Method, device and equipment for determining missile angular guidance law and storage medium

Abstract

The application discloses a missile angle guidance law determination method, device and equipment and a storage medium. Firstly, according to the relative motion relationship between the missile and the maneuvering target, a state equation is established. Secondly, according to the established state equation, a non-singular terminal sliding mode surface is designed, and a double-power fast reaching law is designed to reach the sliding mode surface. Thirdly, the disturbance of the maneuvering target is expanded into a new state quantity, and an expanded state observer is designed to estimate the state quantity. Finally, considering the singularity of the state and the estimation of the disturbance of the maneuvering target by the expanded state observer, the guidance law of the missile is determined based on the double-power fast reaching law of the non-singular terminal sliding mode surface. The missile guidance law method provided by the application has fast convergence speed and high robustness.

Description

Technical Field

[0001] This invention relates to the field of missile guidance and control, and in particular to a method, apparatus, device, and storage medium for determining missile angle guidance law based on non-singular terminal sliding mode control. Background Technology

[0002] A missile is an aircraft carrying a warhead, propelled by its own power unit, and guided by a guidance law of its guidance system. Sliding mode control is a robust control method with strong anti-interference capabilities. Non-singular terminal sliding mode control can bring the system state to converge within a finite time, thus it can be applied to missile guidance law design. When designing the sliding mode approaching law, the convergence speed to the sliding surface needs to be considered. Traditional power-law and exponential-law approaching laws may cause system chattering, which is a problem that needs to be addressed in missile guidance law design. Furthermore, due to the uncertainty of target maneuvers, designing an observer to monitor target maneuvers is crucial. To address the slow convergence speed of guidance laws with angle constraints, the chattering issues inherent in traditional sliding mode control, and the unknown target maneuvers, there is an urgent need to propose a fast-converging and robust specified terminal angle guidance law.

[0003] In existing missile guidance laws for attacking maneuvering targets, the literature (You Hao, Zhao Jiufen, Li Peng, et al. Second-order sliding mode guidance law with landing angle constraint for non-singular fast terminal [J]. Journal of Missiles, Rockets and Guidance, 2019, 39(6):155-159,176.DOI:10.15892 / j.cnki.djzdxb.2019.06.034.) proposes a finite-time sliding mode guidance law with landing angle constraint by utilizing non-singular fast terminal sliding mode and second-order sliding mode control theory. The selection of a non-singular fast terminal sliding surface improves the convergence speed of the system state, and the guidance law designed based on second-order sliding mode control theory effectively suppresses chattering, while avoiding singularity problems during the guidance law design process. A non-homogeneous disturbance observer is designed to estimate and compensate for external disturbances caused by target maneuvering information. However, since the upper bound of the target acceleration derivative is difficult to measure, the non-homogeneous disturbance observer used in this method may not be applicable in practice. The literature (Zhang Wenjie, Lu Tianyu, Xia Qunli. Anti-early warning sliding mode guidance law based on extended state observer [J]. Systems Engineering and Electronics, 2019, 41(5):1087-1093.DOI:10.3969 / j.issn.1001-506X.2019.05.22.) proposes a guidance law with angle constraints based on a state observer. The target's maneuver is observed as a new state variable and compensated into the guidance command, effectively solving the problem of excessive overload required at the interception end. At the same time, the landing angle when attacking the target is constrained, and a sliding mode guidance law with landing angle constraint is designed. However, this guidance law selects a traditional linear sliding surface, which has a slow convergence speed and cannot guarantee finite-time convergence. The literature (Harbin Institute of Technology. An Angle-Constrained Guidance Method Based on Non-Singular Fast Terminal Sliding Mode Control: CN201910816581.9[P]. 2020-05-19.) proposes an angle-constrained guidance law based on non-singular fast terminal sliding mode control using a non-singular fast terminal sliding mode surface and a fast terminal sliding mode reaching law. This guidance law has a fast landing angle convergence speed and high landing point accuracy. However, this method does not consider the target's acceleration when designing the guidance law, treating it merely as an unknown disturbance with an upper bound. Summary of the Invention

[0004] Purpose of the invention: This invention addresses the problems existing in the prior art by providing a method, apparatus, device, and storage medium for determining missile angle guidance laws based on non-singular terminal sliding mode control, which has fast convergence speed and high robustness.

