Multi-missile cooperative guidance method based on fractional order error extended state observer

Abstract

This invention provides a multi-missile cooperative guidance method based on a fractional-order error extended state observer, comprising: acquiring missile swarm state information fed back by the system; determining, based on the missile swarm state information, using a fractional-order error extended state observer and a corresponding sliding mode surface, a predetermined time-converging acceleration command for the missile in the line-of-sight normal direction; determining, based on the missile swarm state information, using a fractional-order error extended state observer, a consensus protocol, and a corresponding sliding mode surface, a predetermined time-converging acceleration command for the missile in the line-of-sight direction; and, based on the acceleration commands in the line-of-sight normal and line-of-sight direction, a multi-missile cooperative guidance interception model to calculate the missile swarm state variables in real time, so as to complete the multi-missile cooperative guidance interception within a predetermined time. This invention solves the problems in existing multi-missile cooperative interception of maneuvering targets, such as the difficulty in intuitively obtaining the upper bound of the convergence time and the reduction of system noise immunity due to increased bandwidth of existing extended state observers.

Description

Technical Field

[0001] This invention relates to the field of multi-missile cooperative interception technology, and in particular to a multi-missile cooperative guidance method based on a fractional-order error expansion state observer. Background Technology

[0002] With the rapid development of multi-agent technology and self-organizing network technology, the modern battlefield situation is gradually shifting towards informatization and intelligence. Multi-missile coordinated strikes will become one of the important combat modes on the future battlefield. In particular, for the interception of mobile targets, multi-missile coordinated operations can effectively accomplish tasks that a single missile cannot, improve the interception success rate and combat effectiveness, and have become a major development direction and research frontier in the field of precision guidance.

[0003] Among these, the design of multi-missile cooperative guidance laws is a key issue in multi-missile cooperative guidance technology research, and it is crucial for improving missile guidance performance and cooperative combat capabilities. In this mission scenario, the missile swarm not only needs to hit the maneuvering target, but also needs to meet a certain attack angle upon impact. These requirements place higher precision and performance demands on the design of the cooperative guidance law. Furthermore, to ensure that multiple missiles can hit the target simultaneously, it is necessary to adjust the remaining flight time of each missile to reduce the deviation in the cooperative attack time, and it is also necessary to ensure the convergence time characteristics of the cooperative guidance law. However, in existing research on multi-missile cooperative interception of maneuvering targets, the guidance system struggles to intuitively obtain the upper bound of the convergence time, and the increased bandwidth of existing extended state observers reduces the system's noise immunity. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a multi-missile cooperative guidance method based on a fractional-order error extended state observer, so as to alleviate the problem that the guidance system is difficult to intuitively obtain the upper bound of the convergence time and that increasing the bandwidth of the existing extended state observer will reduce the system's noise immunity.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0006] In a first aspect, embodiments of the present invention provide a multi-missile cooperative guidance method based on a fractional-order error expansion state observer, comprising: acquiring missile group state information fed back by the system; based on the missile group state information, using a line-of-sight normal fractional-order error expansion state observer and a normal predetermined time convergence sliding surface to determine the acceleration command of the missile in the line-of-sight normal direction that satisfies predetermined time convergence; wherein, the normal predetermined time convergence sliding surface is designed to satisfy a predetermined time convergence stability theorem; based on the missile group state information, using a line-of-sight direction fractional-order error expansion state observer, a consensus protocol, and a line-of-sight direction integral sliding surface to determine the acceleration command of the missile in the line-of-sight direction that satisfies predetermined time convergence; wherein, the line-of-sight direction integral sliding surface is designed to satisfy a consensus protocol and satisfies a predetermined time convergence stability theorem; and calculating the missile group state variables in real time based on the missile acceleration command in the line-of-sight normal direction, the missile acceleration command in the line-of-sight direction, and a pre-determined multi-missile cooperative guidance interception model to complete multi-missile cooperative guidance interception within a predetermined time.

[0007] In one implementation, based on the missile swarm state information, a fractional-order error expansion state observer in the line-of-sight normal and a predetermined-time convergence sliding mode surface in the normal are used to determine the acceleration command of the missile in the line-of-sight normal that satisfies predetermined-time convergence. This includes: treating the target's maneuverability as a disturbance, and determining the disturbance estimate of the fractional-order error expansion state observer in the line-of-sight normal based on the missile swarm state variables in the line-of-sight normal guidance law and the multi-missile cooperative guidance and interception model; determining the predetermined-time convergence sliding mode surface in the normal based on the predetermined-time convergence stability theorem; and determining the line-of-sight normal cooperative guidance law based on the predetermined-time convergence sliding mode surface in the normal and the fractional-order error expansion state observer in the line-of-sight normal.

