line of sight; u max represents the maximum value of the missile maneuvering command; Φ E (t f ,t) represents the augmented state transition matrix; t go represents the remaining flight time; I represents the 12 - dimensional identity matrix; Z E (t) represents the zero - control miss vector at time t; Z E (0) represents the zero - control miss vector at the initial time; D E represents the set constant matrix; represents the transpose of the zero - control miss vector at the termination time; M Φ represents the positive - definite diagonal matrix; Z E (t f ) represents the zero - control miss vector at the termination time; represents the control input at the (k + 1) - th iteration; sign[] represents the sign function; Denote the terminal zero-effort miss vector at the \(k\)th iteration; \(S(t)\) represents the switching vector function at time \(t\). Denote the control input at the \(k\)th iteration; \(t\) s1 Denote the first switching time at the first iteration; \(t\) s2 Denote the second switching time at the first iteration; \(t\) s3 Denote the third switching time at the first iteration; Denote the augmented input matrix.

[0110] Step 106: Control the penetration bomblet to penetrate based on the optimal control command.

[0111] The present invention also provides a specific embodiment as follows.

[0112] To verify whether the maximum expected miss maneuver penetration strategy proposed by the present invention has the expected effect, MATLAB was used for simulation tests and compared with the deterministic optimal maneuver penetration strategy. The deterministic optimal maneuver penetration strategy is a well-known technology in the field of missile guidance.

[0113] The parameter settings of the simulation conditions are as follows.

[0114] (1) Time constants of the interceptor and the penetration bomblet: \(\tau\) M = 0.5 s, \(\tau\) T = 0.5 s.

[0115] (2) Initial velocities of the interceptor and the penetration bomblet: \(V\) M = 400 m / s, \(V\) T = 400 m / s.

[0116] (3) Initial velocity and initial line-of-sight angle of the penetration bomblet and initial velocity and initial line-of-sight angle of the interceptor: \(\delta\) T0 = \(\delta\) M0 = 0°.

[0117] (4) Upper limit \(u\) of the acceleration command of the penetration bomblet max : \(u\) max = 5G, \(G = 9.8\) m / s 2 .

[0118] \(\rho\) 0 takes the minimum value of 800 m and the maximum value of 6400 m, and is divided into 71 groups of conditions at intervals of 80 m, \(t\) f= 1s, 1.1s, 1.2s, ..., 7.9s, 8s. 1000 Monte Carlo simulations are carried out for each group of working conditions. In each simulation, the true guidance coefficient N' of the interceptor using the APN guidance law is sampled from the uniform distribution U(3, 6); the penetration warhead using the maximum expected miss distance maneuver penetration strategy generates control commands according to the above scheme; the penetration warhead using the deterministic optimal maneuver penetration strategy cannot obtain the true guidance coefficient of the interceptor, so the value of N' = 6 is taken when generating control commands.

[0119] The simulation results are shown in the figure. As Figure 2 shown, when the total engagement time is not too short, the expected value of the maximum miss distance generated by the maneuver strategy obtained from the optimal control command based on the present invention is almost twice that of the expected value of the terminal miss distance generated by the deterministic optimal strategy, which shows that the strategy of the present invention has achieved the expected effect.

[0120] As Figure 3 shown, when the total engagement time is greater than 2 seconds, the variance of the terminal miss distance of the expected maximum miss distance strategy generated by the maneuver strategy obtained from the optimal control command based on the present invention is significantly smaller than the variance of the terminal miss distance generated by the deterministic optimal strategy, which shows that the present invention has strong adaptability and the penetration performance will not fluctuate too much when facing interceptors with different guidance coefficients.

[0121] The maximum expected miss distance maneuver penetration strategy proposed by the present invention has two advantages.