[0005] Technical solution: The method for determining the missile angle guidance law based on non-singular terminal sliding mode control as described in this invention includes:

[0006] Step 1: Establish the state equations based on the relative motion between the missile and the maneuvering target;

[0007] Step 2: Based on the established state equations, design a non-singular terminal sliding surface and a double power fast reaching law approaching sliding surface.

[0008] Step 3: Expand the disturbance of the maneuvering target into a new state variable, and design an expanded state observer to estimate the state variable;

[0009] Step 4: Considering the singularity of the state and the estimation of the maneuvering target disturbance by the extended state observer, determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface.

[0010] Furthermore, the method also includes:

[0011] Step 5: Construct the Lyapunov function and use the relevant finite-time convergence theorem to perform convergence analysis on the guidance law determined in Step 4.

[0012] Furthermore, step 1 specifically includes:

[0013] Step 101: Based on the relative motion relationship between the missile and the maneuvering target, establish the relative motion equation as follows:

[0014]

[0015] λ=γ T +φ T =γ M +φ M

[0016] In the formula, r is the relative distance between the missile and the maneuvering target. V represents the first derivative of the corresponding letter with respect to time. M φ M These represent the missile's speed, lead angle, and V, respectively. T φ T Let represent the speed magnitude and lead angle of the maneuvering target, respectively; λ is the line-of-sight angle between the missile and the maneuvering target; and γ... M It is the missile's velocity tilt angle, γ T It is the velocity angle of the maneuvering target;

[0017] Step 102: Set the state variable x1 = λ - λ d State variables Based on the equations of relative motion, the system state equations are established as follows:

[0018]

[0019] In the formula, λ d For the desired viewing angle, This indicates the missile's acceleration along a direction perpendicular to the line of sight. This represents the acceleration of a maneuvering target along a direction perpendicular to the line of sight. This represents the disturbance amount in the system.

[0020] Furthermore, step 2 specifically includes:

[0021] Step 201: Based on the state equations of the missile and the maneuvering target established in Step 1, establish the non-singular terminal sliding surface as: s = x1 + k|x2| β sgn(x2)

[0022] In the formula, s represents a non-singular terminal sliding surface, x1 and x2 represent state variables of the state equation, k and β represent the sliding surface parameters to be designed, k > 0, 1 < β < 2, and sgn() represents the step function;

[0023] Step 202: Design the double power fast reaching law based on the non-singular terminal sliding surface as follows:

[0024]

[0025] In the formula, Let s represent the first derivative of s with respect to time, and let α1, α2, α3a, b, c represent the approach law parameters to be designed, where α1 > 0, α2 > 0, α3 > 0, 0 < b < 1, c > 0.

[0026] Furthermore, step 3 specifically includes:

[0027] Step 301: Extend the state equation by setting the state variable x3 = f(t). The extended state equation is as follows:

[0028]

[0029] In the formula, y represents the state variable, and v(t) represents a function of the derivative of the disturbance.

[0030] Step 302: Design the extended state observer for the extended state equation as follows:

[0031]

[0032] In the formula, z1, z2, and z3 represent the observed quantities, and e1 represents the error function. β 01 β 02 β 03 , m are the parameters to be designed, β 01 >0,β 02 >0,β 03 >0, 0 < m < 1.

[0033] Furthermore, step 4 specifically includes:

[0034] Step 401: Differentiate the non-singular terminal sliding surface and substitute it into the state equation designed in Step 1 to obtain:

[0035]

[0036] Step 402: Based on the double-power fast reaching law designed in Step 2, the formula for calculating the control input is obtained as follows:

[0037]

[0038] In the formula, a m For control input;

[0039] Step 403: Considering the singularity of x2, modify the control input calculation formula as follows:

[0040]

[0041] Step 404: Considering the use of the extended state observer designed in Step 3 to estimate the disturbance, the control input calculation formula is modified as follows:

[0042]

[0043] The above formula represents a definite guidance law.

[0044] The missile angle guidance law determination device based on non-singular terminal sliding mode control described in this invention includes:

[0045] The state equation establishment module is used to establish state equations based on the relative motion relationship between the missile and the maneuvering target.