[0008] In one implementation, after treating the target maneuver as a disturbance, the fractional-order error expansion state observer of the line-of-sight normal is:

[0009]

[0010] Where β1,β2,β3,α e ,β e ,γ e >0 indicates the observer parameter, z 1i x represents 1i The estimated value, x 1i =r i , z 2i x represents 2i Estimated value x 3i =q i -q di q i Let q represent the line-of-sight angle of the i-th missile in the missile swarm. diLet z represent the expected line-of-sight angle of the i-th missile in the missile swarm. 3i This represents an estimate of the disturbance. express The estimated value, w ni This indicates the target's acceleration in the line-of-sight direction.

[0011] In one implementation, the normal-predetermined-time convergence sliding surface is:

[0012]

[0013] Among them, s 2i Let n1, n2, ρ > 0, λ > 1, and λρ > 1. And β(α,ε) is a complete β function. Indicates the line-of-sight angle q i The first derivative, T p2 This indicates the second scheduled time.

[0014] In one implementation, the line-of-sight normal cooperative guidance law is:

[0015]

[0016] Among them, u ni T represents the acceleration command of the i-th missile in the line-of-sight direction within the missile swarm. p1 This indicates that at the first predetermined time, the line-of-sight angles of each missile in the missile group converge to the expected value and the line-of-sight angular rate converges to zero. The upper bound of the overall convergence time is: T pn =T p1 +T p2 .

[0017] In one implementation, based on the missile group state information, a fractional-order error expansion state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction are used to determine the acceleration command of the missile that satisfies a predetermined time convergence in the line-of-sight direction. This includes: determining the integral sliding surface in the line-of-sight direction based on the consensus protocol; and determining the fractional-order error expansion state observer in the line-of-sight direction and the cooperative guidance law that satisfies a predetermined time convergence in the line-of-sight direction based on the integral sliding surface in the line-of-sight direction and a multi-missile cooperative guidance and interception model.

[0018] In one implementation, determining the integral sliding surface of the line-of-sight direction based on a consensus protocol includes: determining the estimated interception time t based on the consensus protocol and a multi-missile cooperative guidance interception model. Ti Consistency protocol; based on estimated interception time t Ti The consensus protocol determines the integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is:

[0019]

[0020] Among them, s 1i Let x represent the first sliding surface of the i-th missile in the missile group. 5i =t tgi Indicates the remaining flight time. r i This represents the relative distance between the i-th missile and the target. Indicates r i The first derivative, l ij =l ji = 0 or 1, 0 < σ < 1, n represents the number of missiles in the missile group.

[0021] In one implementation, after treating the target maneuver as a disturbance, the fractional-order error expansion state observer in the line-of-sight direction is:

[0022]

[0023] in, express The estimated value, w gi This indicates the target's acceleration in the line-of-sight direction.

[0024] In one implementation, the cooperative guidance law that satisfies the convergence of the line-of-sight direction within a predetermined time is as follows:

[0025]

[0026] Among them, u gi The acceleration command of the i-th missile in the missile group in the line-of-sight direction.

[0027] Secondly, embodiments of the present invention provide a multi-missile cooperative guidance device based on a fractional-order error expansion state observer, comprising: an information acquisition module for acquiring missile group state information fed back by the system; a first command determination module for determining, based on the missile group state information, an acceleration command that satisfies predetermined time convergence in the line-of-sight normal direction using a fractional-order error expansion state observer in the line-of-sight normal direction and a predetermined time convergence sliding surface in the line-of-sight normal direction; wherein, the predetermined time convergence sliding surface in the line-of-sight normal direction is designed to satisfy a predetermined time convergence stability theorem; a second command determination module for determining, based on the missile group state information, an acceleration command that satisfies predetermined time convergence in the line-of-sight direction using a fractional-order error expansion state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is designed to satisfy a consensus protocol and satisfies a predetermined time convergence stability theorem; and a guidance module for real-time calculation of missile group state variables based on the missile's acceleration command in the line-of-sight normal direction, the missile's acceleration command in the line-of-sight direction, and a pre-determined multi-missile cooperative guidance and interception model, so as to complete multi-missile cooperative guidance and interception within a predetermined time.

[0028] The embodiments of the present invention bring the following beneficial effects:

[0029] The multi-missile cooperative guidance method based on a fractional-order error extended state observer provided in this embodiment of the invention first acquires the missile group state information fed back by the system; then, based on the missile group state information, a fractional-order error extended state observer in the line-of-sight normal direction and a normal direction predetermined time convergence sliding surface are used to obtain the acceleration command of the missile in the line-of-sight normal direction that satisfies the predetermined time convergence; next, based on the missile group state information, a fractional-order error extended state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction are used to obtain the acceleration command of the missile in the line-of-sight direction that satisfies the predetermined time convergence; finally, based on the missile acceleration command in the line-of-sight normal direction, the missile acceleration command in the line-of-sight direction, and a pre-determined multi-missile cooperative guidance and interception model, the missile group state variables are calculated in real time, and the multi-missile cooperative guidance and interception can be completed within a predetermined time. The above method employs a line-of-sight normal direction cooperative guidance law and a line-of-sight direction cooperative guidance law determined by a stability theorem that satisfies predetermined convergence time, based on a fractional-order error-expanded state observer. This yields the missile's acceleration command in the line-of-sight normal direction and the missile's acceleration command in the line-of-sight direction, enabling the guidance system to accurately estimate the convergence time and adjust it in real time, thus ensuring the stability and accuracy of the guidance system. Simultaneously, the use of a fractional-order error-expanded state observer improves the existing state observer, solving the problem that increasing the system bandwidth reduces noise immunity and improving the observer's performance.