[0122] (1) Adaptability to the uncertainty of the interceptor guidance coefficient. When the guidance coefficient of the APN interceptor is unknown, if the deterministic optimal strategy is used, when the guidance coefficient does not match, there will be a large variance in the terminal miss distance, which not only makes it difficult to exert the original performance, but is even easy to be intercepted; if parameter identification means such as a multi-model adaptive estimator (MMAE) are used, a group of Kalman filters need to be run in parallel in the guidance computer to estimate the guidance coefficient of the interceptor, and the convergence speed of the estimation process is difficult to guarantee. However, the strategy adopted by the present invention aims to maximize the expected value of the terminal miss distance and has good adaptability to different interceptor guidance coefficients; since the duration of the terminal engagement scenario is usually not large, the analysis of uncertainty is accurate enough under the premise of not too much computational effort.

[0123] (2) Rapidity of iterative convergence of optimal control commands. Existing parameter identification methods represented by MMAE require the number of filters to be positively correlated with the required estimation accuracy, significantly increasing the computational resource requirements for the guidance computer. Although in the present invention, the optimal control commands cannot be given in an analytical form and need to be numerically calculated through a fixed-point-like iteration, this iterative process is not sensitive to the initial value and has a very fast convergence speed. Generally speaking, about 10 iterations can achieve good convergence. In addition, the numerical calculation part of the iterative process only includes simple vector numerical integration and matrix operations, and the computational complexity is not large.

[0124] Example 2

[0125] A computer system, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the missile maximum expected miss distance maneuver penetration method in Example 1.

[0126] Example 3

[0127] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the missile maximum expected miss distance maneuver penetration method in Example 1.

[0128] Example 4

[0129] A computer program product, comprising a computer program, and when the computer program is executed by a processor, it implements the steps of the missile maximum expected miss distance maneuver penetration method in Example 1.

[0130] Example 5

[0131] A computer device, which may be a database. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store transactions to be processed. The input / output interface of the computer device is used for the processor to exchange information with external devices. The communication interface of the computer device is used to communicate with an external terminal through a network connection. The computer program is executed by the processor to implement the missile maximum expected miss distance maneuver penetration method in Example 1.

[0132] It should be noted that the object information (including but not limited to object device information, object personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with the relevant laws, regulations, and standards of relevant countries and regions.

[0133] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memories. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The databases involved in the embodiments provided by the present invention can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., and are not limited thereto. The processors involved in the embodiments provided by the present invention can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., and are not limited thereto.

[0134] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0135] In this text, specific examples are used to illustrate the principles and implementation modes of the present invention. The description of the above embodiments is only for helping to understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation modes and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A missile maximum expected miss distance maneuver penetration method, characterized in that: The method comprises: Acquire initial state information of the penetration missile and the interceptor missile; the initial state information includes an angle and an initial speed of an initial line of sight; the initial line of sight is a straight line connecting the penetration missile and the interceptor missile at an initial moment; Determine the termination time based on the initial state information of the penetration missile and the interceptor missile; Construct the linear motion model of the engagement system based on the parameter uncertainty model; The linear motion model of the engagement system is: in, A represents the first-order derivative of the state vector at time t with respect to time; E (t go ) represents the time-varying system matrix; y(t) represents the state vector at time t; b E (t go ) represents the input matrix; It represents the projection of the penetration control command in the normal direction of the initial line of sight; The linear motion model of the engagement system is augmented to obtain an augmented linear engagement model, which specifically includes: The intrusive PCE method is used to augment the linear motion model of the engagement system to obtain the augmented linear engagement model: in, represents the first-order derivative of the augmented state vector at time t with respect to time; represents the augmented time-varying system matrix; represents the augmented input matrix; Y(t) represents the augmented state vector at time t; It represents the projection of the penetration control command in the normal direction of the initial line of sight; Determine the optimal control instructions for the penetration projectile based on the performance index function, augmented state vector, augmented linear engagement model and termination time; The penetration projectile is controlled to penetrate based on the optimal control instruction.

2. The missile maximum expected miss distance maneuver penetration method according to claim 1, characterized in that: The termination time is determined based on the initial state information of the penetration missile and the interceptor missile, specifically including: According to the collision triangle assumption of the combat scenario, the termination time is determined based on the initial state information of the penetration missile and the interceptor missile: Among them, t f represents the termination time; ρ0 represents the initial relative distance between the penetration missile and the interceptor missile; V M Indicates the initial velocity of the interceptor missile; V T represents the initial velocity of the penetration projectile; k M represents the cosine value of the angle between the initial velocity of the interceptor and the initial line of sight; k T It represents the cosine value of the angle between the initial penetration velocity and the initial line of sight.