[0046] The sliding surface design module is used to design non-singular terminal sliding surfaces based on the established state equations, and to design double power fast approaching law approaching sliding surfaces.

[0047] The state observer design module is used to expand the disturbance of the maneuvering target into a new state variable and design an expanded state observer to estimate the state variable.

[0048] The guidance law determination module is used to consider the occurrence of singular phenomena in the state and the estimation of maneuvering target disturbances by the extended state observer, and to determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface.

[0049] Furthermore, the device also includes:

[0050] The convergence analysis module is used to construct Lyapunov functions and perform convergence analysis on a given guidance law using relevant finite-time convergence theorems.

[0051] The missile angle guidance law determination device based on non-singular terminal sliding mode control described in this invention includes:

[0052] One or more processors;

[0053] Memory, used to store one or more programs;

[0054] When the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0055] The present invention describes a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the methods described above.

[0056] Beneficial Effects: Compared with existing technologies, the significant advantages of this invention are as follows: First, this invention selects a non-singular terminal sliding surface, enabling the line-of-sight angle and line-of-sight angular velocity to converge rapidly on the sliding surface. Second, an improved double-power fast reaching law is selected, resulting in faster convergence speed when far from the sliding surface, while reducing the convergence speed when approaching the sliding surface, thereby suppressing chattering. Finally, an extended state observer with an improved nonlinear function is designed to quickly estimate target disturbances. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the method for determining the missile angle guidance law based on non-singular terminal sliding mode control provided by the present invention.

[0058] Figure 2 This is a diagram showing the relative motion between the missile and the target in a two-dimensional plane according to the present invention;

[0059] Figure 3 This is a graph showing the change in the relative distance between a missile and a target over time, based on an example of this invention;

[0060] Figure 4 This is a graph showing the change of the line-of-sight angle of a missile based on an example of the present invention over time;

[0061] Figure 5 This is a graph showing the variation of missile line-of-sight angular velocity over time based on an example of this invention;

[0062] Figure 6 This is a sliding mode switching function diagram based on an example of the present invention;

[0063] Figure 7 This is a graph showing the tracking error of the extended state observer based on an example of the present invention over time.

[0064] Figure 8 This is a schematic diagram of the missile angle guidance law determination device based on non-singular terminal sliding mode control provided by the present invention;

[0065] Figure 9 This is a schematic diagram of the structure of the missile angle guidance law determination device based on non-singular terminal sliding mode control provided by the present invention. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Example 1

[0068] This embodiment provides a method for determining the missile angle guidance law based on non-singular terminal sliding mode control, such as... Figure 1 As shown, it includes:

[0069] Step 1: Establish the state equations based on the relative motion relationship between the missile and the maneuvering target.

[0070] This step specifically includes:

[0071] Step 101: Based on the relative motion between the missile and the maneuvering target, such as... Figure 2 As shown, the equations of relative motion are established as follows:

[0072]

[0073] λ=γ T +φ T (3)

[0074] λ=γ M +φ M (4)

[0075] In the formula, r is the relative distance between the missile and the maneuvering target. V represents the first derivative of the corresponding letter with respect to time. M φ M These represent the missile's speed, lead angle, and V, respectively. T φ T Let represent the speed magnitude and lead angle of the maneuvering target, respectively; λ is the line-of-sight angle between the missile and the maneuvering target; and γ... M It is the missile's velocity tilt angle, γ T It is the velocity angle of the maneuvering target.

[0076] Differentiate (2):

[0077]

[0078] Because the missile and the target are moving at constant speeds, therefore:

[0079]

[0080] Substituting (1) into (6) yields:

[0081]

[0082] make a m and a t These are the accelerations of the missile and the target along a direction perpendicular to the line of sight, respectively.

[0083] Step 102: Set the state variable x1 = λ - λ d State variables Based on the equations of relative motion, the system state equations are established as follows:

[0084]

[0085] In the formula, λ d For the desired viewing angle, This indicates the missile's acceleration along a direction perpendicular to the line of sight. This represents the acceleration of a moving target along a direction perpendicular to the line of sight. Due to the uncertainty of the target's motion, this is set... This represents the disturbance amount in the system.

[0086] Step 2: Based on the established state equations, design a non-singular terminal sliding surface and a double power fast reaching law approaching sliding surface.