[0030] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0031] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0032] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1(a) is a schematic diagram of the planar interception geometry of a single missile intercepting a target according to an embodiment of the present invention;

[0034] Figure 1(b) is a schematic diagram of the planar interception geometry of a target intercepted by multiple missiles according to an embodiment of the present invention;

[0035] Figure 2 A flowchart of a multi-missile cooperative guidance method based on a fractional-order error extended state observer provided in an embodiment of the present invention;

[0036] Figure 3 A flowchart illustrating the overall process of a multi-missile cooperative guidance method based on a fractional-order error-expanded state observer, provided for an embodiment of the present invention.

[0037] Figure 4 A schematic diagram of a multi-missile cooperative guidance device based on a fractional-order error expansion state observer provided in an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions 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, 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.

[0040] Currently, the guidance laws for multi-missile coordinated interception have the following main drawbacks:

[0041] 1. In the problem of multi-missile coordinated interception of maneuvering targets, most existing cooperative guidance laws are based on finite-time or fixed-time convergence designs. Finite-time convergence depends on the initial conditions of the system; if the initial conditions are infinitely large, the estimated convergence time also tends to be infinitely large. While fixed-time convergence is no longer constrained by the initial conditions, it is difficult to find a clear correspondence between system parameters and a fixed time, leading to inaccurate convergence time estimates and difficulty in adjustment. In actual cooperative guidance processes, due to the extremely short terminal guidance interception time, the guidance system needs to satisfy rapid convergence characteristics while possessing a clear and pre-set upper bound on the convergence time to ensure the stability and accuracy of the guidance system.

[0042] 2. In addition, in this type of problem, the target's maneuver is often regarded as a disturbance, and a state observer is used to estimate it and compensate for it in the guidance law. However, expanding the state observer to increase the bandwidth will reduce the system's noise immunity.

[0043] Based on this, the present invention provides a multi-missile cooperative guidance method based on a fractional-order error extended state observer, which can improve the problem that the guidance system has difficulty in intuitively obtaining the upper bound of the convergence time and that increasing the bandwidth of the existing extended state observer will reduce the system's noise immunity.

[0044] To facilitate understanding of this embodiment, the modeling of a multi-missile cooperative interception scenario is first introduced, considering only planar interception. The geometric relationship between the missile group and the target in planar interception is shown in Figure 1 (Figure 1(a) shows a single missile intercepting a target, and Figure 1(b) shows multiple missiles intercepting a target). Wherein, M i and T i Let r represent the centers of mass of the missile and the target, respectively. i q represents the relative distance between the missile and the target. i Indicates the missile's line-of-sight angle. and V represents the velocity directional angle of the missile and the target, respectively. mi and V ti Let i represent the speed of the missile and the speed of the target, respectively, where i = 1, ..., n, and n represents the number of missiles in the missile group.

[0045] The equations of motion between the missile group and the target are:

[0046]

[0047]

[0048] Differentiating formulas (1) and (2) above yields:

[0049]

[0050]

[0051] Among them, u gi and u ni These are the acceleration commands for the missile in the line-of-sight direction and the line-of-sight normal direction, respectively. gi and w ni These represent the target's acceleration in the line-of-sight direction and the normal direction of the line of sight, respectively.

[0052] Based on the above equations of motion, construct the state equations of the guidance system, and let x 1i =r i , x 3i =q i -q di , We can obtain:

[0053]

[0054] Where, q di This represents the expected line-of-sight angle of the i-th missile in the missile group. Indicates r i The first derivative. Furthermore, under the terminal condition constraint of time coordination, it is necessary to ensure that each missile can hit the target simultaneously, i.e., time consistency, thus requiring the introduction of a new state variable: the remaining flight time, denoted as t. tgi Designing corresponding guidance laws in the line-of-sight direction can ensure that the remaining flight time of each missile remains consistent within the predetermined time.

[0055] In terminal guidance interception scenarios, t tgi It can be calculated using the following formula:

[0056]

[0057] Differentiating formula (6) above, we get:

[0058]

[0059] Simplify the above formula (7) by eliminating the constant term and introducing the variable t. Ti This indicates the estimated time of successful target interception at time t, i.e.:

[0060] t Ti =t+t tgi (8)

[0061] Differentiating formula (8) and combining it with formula (7), we get:

[0062]

[0063] Let x 5i =t tgi From this, we can obtain the overall state equation of the guidance system (i.e., the multi-missile cooperative guidance and interception model):

[0064]

[0065] Next, a detailed description of a multi-missile cooperative guidance method based on a fractional-order error extended state observer, as disclosed in an embodiment of the present invention, will be provided. See also... Figure 2 The flowchart shown illustrates a multi-missile cooperative guidance method based on a fractional-order error-expanded state observer, showing that the method mainly includes the following steps S201 to S204:

[0066] Step S201: Obtain the missile group status information fed back by the system.

