Nonlinear optimal time-to-go control guidance for intercepting maneuvering targets

Abstract

The application discloses a nonlinear optimal time of flight control guidance method for intercepting a maneuvering target, and the method comprises the following steps: establishing a nonlinear guidance model in an inertial system and converting to a relative virtual coordinate system; constructing a guidance law basic form which is a sum of a zero-control miss distance control item and a relative flight path error control item; deducing the zero-control miss distance control item based on an optimal control principle to meet a given performance index, determining the relative flight path error control item based on an optimal relative flight path error dynamics equation in an arc length domain, and thus obtaining a nonlinear optimal relative flight path control guidance law; and designing a future average speed prediction algorithm to establish a connection between the relative flight path and the time of flight, so as to realize time of flight control. The application is applied to the fields of aircraft dynamics and guidance and control, can directly design a guidance law for a maneuvering target, and has the advantages of simple form, strong robustness, high feasibility and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aircraft dynamics and guidance, control technology, and relates to a nonlinear optimal flight time control guidance method for intercepting a maneuvering target, in particular to a flight time control guidance method that can meet the collision time constraint under the scenario of intercepting a maneuvering target and ensure the optimal design performance index during the guidance process. BACKGROUND

[0002] Modern war with complex changes requires higher requirements for missile strikes. In order to improve the lethality and interception probability, it is an effective method to impose a terminal time constraint on the missile to achieve simultaneous attack, and the missile guidance law based on the constraint is called flight time control guidance law.

[0003] At present, the flight time control guidance law is mainly for fixed or slow-moving targets, and the flight time control of intercepting a maneuvering target is less studied. Through investigation, there are mainly two methods:

[0004] One is to design a guidance law based on a fixed target, and then use the predicted intercept point method to achieve flight time control of a maneuvering target. The performance of the guidance law under this method depends on the prediction accuracy of the intercept point and the remaining flight time.

[0005] The second is to convert the flight time control problem of intercepting a maneuvering target into a finite time tracking problem, such as tracking the integral state quantity and tracking the expected remaining flight time.

[0006] However, the performance of the guidance law under the first method depends heavily on the prediction accuracy of the intercept point and the remaining flight time. In the second method, the former is an offline optimization of the guidance parameters, which is difficult to cope with complex and variable actual scenarios. The latter requires a strict basic guidance law, and the analytical expression of the remaining flight time needs to be known. In addition, neither of the two methods considers the optimality problem during the guidance process. Therefore, it is necessary to propose a new nonlinear optimal flight time control method for intercepting a maneuvering target. SUMMARY

[0007] The application applies relative virtual coordinate frame and classical differential geometry curve principle to the flight time control problem of intercepting a maneuvering target, and proposes a guidance method combining relative flight distance control and future relative speed prediction. This guidance method can directly design a guidance law for a maneuvering target and meet certain optimal performance index during the guidance process. It has the advantages of simple form, strong robustness, high feasibility, etc. while achieving flight time control of a maneuvering target.

[0008] The technical concept of the present application is: firstly, a relative motion model is established in a relative virtual coordinate frame, and the problem of intercepting a maneuvering target is converted into the problem of attacking a virtual fixed target; secondly, the relative motion model is converted to an arc length domain by using the principle of differential geometry, so as to eliminate the influence of the change of relative velocity; thirdly, a guidance law in the form of "zero-control miss distance control term + relative flight path control term" is designed; then, based on optimal control, the zero-control miss distance term satisfying a specific performance index is deduced to be ideal proportional guidance; then, by fully utilizing the properties of ideal proportional guidance, an analytical solution of the residual relative flight path under ideal proportional guidance in the relative virtual coordinate system is deduced; further, the error dynamics equation of the relative flight path is deduced, and a nonlinear optimal relative flight path control guidance law is obtained by combining the optimal error dynamics in the arc length domain; finally, by fully utilizing the property that the designed guidance law continuously approaches ideal proportional guidance, a future average speed prediction algorithm is designed to establish the relationship between the expected residual relative flight path and the expected residual flight time, so as to realize the control of attack time.