[0087] This step specifically includes:

[0088] Step 201: Based on the state equations of the missile and the maneuvering target established in Step 1, establish the non-singular terminal sliding surface as: s = x1 + k|x2| β sgn(x2) (9)

[0089] In the formula, s represents a non-singular terminal sliding surface, x1 and x2 represent state variables of the state equation, k and β represent the sliding surface parameters to be designed, k>0, 1<β<2, and sgn() represents the step function;

[0090] Step 202: Design the double power fast reaching law based on the non-singular terminal sliding surface as follows:

[0091]

[0092] In the formula, Let s represent the first derivative of s with respect to time, and let α1, α2, α3a, b, c represent the approach law parameters to be designed, where α1 > 0, α2 > 0, α3 > 0, 0 < b < 1, c > 0.

[0093] When the distance from the sliding surface is far It is equivalent to a double-power fast reaching law, and has a faster reaching speed compared to the fast power reaching law and the double-power reaching law. When the distance to the sliding surface is relatively close, Equivalent to a power-law fast approach, it can reduce the speed at which the device enters the sliding surface and effectively suppress chattering.

[0094] Step 3: Expand the disturbance of the maneuvering target into a new state variable, and design an expanded state observer to estimate the state variable.

[0095] This step specifically includes:

[0096] Step 301: Extend the state equation by setting the state variable x3 = f(t). The extended state equation is as follows:

[0097]

[0098] In the formula, y represents the state variable, and v(t) represents a function of the derivative of the disturbance.

[0099] Step 302: Design the extended state observer for the extended state equation as follows:

[0100]

[0101] In the formula, z1, z2, and z3 represent the observed quantities, e1 represents the error function, and β 01 β 02 β 03 , m are the parameters to be designed, β 01 >0,β 02 >0,β 03 >0, 0 < m < 1. By selecting appropriate parameters, system (13) can track system (12), i.e., z n+1 →x n+1 = f(t).

[0102] Step 4: Considering the singularity of the state and the estimation of the maneuvering target disturbance by the extended state observer, determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface.

[0103] This step specifically includes:

[0104] Step 401: Differentiate the non-singular terminal sliding surface (Equation (9)) and substitute it into the state equation designed in Step 1 (Equation (8)) to obtain:

[0105]

[0106] Step 402: Based on the double-power fast reaching law designed in Step 2, the formula for calculating the control input is obtained as follows:

[0107]

[0108] In the formula, a m For control input;

[0109] Step 403: Considering the singularity of x2, modify the control input calculation formula as follows:

[0110]

[0111] Step 404: Considering the use of the extended state observer designed in Step 3 to estimate the disturbance, the control input calculation formula is modified as follows:

[0112]

[0113] The above formula represents a definite guidance law.

[0114] Step 5: Construct the Lyapunov function and use the relevant finite-time convergence theorem to perform convergence analysis on the guidance law determined in Step 4.

[0115] Substituting equation (15) into equation (13) and rearranging, we get:

[0116]

[0117] Choose the Lyapunov function:

[0118]

[0119] Differentiate equation (18) over time and substitute it into equation (17):

[0120]

[0121] in, k3=2α3αβ|x2| β-1 Clearly, k1≥0, k2≥0, k3≥0. therefore:

[0122]

[0123] Definition 1: For the following systems:

[0124]

[0125] Where, x∈R n Let g(x,t) be a continuous function, and let V(x) be a scalar function of x, which is continuously differentiable and positive definite. If it satisfies If κ>0, η>0, 0<α<1, then V(x) can converge to the origin in finite time.

[0126] As can be seen from the above definition, V converges to zero in finite time, which means that s converges to zero in finite time.

[0127] When s = 0, since the designed sliding surface is the terminal sliding surface, the state of the system can approach 0 in a finite time, i.e., λ → λ. d ,