[0067] In one implementation, missile group status information fed back by the guidance system is acquired, wherein the missile group status information includes at least: the relative distance between the missile and the target, the first derivative of the relative distance between the missile and the target, the difference between the missile's line-of-sight angle and the expected value of the line-of-sight angle, the missile's line-of-sight angle, and a predetermined convergence time.

[0068] Step S202: Based on the missile group state information, the fractional-order error expansion state observer of the line-of-sight normal and the normal predetermined time convergence sliding mode surface are used to determine the acceleration command of the missile that satisfies the predetermined time convergence in the line-of-sight normal.

[0069] The normal-predetermined-time convergent sliding surface is designed to satisfy the predetermined-time convergence stability theorem.

[0070] Step S203: Based on the missile group state information, the fractional-order error expansion state observer in the line-of-sight direction, the consensus protocol, and the integral sliding surface in the line-of-sight direction are used to determine the acceleration command of the missile that meets the predetermined time convergence in the line-of-sight direction.

[0071] The integral sliding surface in the line-of-sight direction is designed using a consensus protocol and satisfies the predetermined time convergence stability theorem.

[0072] Step S204: Based on the missile's acceleration command in the line-of-sight direction, the missile's acceleration command in the line-of-sight direction, and the pre-determined multi-missile cooperative guidance and interception model, calculate the missile group's state variables in real time to complete the multi-missile cooperative guidance and interception within a predetermined time.

[0073] In one implementation, after obtaining the acceleration command of the missile in the line-of-sight normal direction and the acceleration command of the missile in the line-of-sight direction, the state variables of the missile group can be calculated in real time according to the predetermined multi-missile cooperative guidance and interception model (i.e., the above formula (10)), so that multi-missile cooperative guidance and interception can be completed within a predetermined time.

[0074] The multi-missile cooperative guidance method based on a fractional-order error-expanded state observer provided in this invention employs a line-of-sight normal direction cooperative guidance law and a line-of-sight direction cooperative guidance law determined by a stability theorem that satisfies predetermined time convergence, based on a fractional-order error-expanded state observer. This yields the missile's acceleration command in the line-of-sight normal direction and the missile's acceleration command in the line-of-sight direction, enabling the guidance system to accurately estimate the convergence time and adjust it in real time, thus ensuring the stability and guidance accuracy of the guidance system. Simultaneously, the use of a fractional-order error-expanded state observer improves upon existing state observers, solving the problem that increasing the system's bandwidth reduces its noise immunity and improving the observer's performance.

[0075] Before introducing how the line-of-sight normal cooperative guidance law is determined, we will first introduce the relevant definitions and lemmas:

[0076] Definition 1: Let α, ε > 0, the complete β function is composed of Euler integrals and the complete γ function, and is calculated as follows:

[0077]

[0078] Where γ(·) denotes a complete γ function, defined by Euler integral operations as:

[0079]

[0080] Lemma 1: If variables satisfy x1, x2, ..., x n If ≥0, and the parameters satisfy 0<α≤1, β>1, then the following relationship exists:

[0081]

[0082] Lemma 2: Consider the following nonlinear system:

[0083]

[0084] in, Let x0 be the state vector of the system corresponding to formula (14), and x0 be the initial state of the system. And satisfy For system internal parameters, For a nonlinear system, assume there exists a continuous, positive definite, radially unbounded function V(x): Such that for any system solution x(t,x0), the following conditions are met:

[0085]

[0086] In formula (15), μ, ω, γ, η>0, γη>1, T m The system internal parameters are calculated using formula (16). The nonlinear system that satisfies the above conditions is a globally predetermined time stable system, and the predetermined time is T. p .

[0087]

[0088] In one implementation, the step of determining the acceleration command that satisfies predetermined time convergence in the line-of-sight normal direction based on missile group state information, using a fractional-order error-expanded state observer in the line-of-sight normal direction and a predetermined-time convergence sliding mode surface in the normal direction, includes:

[0089] First, the target's maneuverability is treated as a disturbance, and based on the line-of-sight normal guidance law and the missile group state variables in the multi-missile cooperative guidance and interception model, the disturbance estimate of the line-of-sight normal fractional error expansion state observer is determined.

[0090] In practical implementation, after treating the target's maneuver as a disturbance, this embodiment of the invention uses a fractional-order error-expanded state observer to estimate it. The general configuration of this observer in a second-order system is as follows:

[0091]

[0092] Where β1,β2,β3,α e ,β e ,γ e >0 indicates observer parameters, Determined by the corresponding nonlinear system, u is the observer input, z1 is the x1 estimate, z2 is the x2 estimate, and z3 is the perturbation estimate.