[0009] To achieve the above object, the present application provides a nonlinear optimal flight time control guidance method for intercepting a maneuvering target, comprising the following steps 1 to 6:

[0010] Step 1: a nonlinear guidance model is established in an inertial system, and the nonlinear guidance model is converted to a relative virtual coordinate system, and the time domain is converted to an arc length domain.

[0011] In one of the embodiments, the process of step 1 is:

[0012] The nonlinear guidance model is established in an inertial system, and is:

[0013]

[0014] Wherein, r represents the relative distance between the missile and the target, and λ represents the line-of-sight angle between the missile and the target; the subscripts M and T respectively represent the missile and the target, V M , V T respectively represent the speed of the missile and the target, a M , a T respectively represent the acceleration of the missile and the target, and the acceleration acts on the vertical speed direction; γ M , γ T respectively represent the flight path angle of the missile and the target, η M , η T respectively represent the speed pre-angle of the missile and the target.

[0015] In the relative virtual coordinate frame, the origin is located at the mass center of the target, and the independent variable in the arc length domain is the relative arc length between the missile and the target, so that the nonlinear guidance model is converted to the relative virtual coordinate system as:

[0016]

[0017] wherein, "x R " represents the variable x as a physical quantity in the virtual relative coordinate system, "x'" represents the derivative of the variable x with respect to the relative arc length s, since the target is a fixed target in the virtual coordinate system, r' and λ' in the above equation (2) represent the relative distance between the missile and the target and the derivative of the line-of-sight angle between the missile and the target with respect to the relative arc length s, respectively, V R , a R , γ R , η R represent the velocity, acceleration, flight path angle, and velocity pre-angle of the missile in the virtual relative coordinate system, respectively, γ' R represents the derivative of the flight path angle of the missile in the virtual relative coordinate system with respect to the relative arc length s, and κ R is the guidance curvature perpendicular to the velocity direction.

[0018] In addition, the time domain is converted to the arc length domain, and the relative arc length and time have the following relationship:

[0019]

[0020] wherein, t represents time;

[0021] The relationship between the state quantities in the relative virtual system and the inertial system is represented as:

[0022]

[0023] wherein, k = V T / V M represents the velocity ratio.

[0024] Under the nonlinear guidance model of the above equation (2) and equation (3), the design of the relative flight path control guidance law is achieved by designing the guidance curvature κ R .

[0025] Step 2, construct the basic form of the relative flight path control guidance law, including the zero-control miss distance control term and the relative flight path error control term.

[0026] In one embodiment, the basic form of the constructed relative flight path control guidance law is specifically:

[0027] κ R = κ ZEM + κ RFR (5)

[0028] wherein, κ ZEM represents the zero-control miss distance control term, which is used to control the zero-control miss distance; and κ RFR represents the relative flight path error control term, which is used to control the relative flight path error.

[0029] Step 3, based on optimal control theory, deduce the analytical expression of the zero-effort miss control term which satisfies the given performance index.

[0030] In one embodiment, the process of step 3 is:

[0031] In the relative virtual coordinate system, the zero-effort miss ZEM is determined as:

[0032] ZEM = -r sin η R (6)

[0033] The optimal control problem is established as follows:

[0034]

[0035] wherein J1 represents the performance index of the optimal control, r0 represents the initial relative distance between the missile and the target, r f represents the terminal relative distance between the missile and the target, N≥3 represents the proportional guidance coefficient, and ZEM(r f ) represents the terminal zero-effort miss.

[0036] Solving the optimal control problem of the above formula (7) can obtain the control term which eliminates the zero-effort miss and satisfies the performance index, which is:

[0037] κ ZEM = Nλ' (8)

[0038] It can be found that the guidance law corresponding to the above formula (8) is equivalent to ideal proportional guidance.

[0039] Step 4, predict the remaining relative flight range of the missile, and deduce the relative flight range error dynamics equation.

[0040] In one embodiment, the process of predicting the remaining relative flight range of the missile is specifically:

[0041] When the missile relative lead angle is less than 90°, the series solution of the remaining relative flight range of the missile under proportional guidance is deduced as:

[0042]

[0043] wherein s go represents the remaining relative flight range of the missile, n is a positive integer, and ∞ represents infinity, and in use, the finite terms of the series solution are usually selected, i.e. {n | n is a positive real number and n = 0, 1, 2, ···, n1}, and n1 is a positive integer greater than zero; N represents the proportional guidance coefficient.