[0128] Simulation verification of this embodiment is performed: Assume the missile and target fly in a two-dimensional longitudinal plane, with the missile's velocity at 1000 m / s and the target's velocity at 800 m / s. Ox and Oy represent the horizontal and vertical directions, respectively. The initial position of the missile is (0, 0) km, and the initial position of the target is (2, 1) km. The missile's velocity angle γ... M (0) = 40°, the target's initial velocity angle γ T (0) = 60°, the target moves along the direction perpendicular to the normal. t =10cos(πt / 4)m / s 2 Maneuverability, missile's desired line-of-sight angle λ d =15°, the missile adopts the guidance law designed in this section. From Figure 5 It is known that the missile's line-of-sight angular velocity approaches 0 within a finite time, which ensures that the missile can accurately hit the target. Figure 3 This also demonstrates that the missile successfully hit its target within a limited time. Figure 4 This demonstrates that the missile ultimately hit the target at the desired line-of-sight angle. Figure 6 This indicates that the sliding surface curve quickly approaches the sliding surface without severe chattering. Figure 7 It can be seen that the extended state observer has errors at the beginning, but the tracking error converges quickly and the error curve is very smooth, which shows the effectiveness and speed of the extended observer in tracking target maneuvers.

[0129] Example 2

[0130] Figure 8 This is a schematic diagram of a missile angle guidance law determination device based on non-singular terminal sliding mode control provided in Embodiment 2 of the present invention. This device can be implemented in software and / or hardware, and can be configured in a terminal device. The device includes:

[0131] The state equation establishment module is used to establish state equations based on the relative motion relationship between the missile and the maneuvering target.

[0132] The sliding surface design module is used to design non-singular terminal sliding surfaces based on the established state equations, and to design double power fast approaching law approaching sliding surfaces.

[0133] The state observer design module is used to expand the disturbance of the maneuvering target into a new state variable and design an expanded state observer to estimate the state variable.

[0134] The guidance law determination module is used to consider the occurrence of singular phenomena in the state and the estimation of maneuvering target disturbances by the extended state observer, and to determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface.

[0135] The convergence analysis module is used to construct Lyapunov functions and perform convergence analysis on a given guidance law using relevant finite-time convergence theorems.

[0136] The apparatus provided in this embodiment of the invention can be used to execute the method provided in Embodiment 1 of the invention, and has the corresponding functions and beneficial effects of executing the method.

[0137] It is worth noting that in the embodiments of the above-mentioned determining device, the various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0138] Example 3

[0139] Figure 9 This is a schematic diagram of the structure of a device provided in Embodiment 3 of the present invention. The present invention provides services for the implementation of the method in Embodiment 1 of the present invention and can be configured with the computing device of the method in Embodiment 1. Figure 9 A block diagram of an exemplary device 12 suitable for implementing embodiments of the present invention is shown. Figure 9 The device 12 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0140] like Figure 9 As shown, device 12 is represented as a general-purpose computing device. Components of device 12 may include, but are not limited to: one or more processors or processing units 16, system memory 28, and a bus 18 connecting different system components, including system memory 28 and processing unit 16.

[0141] Bus 18 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0142] Device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by device 12, including volatile and non-volatile media, removable and non-removable media.

[0143] System memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be used to read and write non-removable, non-volatile magnetic media (…). Figure 9 Not shown; usually referred to as a "hard drive"). Although Figure 9 Not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of the present invention.

[0144] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 typically perform the functions and / or methods described in the embodiments of the present invention.

[0145] Device 12 can also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), and with one or more devices that enable a user to interact with device 12, and / or with any device that enables device 12 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed via input / output (I / O) interface 22. Furthermore, device 12 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 20. Figure 9As shown, network adapter 20 communicates with other modules of device 12 via bus 18. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0146] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28, such as implementing the method provided in Embodiment 1 of the present invention.

[0147] Example 4

[0148] Embodiment 4 of the present invention also provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the method of Embodiment 1.

[0149] The computer storage medium of this invention can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0150] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0151] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0152] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0153] Of course, the computer-executable instructions provided in the embodiments of the present invention are not limited to the above-described method operations, but can also perform related operations in the methods provided in any embodiment of the present invention.