[0093] Based on the above formula (17) and the aforementioned formula (10), the line-of-sight normal perturbation observer can be obtained, that is, the line-of-sight normal fractional error expansion state observer:

[0094]

[0095] In formula (18), z 1i x represents 1i The estimated value, x 1i =r i , z 2i x represents 2i Estimated value, z 3i This represents an estimate of the disturbance. express The estimated value.

[0096] Then, the normal time-converging sliding surface is determined based on the predetermined time convergence stability theorem.

[0097] For a predetermined time convergence guidance law in the line-of-sight normal direction, it is necessary to ensure that the line-of-sight angles of all missiles converge to the desired value and the line-of-sight angular rate converges to zero within a predetermined time. In this embodiment of the invention, the line-of-sight normal cooperative guidance law adopts a predetermined time convergence stability theorem, and the predetermined time includes two parts, namely the sliding surface s. 2i The predetermined time T for convergence to zero p1 And the guidance system reaches the sliding surface s 2i After that, the state variable x 3i ,x 4i The predetermined time T for convergence to zero p2 .

[0098] Specifically, the convergence sliding surface along the line-of-sight normal at a predetermined time is selected as follows:

[0099]

[0100] Among them, s 2i Let n1, n2, ρ > 0, λ > 1, and λρ > 1. And β(α,ε) is a complete β function. Indicates the line-of-sight angle q i The first derivative, T p2 This indicates the second scheduled time.

[0101] Let V 2i =|x 3i |, when s 2i When = 0, the following relationship exists:

[0102]

[0103] For V 2i Differentiation yields:

[0104]

[0105] From Lemma 1 above, we can obtain:

[0106]

[0107] From equation (22) above, it can be seen that the system is a convergent and stable system with a predetermined time, and the predetermined time is T. p2 .

[0108] Finally, the line-of-sight normal cooperative guidance law is determined based on the normal-predetermined-time convergent sliding mode surface and the line-of-sight normal fractional-order error expansion state observer.

[0109] Specifically, the line-of-sight normal cooperative guidance law is determined based on the convergence sliding surface of the normal at a predetermined time according to formula (19). The guidance law is as follows:

[0110]

[0111] By employing the aforementioned line-of-sight normal cooperative guidance law, the sliding surface s can be made 2i At the scheduled time T p1 It converges to zero, as proven below:

[0112] Differentiating formula (19) yields:

[0113]

[0114] Combining the overall state equation (10) of the guidance system and the line-of-sight normal cooperative guidance law (23), we can obtain:

[0115]

[0116] Let V 1i =|s 2i |, Differentiation yields:

[0117]

[0118] As defined by the fractional-order error extended state observer, the perturbation estimation error will tend to zero within a certain time. Therefore, equation (26) can be simplified to:

[0119]

[0120] From the above formula (27), it can be seen that the sliding surface s 2i It can converge to zero within a predetermined time, and the predetermined time is T. p1 The aforementioned line-of-sight normal guidance law enables the line-of-sight angles of each missile in the missile swarm to converge to the desired value and the line-of-sight angular rate to converge to zero. The overall convergence time upper bound is: T pn =T p1 +T p2 .

[0121] In one implementation, the steps described above, based on missile group state information and employing a line-of-sight fractional-order error-expanded state observer, a consensus protocol, and an integral sliding surface in the line-of-sight direction to determine the acceleration command that satisfies a predetermined time convergence in the line-of-sight direction, include:

[0122] First, the integral sliding surface for determining the line-of-sight direction is determined based on a consensus protocol.

[0123] In practical implementation, firstly, based on the consensus protocol and the multi-missile cooperative guidance and interception model, the estimated interception time t is determined. Ti The consensus protocol; then, based on the estimated interception time t Ti The consistency protocol determines the integral sliding surface that converges within a predetermined time for the line of sight.

[0124] Specifically, considering a multi-agent system with n individuals, when its communication topology is undirected and connected, the consensus protocol is as follows:

[0125]

[0126] Among them, l ij =l ji =0 or 1, 0<σ<1, combined with the overall state equation (10) of the guidance system, the consistency protocol under this mission scenario is determined, that is, the estimated interception time t. Ti Consistency protocol:

[0127]

[0128] Based on formula (29), determine the integral sliding surface in the line-of-sight direction:

[0129]

[0130] Then, based on the integral sliding surface in the line-of-sight direction and the multi-missile cooperative guidance and interception model, the fractional-order error expansion state observer and the line-of-sight cooperative guidance law are determined.

[0131] In practical implementation, similar to the line-of-sight normal, after treating the target maneuver as a disturbance, based on the overall state equation (10) of the guidance system, the line-of-sight disturbance observer, that is, the line-of-sight fractional error expansion state observer, can be obtained as follows:

[0132]

[0133] in, express The estimated value.