[0044] In specific application, the finite terms of the series solution of the remaining relative flight range in formula (9) are usually selected, and the estimation accuracy can already meet the requirements.

[0045] In one of the embodiments, the process of deriving the relative flight path error dynamics equation under the control of the relative flight path control guidance law is as follows:

[0046] Based on the remaining relative flight path s of the missile go With the desired remaining relative flight path s go,d The error ε is constructed s , which is:

[0047] ε s = s go -s go,d (10)

[0048] The ideal proportional guidance term κ ZEM is taken as the basic term, the relative flight path error control term κ RFR is taken as the bias term, and the relative flight path error dynamics equation is derived, which is:

[0049]

[0050] wherein ε s ' represents the derivative of the relative flight path error with respect to the relative flight path s, C2(r,η R ) represents that C2 is a function of r and η R .

[0051] Step 5, based on the optimal relative flight path error dynamics equation in the arc length domain, the relative flight path error control term is determined, and a nonlinear optimal relative flight path control guidance law is obtained.

[0052] In one of the embodiments, the process of determining the relative flight path error control term based on the optimal relative flight path error dynamics equation in the arc length domain is as follows:

[0053] The optimal error dynamics in the arc length domain is selected, which is:

[0054]

[0055] wherein K≥1 represents the guidance coefficient, ε s '(s), ε s (s) represent that ε s ', ε s are functions of s;

[0056] When the relative lead angle is a small angle, for example, the relative lead angle and the sine value, the tangent value are approximately equal, that is, under the linearization assumption, Therefore, the optimal performance index J2 corresponding to the above formula (12) is:

[0057]

[0058] where s f denotes the terminal relative flight path, denotes the integral argument;

[0059] Combining the relative flight path error dynamics, the relative flight path error control term is obtained as:

[0060]

[0061] In one embodiment, the obtained nonlinear optimal relative flight path control guidance law is:

[0062] Substituting equation (8) and equation (14) into equation (5), and further substituting into the third equation in equation (2), the nonlinear optimal relative flight path control guidance law in the relative virtual coordinate frame is obtained as:

[0063]

[0064] The corresponding guidance command in the inertial frame is:

[0065]

[0066] Step 6: Design a future average speed prediction algorithm based on ideal proportional guidance, establish the relationship between relative flight path and flight time, and achieve flight time control.

[0067] In one embodiment, the process of step 6 is:

[0068] Define the difference between the flight path angle of the missile and the target as ξ:

[0069] ξ = γ M - γ T (17)

[0070] Differentiate the difference between the flight path angle of the missile and the target in the time domain of equation (17) to obtain:

[0071]

[0072] If equation (15) is used to predict ξ, it can be found that each prediction depends on the last prediction result to estimate the expected remaining relative flight path, which is difficult to meet the stable prediction requirement, and the prediction speed is slow, which is difficult to meet the real-time requirement. However, since the basic term of the designed guidance law is ideal proportional guidance, the guidance law will continuously approach ideal proportional guidance as the guidance proceeds. Therefore, ideal proportional guidance law is selected for prediction, which is:

[0073]

[0074] The profile of ξ is obtained by numerically integrating equation (18), and substituted into the following equation (20)

[0075]

[0076] The missile relative velocity profile in the virtual relative coordinate system is obtained, and the corresponding future relative average velocity is:

[0077]

[0078] Wherein, t f represents the terminal flight time;

[0079] The expected remaining relative flight distance is related to the expected remaining flight time as:

[0080]

[0081] Wherein, The estimated value of the expected remaining relative flight distance, t d represents the expected flight time.

[0082] During the flight of the missile, the expected remaining relative flight distance is estimated according to the above formula (22) in real time, that is, the expected remaining relative flight distance of the missile can be obtained according to the set expected remaining flight time, and the expected remaining relative flight distance is substituted into formula (16) to generate a guidance command, so that the missile can successfully intercept the target at the expected attack time, that is, the flight time control guidance of the missile for intercepting the maneuvering target is completed.

