An adaptive fast sliding mode guidance method for air-to-air missile in simulated environment

Abstract

The application discloses a kind of adaptive fast sliding mode guidance methods of air-to-air missile in simulation environment, comprising: establishing missile target relative motion model under line-of-sight coordinate system, and establishing missile three-dimensional guidance model according to missile target relative motion model;Based on the three-dimensional guidance model of missile, the line-of-sight normal pitch guidance law and the line-of-sight normal yaw guidance law are designed respectively;The first radial basis function RBF neural network trained in advance is used to estimate the parameters to be estimated in line-of-sight normal pitch guidance law, and the first estimated value obtained is substituted into line-of-sight normal pitch guidance law, and the second radial basis function RBF neural network is used to estimate the parameters to be estimated in line-of-sight normal yaw guidance law, and the second estimated value obtained is substituted into line-of-sight normal yaw guidance law, to obtain angle-constrained fixed-time nonsingular fast terminal sliding mode guidance law.The application avoids singularity while improving the convergence speed of the system, and the convergence time upper bound of the system can be set.

Description

Technical Field

[0001] This invention belongs to the field of missile guidance technology, specifically relating to an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment. Background Technology

[0002] In simulated air combat, the missile's interception and engagement of the target based on the target information provided by the seeker is called terminal guidance. Terminal guidance directly affects the effectiveness of target interception throughout the entire missile interception process. To improve the missile's ability to intercept targets during the terminal guidance phase, efforts are typically made from two aspects: the target detection accuracy of the seeker and the design of the guidance law. A well-designed and effective terminal guidance law can reduce the missile's miss distance, thereby improving guidance accuracy. With the continuous improvement of target aircraft performance, especially supersonic characteristics and high maneuverability, the next generation of air-to-air missiles is required to develop towards high-precision hits, high-maneuverability target tracking, and long-range strikes. This places higher demands on guidance and control technology, thus necessitating the development of a terminal guidance law suitable for highly maneuverable targets.

[0003] Currently, most research is based on modern control theories such as optimal control, differential game theory, and variable structure control. To address singular problems while controlling the convergence time of the guidance law, existing techniques employ continuous piecewise functions to construct the terminal sliding surface, proposing a fixed-time convergent non-singular terminal sliding mode guidance law. Furthermore, existing techniques also include a sliding mode approach law based on adaptive parameters, which uses a fixed-time disturbance observer to estimate the target's unknown maneuvers, thereby accelerating the convergence speed.

[0004] However, the above method still has the following problems:

[0005] (1) The target maneuvering range is set relatively small in air combat. With the emergence of new generation air combat weapons such as fifth-generation fighter jets and unmanned combat aircraft, air-to-air missiles will face targets with stronger maneuverability, more complex escape methods, and poorer detectability in future wars. The target maneuvering methods considered in the existing guidance law are no longer applicable, and the simulation results obtained are not reliable.

[0006] (2) Insufficient consideration was given to the speed of convergence of the guidance system. The designed guidance law could not guarantee that the system would converge to the expected value within a given time. Furthermore, the constraints on the terminal attack angle were not adequately considered. Some targets required to be hit at a specific angle to achieve a better damage effect. In addition, in order to meet the requirements of fast convergence time while avoiding singularities, some guidance laws were designed to be complex and have poor stability, which is not conducive to practical engineering applications.

[0007] (3) The estimation accuracy for large maneuvers of unknown targets is insufficient. In some guidance law designs, these maneuvers are treated as interference and compensated for by adaptive terms. In other guidance laws, the target maneuvers are estimated by constructing conventional interference observers, but the estimation accuracy is low. Therefore, large maneuvers of unknown targets will affect the terminal line-of-sight angular velocity and normal overload, thus affecting the guidance accuracy. Summary of the Invention

[0008] To address the aforementioned problems in the existing technology, this invention provides an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment. The technical problem to be solved by this invention is achieved through the following technical solution:

[0009] This invention provides an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment, comprising:

[0010] A relative motion model of the missile target is established in the line-of-sight coordinate system, and a three-dimensional guidance model of the missile is established based on the relative motion model of the missile target.

[0011] Based on the missile's three-dimensional guidance model, line-of-sight normal pitch guidance law and line-of-sight normal yaw guidance law are designed respectively.