3. The missile maximum expected miss distance maneuver penetration method according to claim 1, characterized in that: The optimal control instructions for the penetration projectile are determined based on the performance index function, augmented state vector, augmented linear engagement model and termination time, including: The optimal control problem model is constructed based on the performance index function, augmented state vector and augmented linear engagement model: The augmented state transfer matrix is ​​calculated based on the termination time: Determine the zero control de-targeting quantity based on the augmented state transfer matrix and augmented state vector: Z E (t)=D E Φ E (t f ,t)Y(t),0≤t≤t f ; The performance index function is transformed based on the zero-control de-targeting metric to obtain the transformed performance index function: According to the minimum principle and based on the augmented linear engagement model, the optimal control problem model is processed to obtain the control instruction model in the normal direction of the initial line of sight of the penetration projectile: Construct the control input for the kth iteration, setting the value of k to 1: Based on the zero-control de-target quantity at the initial moment, the augmented state transfer matrix and the control input of the k-th iteration, the terminal zero-control de-target quantity of the k-th iteration is calculated: The terminal zero control de-targeting quantity of the kth iteration is input into the control instruction model of the initial line of sight normal direction of the penetration projectile to obtain the control input of the k+1th iteration; Determine whether the terminal zero-control de-targeting target of the k-th iteration meets a preset condition, and obtain a first determination result; If the first judgment result is yes, the control input of the k+1th iteration is used as the optimal control input, and the optimal control instruction for penetrating the projectile is calculated based on the optimal control input; If the first judgment result is no, then the value of k is increased by 1, and the zero control de-targeting quantity at the initial moment, the augmented state transfer matrix and the control input of the kth iteration are returned to obtain the step of calculating the terminal zero control de-targeting quantity of the kth iteration; Among them, maximize means maximization; J E represents the performance index function; J' E represents the performance index function after transformation; Y(t f ) represents the augmented state vector at the termination time; t f Indicates the termination time; subject to indicates the constraint group; represents the first-order derivative of the augmented state vector at time t with respect to time; represents the augmented time-varying system matrix; represents the augmented input matrix; Y(t) represents the augmented state vector at time t; Indicates the control command of the penetration control command in the normal direction of the initial line of sight; k represents the maximum value of the control command of the penetration control command in the normal direction of the initial line of sight; T Indicates the cosine value of the angle between the initial velocity of the penetration and the initial line of sight; u max Indicates the maximum value of the missile maneuver command; Φ E (t f ,t) represents the augmented state transfer matrix; t go represents the waiting time; I represents the 12-dimensional unit matrix; Z E (t) represents the zero control de-targeting quantity at time t; D E Represents the set constant matrix; The transpose of the zero control de-targeting vector at the termination time; Z E (0) represents the zero control de-targeting quantity at the initial moment; M Φ represents a positive definite diagonal matrix; Z E (t f ) represents the zero control de-targeting quantity at the termination time; represents the control input of the k+1th iteration; sign[] represents the sign function; represents the terminal zero control de-targeting vector of the kth iteration; S(t) represents the switching vector function at time t; represents the control input of the kth iteration; t s1 represents the first switching moment of the first iteration; t s2 represents the second switching time of the first iteration; t s3 represents the third switching time of the first iteration.

4. The missile maximum expected miss distance maneuver penetration method according to claim 3, characterized in that: The optimal control instructions for penetrating missiles are calculated based on the optimal control input, including: The optimal control command formula is used to calculate the optimal control command of the penetration projectile based on the optimal control input: Among them, (u T )* represents the optimal control instruction for penetrating the defense; represents the optimal control input; k T It represents the cosine value of the angle between the initial penetration velocity and the initial line of sight.

5. A computer system comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the missile maximum expected miss distance maneuver penetration method described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the missile maximum expected miss amount maneuver penetration method described in any one of claims 1-4 are implemented.

7. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the missile maximum expected miss amount maneuver penetration method described in any one of claims 1-4 are implemented.

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