[0134] Furthermore, based on formula (30), the cooperative guidance law that satisfies the predetermined time convergence in the line-of-sight direction can be obtained as follows:

[0135]

[0136] By employing the aforementioned line-of-sight direction coordinated guidance law, the sliding surface s can be made 1i At the scheduled time T p3 It converges to zero, as proven below:

[0137] The derivative of formula (30) is as follows:

[0138]

[0139] Combining the overall state equation (10) of the guidance system and the line-of-sight cooperative guidance law formula (32), the above formula (33) can be converted into:

[0140]

[0141] Let V 3i =|s 1i |, Differentiation yields:

[0142]

[0143] Similar to the line-of-sight normal, the disturbance estimation error will also tend to zero over a certain period of time. Therefore, formula (35) can be simplified to:

[0144]

[0145] As can be seen from the above, the sliding surface s 1i It can converge to zero within a predetermined time, and the predetermined time is T. p3 The aforementioned line-of-sight guidance law enables multiple missiles to simultaneously intercept maneuvering targets, with an overall convergence time upper bound of T. pg =T p3 .

[0146] For ease of understanding, this embodiment of the invention also provides an overall flowchart of a multi-missile cooperative guidance method based on a fractional-order error extended state observer, see [link to flowchart]. Figure 3 As shown, it can be divided into two main parts: The first part is in the line-of-sight direction. Based on the consensus protocol, the acceleration command in the line-of-sight direction is obtained by combining integral sliding mode and fractional-order error expansion state observer, so as to ensure that all missiles can intercept maneuvering targets simultaneously within a predetermined time. The second part is in the line-of-sight normal direction. The acceleration command in the line-of-sight normal direction is obtained by using the predetermined time convergence stability theorem and fractional-order error expansion state observer, so as to ensure that the line-of-sight angular rate between each missile and the target converges to zero and the line-of-sight angle converges to the expected value within a predetermined time.

[0147] The method provided in this embodiment of the invention adopts the predetermined time convergence stability theorem and designs a cooperative sliding mode guidance law for the line-of-sight normal and line-of-sight direction of the multi-missile interception system, respectively, to ensure that the missile group can simultaneously intercept maneuvering targets within a predetermined time and converge to the desired line-of-sight angle, thereby achieving spatiotemporal coordination. A fractional-order error expansion state observer is used to estimate the target maneuver. By introducing two fractional-order differential operators, the cross frequency of the system is adjusted, the system balance adjustment space is expanded, and the observer has better noise resistance.

[0148] In addition to the multi-missile cooperative guidance method based on a fractional-order error extended state observer provided in the foregoing embodiments, this invention also provides a multi-missile cooperative guidance device based on a fractional-order error extended state observer. (See [link to previous document]). Figure 4 The schematic diagram shown illustrates the structure of a multi-missile cooperative guidance device based on a fractional-order error expansion state observer, showing that the device mainly includes the following parts:

[0149] The information acquisition module 401 is used to acquire the missile group status information fed back by the system.

[0150] The first command determination module 402 is used to determine the acceleration command of the missile in the line-of-sight normal direction based on the missile group state information, using a fractional-order error expansion state observer in the line-of-sight normal direction and a normal predetermined time convergence sliding surface; wherein, the normal predetermined time convergence sliding surface is designed to satisfy the predetermined time convergence stability theorem.

[0151] The second command determination module 403 is used to determine the acceleration command of the missile in the line-of-sight direction based on the missile group state information, using a fractional-order error expansion state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is designed by the consensus protocol and satisfies the predetermined time convergence stability theorem.

[0152] The guidance module 404 is used to calculate the state variables of the missile group in real time based on the missile's acceleration command in the line-of-sight direction, the missile's acceleration command in the line-of-sight direction, and a pre-determined multi-missile cooperative guidance and interception model, so as to complete the multi-missile cooperative guidance and interception within a predetermined time.

[0153] The multi-missile cooperative guidance device based on a fractional-order error-expanded state observer provided in this invention employs a line-of-sight normal cooperative guidance law and a line-of-sight direction cooperative guidance law determined by a stability theorem that satisfies predetermined time convergence, based on a fractional-order error-expanded state observer. This allows the missile to obtain acceleration commands in the line-of-sight normal direction and acceleration commands in the line-of-sight direction, enabling the guidance system to accurately estimate the convergence time range and adjust it in real time, thus ensuring the stability and guidance accuracy of the guidance system. Simultaneously, the use of a fractional-order error-expanded state observer improves upon existing state observers, solving the problem that increasing the system bandwidth reduces noise immunity and improving observer performance.

[0154] In one embodiment, the first instruction determination module 402 is further configured to: treat the target's maneuverability as a disturbance, and determine the disturbance estimate of the fractional-order error expansion state observer of the line-of-sight normal based on the line-of-sight normal guidance law and the missile group state variables in the multi-missile cooperative guidance and interception model; determine the predetermined time convergence sliding surface of the normal based on the predetermined time convergence stability theorem; and determine the line-of-sight normal cooperative guidance law based on the predetermined time convergence sliding surface of the normal and the fractional-order error expansion state observer of the line-of-sight normal.