[0012] After estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, the obtained first estimated value is substituted into the line-of-sight normal pitch guidance law. Then, the parameters to be estimated in the line-of-sight normal yaw guidance law are estimated using a second radial basis function (RBF) neural network, and the obtained second estimated value is substituted into the line-of-sight normal yaw guidance law to obtain a fixed-time non-singular fast terminal sliding mode guidance law with angle constraints.

[0013] In one embodiment of the present invention, the relative motion model of the missile target is as follows:

[0014]

[0015] In the formula, r represents the relative distance between the missile and the target. The first and second derivatives of r and q are respectively. ε q β These represent the missile's line-of-sight tilt angle and line-of-sight deflection angle, respectively. mr a mε a mβ Let a represent the tangential component, normal pitch component, and normal yaw component of the missile's acceleration in the line-of-sight coordinate system, respectively. tr a tε a tβ These represent the tangential, pitch, and yaw components of the target acceleration in the line-of-sight coordinate system, respectively. q ε and q β The first derivative.

[0016] In one embodiment of the present invention, the missile three-dimensional guidance model is:

[0017]

[0018] In the formula, x1, x2, x3, and x4 are all state variables, where x1 = q ε -q εd , x3 = q β -q βd , q εd q βd These represent the missile's desired pitch line-of-sight angle and desired yaw line-of-sight angle, respectively.

[0019] In one embodiment of the present invention, the line-of-sight normal pitch guidance law is designed according to the following steps:

[0020] Construct a fixed-time nonsingular fast terminal sliding surface s1;

[0021] Based on the fixed-time non-singular fast terminal sliding surface design, the approach law of the line-of-sight normal pitch direction is used.

[0022] Based on the missile's three-dimensional guidance model, the fixed-time non-singular fast terminal sliding surface s1, and the approach law of the line-of-sight normal pitch direction, a line-of-sight normal pitch guidance law is designed.

[0023] In one embodiment of the present invention, the fixed-time non-singular fast terminal sliding surface s1 is:

[0024]

[0025]

[0026] In the formula,

[0027]

[0028]

[0029]

[0030]

[0031] δ1, δ2, β1, and β2 are all constants, and δ1 > 0, δ2 > 0, β1 ≥ 1, β2 ≥ 1, and β1 ≠ β2. sign(·) is the sign function, and η is a positive constant less than 1.

[0032] In one embodiment of the present invention, the approach law of the line-of-sight normal pitch direction is:

[0033]

[0034] In the formula, ε1, n1, n2, k1, and k2 are all constants, and ε1 > 0 and n1 > 1. k1 > 0, k2 > 0.

[0035] In one embodiment of the present invention, the line-of-sight normal pitch guidance law is:

[0036]

[0037] In the formula, This indicates the normal pitch disturbance caused by the target's maneuver that needs to be estimated.

[0038] In one embodiment of the present invention, the line-of-sight normal yaw guidance law is designed according to the following steps:

[0039] Construct a fixed-time nonsingular fast terminal sliding surface s2:

[0040]

[0041]

[0042] In the formula,

[0043]

[0044]

[0045]

[0046]

[0047] δ3, δ4, β3, and β4 are all constants, and δ3 > 0, δ4 > 0, β3 ≥ 1, β4 ≥ 1, and β3 ≠ β4. sign(·) is the sign function, and η is a positive constant less than 1;

[0048] Based on the aforementioned fixed-time non-singular fast terminal sliding surface design, the approach law for the line-of-sight normal yaw direction is as follows:

[0049]

[0050] In the formula, ε2, n3, n4, k3, and k4 are all constants, and ε2 > 0 and n3 > 1. k3 > 0, k4 > 0;

[0051] Based on the missile's three-dimensional guidance model, the fixed-time non-singular fast terminal sliding surface s2, and the approach law of the line-of-sight normal yaw direction, the line-of-sight normal yaw guidance law is designed as follows:

[0052]

[0053] In the formula, This indicates the normal yaw disturbance caused by the target maneuver that needs to be estimated.

[0054] In one embodiment of the present invention, the step of estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, and then substituting the obtained first estimated value into the line-of-sight normal pitch guidance law, includes:

[0055] The fixed-time nonsingular fast terminal sliding surface s1 and its first derivative are given. By inputting a pre-trained first radial basis function (RBF) neural network, the normal pitch component 'a' of the target acceleration in the line-of-sight coordinate system is estimated. tε ;

[0056] Based on the estimated target acceleration normal pitch component a in the line-of-sight coordinate system tε Calculate the normal pitch disturbance d caused by the target maneuver. ε ;

[0057] The calculated normal pitch disturbance d caused by the target maneuver is... ε Substituting the line-of-sight normal pitch guidance law into the given law, we obtain the line-of-sight normal pitch guidance law.