Claims

1. A method for determining the missile angle guidance law based on non-singular terminal sliding mode control, characterized in that... The method includes: Step 1: Establish the state equations based on the relative motion between the missile and the maneuvering target; Step 2: Based on the established state equations, design a non-singular terminal sliding surface and a double power fast reaching law approaching sliding surface. Step 3: Expand the disturbance of the maneuvering target into a new state variable, and design an expanded state observer to estimate the state variable; Step 4: Considering the singularity of the state and the estimation of the maneuvering target disturbance by the extended state observer, determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface. Step 1 specifically includes: Step 101: Based on the relative motion relationship between the missile and the maneuvering target, establish the relative motion equation as follows: λ=γ T +φ T =c M +φ M In the formula, r is the relative distance between the missile and the maneuvering target. V represents the first derivative of the corresponding letter with respect to time. M φ M These represent the missile's speed, lead angle, and V, respectively. T φ T Let represent the speed magnitude and lead angle of the maneuvering target, respectively; λ is the line-of-sight angle between the missile and the maneuvering target; and γ... M It is the missile's velocity tilt angle, γ T It is the velocity angle of the maneuvering target; Step 102: Set the state variable x1 = λ - λ d State variables Based on the equations of relative motion, the system state equations are established as follows: In the formula, λ d For the desired viewing angle, This indicates the missile's acceleration along a direction perpendicular to the line of sight. This represents the acceleration of a maneuvering target along a direction perpendicular to the line of sight. This represents the disturbance quantity of the system; Step 2 specifically includes: Step 201: Based on the state equations of the missile and the maneuvering target established in Step 1, establish the non-singular terminal sliding surface as: s = x1 + k|x2| β sgn(x2) In the formula, s represents a non-singular terminal sliding surface, x1 and x2 represent state variables of the state equation, k and β represent the sliding surface parameters to be designed, k > 0, 1 < β < 2, and sgn() represents the step function; Step 202: Design the double power fast reaching law based on the non-singular terminal sliding surface as follows: In the formula, Let denot s = α1, α2, α3a, b, and c represent the reaching law parameters to be designed, and α1>0, α2>0, α3>0, α4>0, α5>0. <b<1,c> 0; Step 3 specifically includes: Step 301: Extend the state equation by setting the state variable x3 = f(t), and the extended state equation is: In the formula, y represents the state variable, and v(t) represents a function of the derivative of the disturbance. Step 302: Design the extended state observer for the extended state equation as follows: In the formula, z1, z2, and z3 represent the observed quantities, and e1 represents the error function. β 01 β 02 β 03 , m are the parameters to be designed, β 01 >0,β 02 >0,β 03 >0, 0 < m < 1.

2. The method for determining the missile angle guidance law based on non-singular terminal sliding mode control according to claim 1, characterized in that... The method also includes: Step 5: Construct the Lyapunov function and use the relevant finite-time convergence theorem to perform convergence analysis on the guidance law determined in Step 4.

3. The method for determining the missile angle guidance law based on non-singular terminal sliding mode control according to claim 1, characterized in that: Step 4 specifically includes: Step 401: Differentiate the non-singular terminal sliding surface and substitute it into the state equation designed in Step 1 to obtain: Step 402: Based on the double-power fast reaching law designed in Step 2, the formula for calculating the control input is obtained as follows: In the formula, a m For control input; Step 403: Considering the singularity of x2, modify the control input calculation formula as follows: Step 404: Considering the use of the extended state observer designed in Step 3 to estimate the disturbance, the control input calculation formula is modified as follows: The above formula represents a definite guidance law.

4. A missile angle guidance law determination device based on non-singular terminal sliding mode control for performing the method of claim 1, characterized in that... The device includes: The state equation establishment module is used to establish state equations based on the relative motion relationship between the missile and the maneuvering target. The sliding surface design module is used to design non-singular terminal sliding surfaces based on the established state equations, and to design double power fast approaching law approaching sliding surfaces. The state observer design module is used to expand the disturbance of the maneuvering target into a new state variable and design an expanded state observer to estimate the state variable. The guidance law determination module is used to consider the occurrence of singular phenomena in the state and the estimation of maneuvering target disturbances by the extended state observer, and to determine the missile's guidance law based on the double power fast approach law of the non-singular terminal sliding surface.

5. The missile angle guidance law determination device based on non-singular terminal sliding mode control according to claim 4, characterized in that... The device also includes: The convergence analysis module is used to construct Lyapunov functions and perform convergence analysis on a given guidance law using relevant finite-time convergence theorems.

6. A missile angle guidance law determination device based on non-singular terminal sliding mode control, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-3.

7. A storage medium containing computer-executable instructions, characterized in that, The computer-executable instructions, when executed by a computer processor, are used to perform the method as described in any one of claims 1-3.

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