[0155] In one implementation, the fractional-order error expansion state observer for the line-of-sight normal is:

[0156]

[0157] Where β1,β2,β3,α e ,β e ,γ e >0 indicates the observer parameter, z 1i x represents 1i The estimated value, x 1i =r i , z 2i x represents 2i Estimated value x 3i =q i -q di q i Let q represent the line-of-sight angle of the i-th missile in the missile swarm. di Let z represent the expected line-of-sight angle of the i-th missile in the missile swarm. 3i This represents an estimate of the disturbance. express The estimated value, w ni This indicates the target's acceleration in the line-of-sight direction.

[0158] In one implementation, after treating the target maneuver as a disturbance, the aforementioned normal-predetermined-time convergence sliding surface is:

[0159]

[0160] Among them, s 2i Let n1, n2, ρ > 0, λ > 1, and λρ > 1. And β(α,ε) is a complete β function. Indicates the line-of-sight angle q i The first derivative, T p2 This indicates the second scheduled time.

[0161] In one implementation, the aforementioned line-of-sight normal cooperative guidance law is:

[0162]

[0163] Among them, u ni T represents the acceleration command of the i-th missile in the line-of-sight direction within the missile swarm. p1 This indicates that at the first predetermined time, the line-of-sight angles of each missile in the missile group converge to the expected value and the line-of-sight angular rate converges to zero. The upper bound of the overall convergence time is: T pn =T p1 +T p2 .

[0164] In one embodiment, the second instruction determination module 403 is further configured to: determine the integral sliding surface of the line-of-sight direction based on a consensus protocol; and determine the fractional-order error expansion state observer of the line-of-sight direction and the cooperative guidance law that satisfies the predetermined time convergence of the line-of-sight direction based on the integral sliding surface of the line-of-sight direction and the multi-missile cooperative guidance and interception model.

[0165] In one implementation, the second instruction determination module 403 is further configured to: determine the estimated interception time t based on the consensus protocol and the multi-missile cooperative guidance and interception model. Ti Consistency protocol; based on estimated interception time t Ti The consensus protocol determines the integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is:

[0166]

[0167] Among them, s 1i Let x represent the first sliding surface of the i-th missile in the missile group. 5i =t tgi Indicates the remaining flight time. r i This represents the relative distance between the i-th missile and the target. Indicates r i The first derivative, l ij =l ji = 0 or 1, 0 < σ < 1, n represents the number of missiles in the missile group.

[0168] In one implementation, after treating the target maneuver as a disturbance, the fractional-order error expansion state observer in the aforementioned line-of-sight direction is:

[0169]

[0170] in, express The estimated value, w gi This indicates the target's acceleration in the line-of-sight direction.

[0171] In one implementation, the aforementioned line-of-sight direction satisfies a cooperative guidance law that converges within a predetermined time:

[0172]

[0173] Among them, u gi The acceleration command of the i-th missile in the missile group in the line-of-sight direction.

[0174] The device provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned method embodiment. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0175] This invention also provides an electronic device, specifically, the electronic device includes a processor and a storage device; the storage device stores a computer program, and the computer program, when run by the processor, executes the method described in any of the above embodiments.

[0176] Figure 5 The present invention provides a schematic diagram of the structure of an electronic device 100, which includes a processor 50, a memory 51, a bus 52 and a communication interface 53. The processor 50, the communication interface 53 and the memory 51 are connected through the bus 52. The processor 50 is used to execute executable modules, such as computer programs, stored in the memory 51.

[0177] The memory 51 may include high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 53 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc.

[0178] Bus 52 can be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 5 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0179] The memory 51 is used to store programs. After receiving an execution instruction, the processor 50 executes the programs. The method executed by the device for defining the flow process disclosed in any of the foregoing embodiments of the present invention can be applied to the processor 50 or implemented by the processor 50.

[0180] Processor 50 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 50 or by instructions in software form. Processor 50 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 51. The processor 50 reads the information in memory 51 and, in conjunction with its hardware, completes the steps of the above method.

[0181] The computer program product of the readable storage medium provided in the embodiments of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the foregoing method embodiments. For specific implementation, please refer to the foregoing method embodiments, which will not be repeated here.