[0083] Compared with the prior art, the present application has the following beneficial technical effects:

[0084] The present application is aimed at the flight time control problem of intercepting a maneuvering target, and a guidance method combining relative flight distance control and future relative velocity prediction algorithm is proposed by applying a relative virtual coordinate frame and classical differential geometry curve principle. The guidance method proposed in the present application is derived analytically under specific performance indicators and completely nonlinear conditions, so the capture area is larger, and the physical meaning in the guidance process is clearer. On the other hand, the properties of ideal proportional guidance are fully utilized, which not only provides accurate remaining relative flight distance estimation for the guidance law, but also makes the prediction algorithm faster and each prediction result independent, so that real-time and stable prediction in the guidance process is realized. Overall, the proposed method has the advantages of simple form, strong robustness, high feasibility and the like. BRIEF DESCRIPTION OF DRAWINGS

[0085] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only need to be some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor.

[0086] Figure 1 Flow chart of the nonlinear optimal flight time control guidance method for intercepting a maneuvering target in the embodiments of the present application;

[0087] Figure 2 Schematic diagram of the future average relative velocity profile and the prediction error curve of the prediction method provided in the embodiments of the present application;

[0088] Figure 3 Schematic diagram of the trajectory of the missile in the inertial system according to the guidance method provided in the embodiments of the present application;

[0089] Figure 4 Schematic diagram of the trajectory of the missile in the relative virtual coordinate system according to the guidance method provided in the embodiments of the present application;

[0090] Figure 5 Schematic diagram of the guidance curvature curve of the missile in the relative virtual coordinate system according to the guidance method provided in the embodiments of the present application;

[0091] Figure 6 Schematic diagram of the guidance acceleration curve of the missile in the inertial system according to the guidance method provided in the embodiments of the present application;

[0092] Figure 7 Schematic diagram of the relative flight distance error curve of the missile according to the guidance method provided in the embodiments of the present application.

[0093] The implementation, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0094] The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0095] In addition, the technical solutions among various embodiments of the present application can be combined with each other, but it must be based on that a person skilled in the art can realize, when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope required by the present application.

[0096] The present embodiment verifies the correctness of the designed time-of-flight control guidance method for intercepting a maneuvering target by using simulation software. A constant-speed missile intercepts a constant-value maneuvering target scene, the initial relative distance r0 of the missile and the target is 10000 m, the initial flight path angle of the missile is γ M0 = 20°, the initial flight path angle of the target is γ T0 = 10°. The blind distance of the seeker is 50 m. The simulation step is 10 ms. The missile and the target are constant speed and the sizes are 300 m / s and 100 m / s respectively.

[0097] Reference Figure 1 , the nonlinear optimal time-of-flight control guidance method for intercepting a maneuvering target in the present embodiment specifically includes the following steps:

[0098] Step 1, a nonlinear guidance model is established in an inertial system, and the nonlinear guidance model is converted to a relative virtual coordinate system, and the time domain is converted to an arc length domain, and the specific implementation process is as follows:

[0099] A nonlinear guidance model is established in an inertial system, which is:

[0100]

[0101] Wherein, r represents the relative distance of the missile and the target, λ represents the line-of-sight angle of the missile and the target, the subscripts M and T represent the missile and the target respectively, V M , V T represent the speed of the missile and the target respectively, a M , a T represent the acceleration of the missile and the target respectively, γ M , γ T represent the flight path angle of the missile and the target respectively, η M , η T represent the speed pre-angle of the missile and the target respectively.

[0102] In the relative virtual coordinate frame, the origin is located at the mass center of the target, and the independent variable in the arc length domain is the relative arc length of the missile and the target, so the nonlinear guidance model is converted to the relative virtual coordinate system as follows:

[0103]

[0104] Wherein, r', λ' represent the derivative of the relative distance of the missile and the target and the line-of-sight angle of the missile and the target with respect to the relative arc length s, V R , aR γ R η R These represent the missile's velocity, acceleration, flight path angle, and velocity lead angle in the virtual relative coordinate system, respectively. R κ represents the derivative of the missile's flight path angle with respect to the relative arc length s in a virtual relative coordinate system. R The guidance curvature is perpendicular to the velocity direction;

[0105] Furthermore, the relative arc length has the following relationship with time:

[0106]

[0107] The relationship between the state quantities in the relative virtual frame and the inertial frame is expressed as follows:

[0108]

[0109] Under the aforementioned nonlinear guidance model, by designing the guidance curvature κ... R The design of a guidance law for controlling relative flight path was realized.