[0058] In one embodiment of the present invention, the step of estimating the parameters to be estimated in the line-of-sight normal yaw guidance law using a second radial basis function (RBF) neural network, and substituting the obtained second estimated value into the line-of-sight normal yaw guidance law, includes:

[0059] The fixed-time nonsingular fast terminal sliding surface s2 and its first derivative are given. By inputting a pre-trained second radial basis function (RBF) neural network, the normal yaw component 'a' of the target acceleration in the line-of-sight coordinate system is estimated. tβ ;

[0060] Based on the estimated target acceleration normal yaw component a in the line-of-sight coordinate system tβ Calculate the normal yaw disturbance d caused by the target maneuver. β ;

[0061] The calculated normal yaw disturbance d caused by the target maneuver is... βSubstituting the line-of-sight normal yaw guidance law into the above, a line-of-sight normal yaw direction guidance law is generated.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] This invention provides an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment. It employs a segmented, fast-converging sliding mode surface. In the design of the sliding mode surface and the reaching law, a variable exponent term is used instead of a constant exponent term in the traditional fixed-time convergence system. This avoids singularities while improving the system's convergence speed, and allows for setting the upper bound of the convergence time. Furthermore, this invention utilizes an RBF neural network observer to estimate the target's unknown acceleration, compensating for the coupling between the pitch and yaw channels of the guidance system, accelerating the convergence speed. Moreover, its parameter configuration is simple and it exhibits strong adaptability.

[0064] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0065] Figure 1 This is a flowchart of an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment, provided in an embodiment of the present invention.

[0066] Figure 2 This is a three-dimensional geometric model of the relative motion of a missile intercepting a maneuvering target, provided in an embodiment of the present invention.

[0067] Figure 3a This is a schematic diagram of a missile interception trajectory provided in an embodiment of the present invention;

[0068] Figure 3b This is a schematic diagram of the target's maneuver estimation error in the pitch and yaw directions provided in an embodiment of the present invention;

[0069] Figure 3c This is a schematic diagram of the pitch and yaw plane line of sight angles provided in an embodiment of the present invention;

[0070] Figure 3d This is a schematic diagram of the pitch and yaw plane line-of-sight angular rates provided in an embodiment of the present invention;

[0071] Figure 3e This is a schematic diagram of line-of-sight normal pitch and yaw acceleration provided in an embodiment of the present invention;

[0072] Figure 4a This is a comparison diagram of missile interception trajectories provided in an embodiment of the present invention;

[0073] Figure 4b This is a comparison diagram of the pitch and yaw plane line-of-sight angles provided in an embodiment of the present invention;

[0074] Figure 4cThis is a comparison diagram of pitch and yaw plane line-of-sight angular rates provided in an embodiment of the present invention;

[0075] Figure 4d This is a comparison diagram of pitch and yaw plane sliding modes provided in an embodiment of the present invention;

[0076] Figure 4e This is a comparison diagram of line-of-sight normal pitch and yaw acceleration provided in an embodiment of the present invention. Detailed Implementation

[0077] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0078] Figure 1 This is a flowchart of an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment, provided in an embodiment of the present invention. Figure 1 As shown, this embodiment of the invention provides an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment, comprising:

[0079] S1. Establish a relative motion model of the missile target in the line-of-sight coordinate system, and establish a three-dimensional guidance model of the missile based on the relative motion model of the missile target;

[0080] S2. Based on the missile's three-dimensional guidance model, design the line-of-sight normal pitch guidance law and the line-of-sight normal yaw guidance law respectively.

[0081] S3. After estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, the obtained first estimated value is substituted into the line-of-sight normal pitch guidance law. Then, the parameters to be estimated in the line-of-sight normal yaw guidance law are estimated using a second radial basis function (RBF) neural network. The obtained second estimated value is substituted into the line-of-sight normal yaw guidance law to obtain a fixed-time non-singular fast terminal sliding mode guidance law with angle constraints.