[0182] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0183] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-missile cooperative guidance method based on a fractional-order error-expanded state observer, characterized in that, include: Obtain missile group status information from the system feedback; Based on the missile group state information, a line-of-sight normal fractional-order error expansion state observer and a normal predetermined-time convergence sliding mode surface are used to determine the acceleration command of the missile that satisfies predetermined-time convergence in the line-of-sight normal direction; wherein, the normal predetermined-time convergence sliding mode surface is designed to satisfy the predetermined-time convergence stability theorem. Based on the missile group state information, a fractional-order error expansion state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction are used to determine the acceleration command of the missile that satisfies a predetermined time convergence in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is designed by the consensus protocol and satisfies a predetermined time convergence stability theorem. Based on the missile's acceleration command in the line-of-sight direction, the missile's acceleration command in the line-of-sight direction, and the pre-determined multi-missile cooperative guidance and interception model, the missile group's state variables are calculated in real time to complete the multi-missile cooperative guidance and interception within a predetermined time. The fractional-order error expansion state observer for the line-of-sight normal is: in, Indicates the observer parameters, z 1i express x 1i The estimated value, , z 2i express x 2i Estimated value , , Indicates the first missile group i The line-of-sight angle of a missile q di Indicates the first missile group i The expected line-of-sight angle of a missile. z 3i This represents an estimate of the disturbance. express The estimated value, This indicates the target's acceleration in the normal direction of line of sight. The normal-predetermined-time convergence sliding surface is: in, s 2i Indicates the normal-oriented sliding surface that converges within a predetermined time. , , , ,and For complete function, Indicates the line of sight angle The first derivative, Indicates the second scheduled time; The line-of-sight normal cooperative guidance law is: in, Indicates the first missile group i The acceleration command for each missile in the line-of-sight direction. This indicates that at the first predetermined time, the line-of-sight angles of each missile in the missile group converge to the desired value and the line-of-sight angular rate converges to zero. The upper bound of the overall convergence time is: .

2. The method according to claim 1, characterized in that, Based on the missile group state information, a fractional-order error-expanded state observer along the line-of-sight normal and a predetermined-time convergence sliding mode surface along the normal are used to determine the acceleration command of the missile that satisfies predetermined-time convergence along the line-of-sight normal, including: The target's maneuverability is treated as a disturbance, and based on the line-of-sight normal guidance law and the missile group state variables in the multi-missile cooperative guidance and interception model, the disturbance estimate of the line-of-sight normal fractional error expansion state observer is determined. The normal time-convergent sliding surface is determined based on the predetermined time convergence stability theorem. The line-of-sight normal cooperative guidance law is determined based on the convergent sliding surface of the normal at a predetermined time and the fractional-order error expansion state observer of the line-of-sight normal.

3. The method according to claim 1, characterized in that, Based on the missile group state information, a line-of-sight fractional-order error-expanded state observer, a consensus protocol, and an integral sliding surface in the line-of-sight direction are used to determine the acceleration command of the missile that satisfies a predetermined time convergence in the line-of-sight direction, including: Integral sliding surface for determining line-of-sight direction based on consensus protocol; Based on the integral sliding surface in the line-of-sight direction and the multi-missile cooperative guidance and interception model, the fractional-order error expansion state observer in the line-of-sight direction and the cooperative guidance law that satisfies the predetermined time convergence in the line-of-sight direction are determined.

4. The method according to claim 3, characterized in that, The integral sliding surface for determining the line-of-sight direction based on the consensus protocol includes: Based on the consensus protocol and the aforementioned multi-missile cooperative guidance and interception model, the estimated interception time is determined. Consistency protocol; Based on the estimated interception time The consistency protocol determines the integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is: in, Indicates the first missile group i The first sliding surface of a missile, Indicates the remaining flight time. , Indicates the first i The relative distance between the missile and the target express The first derivative, , , , n This indicates the number of missiles in a missile group.

5. The method according to claim 3, characterized in that, Treating the target maneuver as a disturbance, the fractional-order error expansion state observer along the line of sight is: in, express The estimated value, This indicates the target's acceleration in the line-of-sight direction.

6. The method according to claim 3, characterized in that, The cooperative guidance law that satisfies the predetermined time convergence for the line of sight direction is as follows: in, The first in the missile group i Acceleration command for a missile in the line-of-sight direction.

7. A multi-missile cooperative guidance device based on a fractional-order error-expanded state observer, characterized in that, To implement the method of claim 1, the method comprises: The information acquisition module is used to acquire the status information of the missile group fed back by the system; The first command determination module is used to determine the acceleration command of the missile in the line-of-sight normal direction that satisfies the predetermined time convergence based on the missile group state information, using a line-of-sight normal fractional error expansion state observer and a normal predetermined time convergence sliding surface; wherein, the normal predetermined time convergence sliding surface is designed to satisfy the predetermined time convergence stability theorem. The second command determination module is used to determine the acceleration command of the missile in the line-of-sight direction that satisfies a predetermined time convergence based on the missile group state information, using a fractional-order error expansion state observer in the line-of-sight direction, a consensus protocol, and an integral sliding surface in the line-of-sight direction; wherein, the integral sliding surface in the line-of-sight direction is designed by the consensus protocol and satisfies a predetermined time convergence stability theorem. The guidance module is used to calculate the state variables of the missile group in real time based on the missile's acceleration command in the line-of-sight direction, the missile's acceleration command in the line-of-sight direction, and a pre-determined multi-missile cooperative guidance and interception model, so as to complete the multi-missile cooperative guidance and interception within a predetermined time.

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