[0110] Step 2: Construct the basic form of the relative flight path control guidance law, including a zero-control miss distance control term and a relative flight path error control term. Specifically: the relative flight path control guidance law consists of two terms. The first term controls the zero-control miss distance, and the second term controls the relative flight path error. Its expression is:

[0111] κ R =κ ZEM +κ RFR (27)

[0112] Among them, κ ZEM This represents the zero-control miss distance control term, used to control the zero-control miss distance; κ RFR This represents the relative flight distance error control term, used to control the relative flight distance error.

[0113] Step 3: Based on optimal control theory, derive the zero-control miss quantity control term that satisfies the given performance index. The specific implementation process is as follows:

[0114] Within the relative virtual coordinate system, the zero-control miss distance ZEM is determined as follows:

[0115] ZEM=-rsinη R (28)

[0116] The optimal control problem is as follows:

[0117]

[0118] where J1 represents the performance index of optimal control, r0 represents the initial relative distance between missile and target, r f represents the relative distance between terminal missile and target, N≥3 represents the proportional guidance coefficient, ZEM(r f ) represents the terminal zero-effort miss distance;

[0119] Solving the optimal control problem of the above formula (29), the zero-effort miss distance control term satisfying the given performance index is obtained as

[0120] κ ZEM =Nλ′(30)

[0121] It can be found that the guidance law corresponding to the above formula (30) is equivalent to ideal proportional guidance.

[0122] Step 4, the residual relative flight range of the missile is predicted, and the relative flight range error dynamics equation is derived, and the specific implementation process is as follows:

[0123] When the missile relative lead angle is less than 90°, the residual relative flight range series solution of the missile under proportional guidance is derived as:

[0124]

[0125] where s go represents the residual relative flight range of the missile, n is a positive integer, and ∞ represents infinity, and in use, the finite term before the series solution is usually selected, that is, {n|n is a positive real number and n=0, 1, 2, ···, n1}, n1 is a positive integer greater than zero; N represents the proportional guidance coefficient.

[0126] In specific application, the finite term of the residual relative flight range series solution in formula (31) is usually selected, and the estimation accuracy can meet the requirements;

[0127] Based on the residual relative flight range s go of the missile and the expected residual relative flight range s go,d , the error ε s is constructed as:

[0128] ε s =s go -s go,d (32)

[0129] Taking the ideal proportional guidance term κ ZEM as the basic term and the relative flight range error control term κ RFR as the bias term, the relative flight range error dynamics equation is derived as:

[0130]

[0131] where ε sdenotes the derivative of the relative flight path error with respect to the relative flight path s, C2(r, η R ) denotes that C2 is a function of r, η R .

[0132] Step 5, based on the optimal relative flight path error dynamics equation in the arc length domain, the relative flight path error control term is determined, and a nonlinear optimal relative flight path control guidance law is obtained, and the specific implementation process is as follows:

[0133] The optimal error dynamics in the arc length domain is selected as:

[0134]

[0135] Wherein, K≥1 denotes the guidance coefficient, ε s '(s), ε s (s) denotes that ε s ', ε s is a function of s;

[0136] The optimal performance index J2 corresponding to the above formula (34) is:

[0137]

[0138] Wherein, s f denotes the terminal relative flight path, denotes the integral independent variable;

[0139] The relative flight path error control term can be obtained by combining the relative flight path error dynamics, which is:

[0140]

[0141] Substituting formula (30) and formula (36) into formula (27), and further substituting into the third formula of formula (24), the nonlinear optimal relative flight path control guidance law in the relative virtual coordinate frame is obtained as:

[0142]

[0143] The corresponding guidance command in the inertial system is:

[0144]

[0145] Step 6, based on the ideal proportional guidance, the future average speed prediction algorithm is designed, and the relationship between the relative flight path and the flight time is established to realize the flight time control, and the specific implementation process is as follows:

[0146] The difference ξ between the flight path angle of the missile and the target is defined as:

[0147] ξ = γ M - γT (39)

[0148] The derivative of the difference between the flight path angles of the missile and the target with respect to time for equation (39) is taken to obtain:

[0149]

[0150] If equation (37) is used to predict ξ, it can be found that each prediction relies on the last prediction result to estimate the expected remaining relative flight distance, which is difficult to meet the requirements of stable prediction and real-time performance. However, since the basic term of the designed guidance law is ideal proportional navigation, the guidance law will gradually approach ideal proportional navigation as the guidance proceeds. Therefore, ideal proportional navigation is selected for prediction, which is:

[0151]

[0152] The relative velocity profile of the missile in the virtual relative coordinate system can be obtained by numerically integrating equation (40) and substituting equation (42) into it:

[0153]

[0154] The corresponding future relative average velocity is:

[0155]

[0156] where t f represents the terminal flight time;

[0157] The expected remaining relative flight distance is related to the expected remaining flight time as:

[0158]

[0159] where is the estimated value of the expected remaining relative flight distance, and t d represents the expected flight time.

[0160] Figure 2 The future average relative velocity profile and the prediction error are shown. The solid and dashed lines represent the true value and the predicted value, respectively. The dotted line represents the error between the true value and the predicted value. It can be found that the predicted value obtained by IPN (ideal proportional navigation) is constantly approaching the true value, and the error between the true value and the predicted value is gradually converging to zero.

[0161] In the missile flight process, the estimation of the expected residual relative flight range is carried out according to the above formula (44) in real time, that is, the expected residual relative flight range of the missile can be obtained according to the set expected residual flight time, and then the expected residual relative flight range is substituted into formula (38) to generate a guidance command, so that the missile can successfully intercept the target at the expected attack time, that is, the missile for intercepting the maneuvering target is controlled to perform the nonlinear optimal flight time control guidance.

[0162] In the simulation scene of the constant-speed missile intercepting the constant-value maneuvering target, the proportional guidance coefficient is N=3, the guidance coefficient is K=5, the expected attack time t of the four missiles is 40s, 42s, 44s and 46s respectively, and the maneuvering acceleration of the target is 10m / s d 2 The simulation results are shown in Figures 3 to 7 .

[0163] The flight trajectories of the four missiles in the inertial system and the relative virtual coordinate system are shown in Figure 3 , Figure 4 .The guidance curvature in the relative virtual coordinate system is shown in Figure 5 . The four missiles all hit the target at the expected flight time, and the terminal relative guidance curvature is zero. Figure 6 The command acceleration curve in the inertial system can be seen that the greater the expected flight time is, the greater the initial guidance command is, but the terminal acceleration is less than or equal to the target acceleration. Figure 7 The residual relative flight range error change curve is shown in

[0164] The above only describes the preferred embodiments of the present application, and does not limit the patent range of the present application, and any equivalent structural transformation made under the inventive concept of the present application, or direct / indirect application in other related technical fields is included in the patent protection range of the present application.

Claims

1. A nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets, characterized in that, Includes the following steps: Step 1: Establish a nonlinear guidance model in the inertial frame and transform the nonlinear guidance model to a relative virtual coordinate system, transforming the time domain to the arc length domain; Step 2: Construct the basic form of the relative flight path control guidance law, including the zero-control miss distance control term and the relative flight path error control term; Step 3: Based on optimal control theory, derive the analytical expression of the zero-control miss quantity control term that satisfies the given performance index; Step 4: Predict the missile's remaining relative flight path and derive the dynamic equation for the relative flight path error; Step 5: Based on the optimal relative flight path error dynamic equation in the arc length domain, determine the relative flight path error control term and obtain the nonlinear optimal relative flight path control guidance law; Step 6: Based on the ideal proportional guidance, design a future average speed prediction algorithm to establish the relationship between relative flight distance and flight time, so as to achieve flight time control. The process is as follows: Define the difference in flight path angle between the missile and the target. for: in, γ M , γ T These represent the flight path angles of the missile and the target, respectively. Differentiating the difference in the flight path angles between the missile and the target in the time domain, we obtain: in, K Indicates the guidance coefficient. V M , V T These represent the speeds of the missile and the target, respectively. a T Indicates the target's acceleration. V R , a R , γ R These represent the missile's velocity, acceleration, and flight path angle in the virtual relative coordinate system, respectively. Select ideal proportion guide Substituting the predicted values ​​into the analytical expression for relative velocity, we obtain the relative velocity profile of the missile in the virtual relative coordinate system, which is: Further obtain the corresponding future relative average speed for: in, Indicates terminal flight time; The relationship between the expected remaining relative flight distance and the expected remaining flight time is as follows: in, The expected estimated remaining relative flight distance, Indicates the expected flight time.

2. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 1, characterized in that, The process of step 1 is as follows: A nonlinear guidance model is established within the inertial frame as follows: in, r Indicates the relative distance between the target and the target. λ Indicates the line-of-sight angle of the bullet, subscript M , T They represent the missile and the target, respectively. a M Indicates the missile's acceleration. η M , η T These represent the velocity lead angles of the missile and the target, respectively. The nonlinear guidance model is transformed to a relative virtual coordinate system, and the time domain is transformed to the arc length domain, as follows: in, r ′、 λ ′ represent the relative distance between the projectile and the target, and the relative arc length of the projectile's line of sight to the target, respectively. s The derivative of η R This indicates the missile's velocity lead angle in a virtual relative coordinate system. γ ′ R This represents the missile's flight path angle relative to the relative arc length in a virtual relative coordinate system. s The derivative of κ R The guidance curvature is perpendicular to the velocity direction; The relationship between relative arc length and relative velocity is expressed as: in, t Indicates time; Furthermore, the relationship between the state quantities within the relative virtual frame and the inertial frame is expressed as follows: in, k = V T / V M Indicates the speed ratio; Under the aforementioned nonlinear guidance model, the guidance curvature is designed... κ R The design of a guidance law for controlling relative flight path was realized.

3. In the nonlinear optimal flight time control guidance method for intercepting maneuvering targets according to claim 2, step 2, the basic form of constructing the relative flight path control guidance law, specifically includes: in, This indicates the zero-control miss distance control item. This indicates the relative flight distance error control item.

4. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 2 or 3, characterized in that, Step 3 is as follows: Determine the zero-control miss distance within a relative virtual coordinate system. ZEM for: The optimal control problem is as follows: in, J 1 represents the performance index of optimal control. r 0 indicates the initial relative distance between the projectile and the target. r f Indicates the relative distance between the terminal missile and the target. N Indicates the proportional guidance coefficient. Indicates the terminal zero-control miss distance; Solving the above optimal control problem yields the zero-control miss quantity control term that satisfies the performance index. That is, ideal proportion guidance.

5. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 2 or 3, characterized in that, In step 4, the predicted remaining relative flight path of the missile is specifically as follows: When the relative lead angle of the missile is less than 90°, the series solution for the remaining relative flight path of the missile under proportional guidance is derived as follows: in, s go Indicates the missile's remaining relative flight path. n For positive integers, ∞ represents infinity. When using it, select the first finite terms of the series solution, i.e., { n | n are positive real numbers and n = 0, 1, 2, ... n 1}, n 1 is a positive integer greater than zero; N This represents the proportional guidance coefficient.

6. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 5, characterized in that, In step 4, the derivation of the dynamic equation for the relative flight path error specifically involves: Based on the missile's remaining relative flight path s go Relative flight distance as expected s go,d Construction error ε s ,for: Differentiating the error in the above equation over the arc length domain, we derive the dynamic equation for the relative flight path error as follows: in, This indicates the error in relative flight path with respect to relative arc length. s The derivative of This indicates the relative flight distance error control term. express C 2 is about r , η R The function.

7. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 6, characterized in that, In step 5, the determination of the relative flight path error control term based on the optimal relative flight path error dynamic equation within the arc length domain is specifically as follows: The optimal error dynamics within the arc-length domain are selected as follows: in, K Indicates the guidance coefficient. , express , ε s For about s The function; The optimal performance index of the above formula under the linearization assumption J 2, for: in, s f Indicates the terminal's relative flight distance. Indicates the independent variable of the integral; The relative flight path error control term can be obtained by combining the relative flight path error dynamics. .

8. The nonlinear optimal time-of-flight control guidance method for intercepting maneuvering targets according to claim 7, characterized in that, In step 5, the obtained nonlinear optimal relative flight path control guidance law is: Corresponding inertial frame guidance commands a M for: .

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