[0082] Figure 2 This is a three-dimensional geometric model of the relative motion of a missile intercepting a maneuvering target, provided in an embodiment of the present invention. Please refer to... Figure 2 Ox g y g z g For the inertial coordinate system, Ox h y h z h For the missile's ballistic coordinate system and the target's trajectory coordinate system, Ox l y l z l Let v be the line-of-sight coordinate system, where v M and v T Let q represent the velocities of the missile and the target, respectively, and r represent the relative distance between the missile and the target. ε and qβ θ represents the missile's line-of-sight tilt angle and line-of-sight deflection angle, respectively. M , θ T , These represent the missile's trajectory inclination and deflection angles, as well as the target's trajectory inclination and deflection angles, respectively.

[0083] In this embodiment, the relative motion model of the missile target is as follows:

[0084]

[0085] In the formula, r represents the relative distance between the missile and the target. The first and second derivatives of r and q are respectively. ε q β These represent the missile's line-of-sight tilt angle and line-of-sight deflection angle, respectively. mr a mε a mβ Let a represent the tangential component, normal pitch component, and normal yaw component of the missile's acceleration in the line-of-sight coordinate system, respectively. tr a tε a tβ These represent the tangential, pitch, and yaw components of the target acceleration in the line-of-sight coordinate system, respectively. q ε and q β The first derivative.

[0086] The missile's three-dimensional guidance model is as follows:

[0087]

[0088] In the formula, x1, x2, x3, and x4 are all state variables, where x1 = q ε -q εd , x3 = q β -q βd , q εd q βd These represent the missile's desired pitch line-of-sight angle and desired yaw line-of-sight angle, respectively.

[0089] To avoid system singularities and achieve faster convergence, this embodiment introduces a fixed-time nonsingular fast terminal sliding mode guidance law with angle constraints. It employs a piecewise fast convergence sliding surface and uses variable exponent terms instead of constant exponent terms in the design of the sliding surface and the reaching law. Compared to finite-time guidance laws, the upper bound of the convergence time of this fixed-time guidance law is independent of the initial guidance conditions.

[0090] Optionally, in step S2 above, the line-of-sight normal pitch guidance law is designed according to the following steps:

[0091] Construct a fixed-time nonsingular fast terminal sliding surface s1;

[0092] Approach law of the line-of-sight normal pitch direction based on fixed-time nonsingular fast terminal sliding surface design;

[0093] Based on the missile's three-dimensional guidance model, the fixed-time non-singular fast terminal sliding surface s1, and the approach law of the line-of-sight normal pitch direction, a line-of-sight normal pitch guidance law is designed.

[0094] Specifically, when designing the line-of-sight normal pitch guidance law, the fixed-time non-singular fast terminal sliding surface s1 is first constructed based on the fixed-time convergence theory as follows:

[0095]

[0096]

[0097] In the formula,

[0098]

[0099] Then the derivative of f(x1) is

[0100]

[0101] In the formula, δ1, δ2, β1, and β2 are all constants, and δ1 > 0, δ2 > 0, β1 ≥ 1, β2 ≥ 1, and β1 ≠ β2. sign(·) is the sign function, and η is a positive constant less than 1.

[0102] Next, the approach law for the normal pitch direction of the line of sight is designed as follows:

[0103]

[0104] In the formula, in the formula, ε1, n1, n2, k1, and k2 are all constants, and ε1 > 0 and n1 > 1. k1 > 0, k2 > 0.

[0105] Obviously, as r decreases, the approach law of the line-of-sight normal pitch direction gradually increases, which accelerates the convergence speed of the sliding surface s1.

[0106] Furthermore, from equations (2), (3), and (7) above, the line-of-sight normal pitch guidance law is obtained as follows:

[0107]

[0108] In the formula, This indicates the normal pitch disturbance caused by the target's maneuver that needs to be estimated.

[0109] As can be seen from equations (3) and (6), the fixed-time non-singular fast terminal sliding surface s1 and its derivative are continuous in this embodiment. When |x1|>η, the system is formally similar to the traditional fixed-time convergent terminal sliding surface. In the design of the approach law of the sliding surface s1 and the line-of-sight normal pitch direction, this embodiment adopts a variable exponent power term. and Instead of the constant power term in traditional fixed-time convergent systems, when |x1|>1 or |s1|>1, the system is far from the stable point. Convert to Convert to Since m1 > 1 and n1 > 1, this term plays a major role in the convergence of the system, enabling it to converge relatively quickly; when |x1| < 1 or |s1| < 1, the system approaches its stable point. Convert to Convert to because Therefore, this term plays a major role in system convergence, ensuring the system's convergence in this region; when |x1|≤η, the sliding surface transforms into... Since β1 > 1 and β2 > 1, formula (3) and its derivative (6) do not contain negative power terms, thus avoiding the singularity of the system.

[0110] Furthermore, in this embodiment, the design process of the line-of-sight normal yaw guidance law is similar to that of the line-of-sight normal pitch guidance law. Specifically, the line-of-sight normal yaw guidance law is designed according to the following steps:

[0111] Construct a fixed-time nonsingular fast terminal sliding surface s2:

[0112]

[0113]

[0114] In the formula,

[0115]

[0116]

[0117]

[0118]

[0119] δ3, δ4, β3, and β4 are all constants, and δ3 > 0, δ4 > 0, β3 ≥ 1, β4 ≥ 1, and β3 ≠ β4. sign(·) is the sign function, and η is a positive constant less than 1;

[0120] The approach law for the line-of-sight normal yaw direction based on the fixed-time nonsingular fast terminal sliding surface design is as follows:

[0121]

[0122] In the formula, ε2, n3, n4, k3, and k4 are all constants, and ε2 > 0 and n3 > 1. k3 > 0, k4 > 0;

[0123] Based on the missile's three-dimensional guidance model, the fixed-time non-singular fast terminal sliding surface s2, and the approach law of the line-of-sight normal yaw direction, the line-of-sight normal yaw guidance law is designed:

[0124]

[0125] In the formula, This indicates the normal yaw disturbance caused by the target maneuver that needs to be estimated.

[0126] It should be noted that, due to the bounded acceleration of the target during actual guidance, and the fact that the missile-target distance r stops decreasing when it reaches a set value, the aforementioned interference d... ε d β It is bounded, meaning there exists a positive value e. ε e β , so that |d ε |<e ε 、|d β |<e β Established.

[0127] Optionally, in step S3, the step of estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, and then substituting the obtained first estimated value into the line-of-sight normal pitch guidance law, includes:

[0128] The fixed-time nonsingular fast terminal sliding surface s1 and its first derivative are given. By inputting a pre-trained first radial basis function (RBF) neural network, the normal pitch component 'a' of the target acceleration in the line-of-sight coordinate system is estimated. tε ;

[0129] Based on the estimated target acceleration normal pitch component a in the line-of-sight coordinate system tε Calculate the normal pitch disturbance d caused by the target maneuver. ε ;

[0130] The calculated normal pitch disturbance d caused by the target maneuver is...ε Substituting the line-of-sight normal pitch guidance law, we obtain the line-of-sight normal pitch guidance law.

[0131] Furthermore, the step of estimating the parameters to be estimated in the line-of-sight normal yaw guidance law using a second radial basis function (RBF) neural network, and substituting the obtained second estimated values ​​into the line-of-sight normal yaw guidance law, includes:

[0132] The fixed-time nonsingular fast terminal sliding surface s2 and its first derivative are given. By inputting a pre-trained second radial basis function (RBF) neural network, the normal yaw component 'a' of the target acceleration in the line-of-sight coordinate system is estimated. tβ ;

[0133] Based on the estimated target acceleration normal yaw component a in the line-of-sight coordinate system tβ Calculate the normal yaw disturbance d caused by the target maneuver. β ;

[0134] The calculated normal yaw disturbance d caused by the target maneuver is... β Substituting the line-of-sight normal yaw guidance law into the above, a line-of-sight normal yaw direction guidance law is generated.

[0135] Due to the interference caused by the unknown acceleration of the target in the above-mentioned line-of-sight normal pitch guidance law and line-of-sight normal yaw guidance law. ε d β While direct measurement is not possible, RBF neural networks possess excellent local nonlinear approximation, capable of approximating continuous functions with arbitrarily high precision. Therefore, this embodiment utilizes an intelligent interference observer based on RBF neural networks to achieve rapid approximation of target maneuvers, thereby improving the system's adaptability.

[0136] In this embodiment, the network structures of the first RBF neural network and the second RBF neural network are the same. The difference between the two is that pitch direction data and yaw direction data are used respectively during training.

[0137] Specifically, for the RBF neural network perturbation observer, let d1(t) = a tε d2(t)=a tβ Using an RBF neural network to estimate d1(t) and d2(t), we have:

[0138]

[0139] In the formula, h(x) represents the weights of the RBF neural network. i ) represents the hidden layer basis functions, σ i This indicates the reconstruction error.

[0140] The input to the RBF neural network is the sliding surface and its derivative. The output is the perturbation d i The estimated value of (t) Let represent the weight estimates of the RBF neural network. The hidden layer basis functions can optionally use Gaussian functions. If the number of hidden layer nodes is set to 5, then:

[0141]

[0142] For the pitch channel, the error is defined as e1 = s1 - s 1d Since the purpose of guidance is to make S 1d =0, therefore the loss function is defined as Each weight parameter is updated using the gradient descent algorithm:

[0143]

[0144] From equations (3) and (8), it can be seen that, Since the value is positive, it can be compensated by the weight, so it is set to 1. The above formula can be simplified to:

[0145] Δω j ==-γs1h j (x),j=1,2,...,5 (16)

[0146]

[0147]

[0148] For a yaw channel, the error is defined as e2 = s2 - s 2d The purpose of guidance is to make S 2d =O, the loss function is defined as The method for updating each parameter is the same as that for the pitch channel, so it will not be repeated here.

[0149] The following simulation experiment further illustrates the adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment provided by this invention.

[0150] This embodiment performs guidance simulations on the same moving target under four different end-point line-of-sight (LOS) constraints. Specifically, the parameters of the LOS normal pitch guidance law and the LOS normal yaw guidance law are set as follows: k1 = k2 = 0.25, k3 = k4 = 0.22, δ1 = δ2 = 15, δ3 = δ4 = 15, ε1 = ε2 = 250, m1 = n1 = 4 / 3, m2 = n2 = 3 / 4, υ = 100, η ​​= 0.1, β1 = β3 = 1.25, β2 = β4 = 1.75; the RBF neural network learning rate γ = 0.9, the initial weight value is 1, the number of hidden layer neurons is 5, and the center point b... jc j Clustering was performed using the k-means algorithm. The upper bound of the missile's acceleration was set to 25g; the target's maneuver was defined as a. txh =0, a tyh =5gcos(0.2t), a tzh =5gcos(0.2t), a txh a tyh a tzh The magnitude of the target's acceleration in the trajectory system.

[0151] The initial guidance conditions for the missile and target are shown in Table 1 below, and the simulation results are shown in Table 2 and below. Figures 3a-3e .

[0152] Table 1 Initial Guidance Conditions

[0153]

[0154]

[0155] Table 2 Guidance Simulation Results

[0156]

[0157] As shown in Table 2, under the four constraints, the miss distance of the missile when intercepting highly maneuvering targets is less than 0.5m, and the line-of-sight angle error of the pitch and yaw channels is almost converged to 0, which shows high guidance accuracy.

[0158] Figure 3a This is a schematic diagram of a missile interception trajectory provided in an embodiment of the present invention. Figure 3b This is a schematic diagram illustrating the maneuver estimation error of a target in the pitch and yaw directions, provided in an embodiment of the present invention. Figure 3a As shown, under different terminal line-of-sight constraints, the missile can accurately intercept the target with a smooth trajectory. Further details can be found in [link to relevant documentation]. Figure 3b The RBF neural network state observer can estimate the target maneuver in a short time, reducing the impact of large target maneuvers on guidance accuracy.

[0159] Figure 3c This is a schematic diagram of the pitch and yaw plane line-of-sight angles provided in an embodiment of the present invention. Figure 3d This is a schematic diagram of the pitch and yaw plane line-of-sight angular rates provided in an embodiment of the present invention. (See diagram below.) Figures 3c-3d As shown, both the line-of-sight angle and the line-of-sight angular rate converge to the desired value within the designed time limit, and because the target acceleration is estimated, the system does not produce chatter at the end of guidance. Figure 3e This is a schematic diagram of the line-of-sight normal pitch and yaw acceleration provided in an embodiment of the present invention. Figure 3eAs shown, in order to make the sliding surface converge in a short time, the normal acceleration in the initial guidance phase is relatively large; as guidance progresses, the line-of-sight angle and angular rate quickly converge to the expected value, the estimation error of the target acceleration gradually decreases, and the normal acceleration on the line of sight begins to decrease; at the end of guidance, the line-of-sight angle and angular rate do not fluctuate, and the missile's normal overload is very stable, meeting the requirements of actual engineering operation.

[0160] Furthermore, to demonstrate the superiority of the fixed-time convergence adaptive non-singular fast terminal sliding mode (FixT-ANFTSM) guidance law in this invention, simulations were performed to verify and compare the existing finite-time convergence non-singular terminal sliding mode (FT-NTSM) guidance law and the fixed-time convergence non-singular terminal sliding mode (FixT-NTSM) guidance law. The initial conditions for both the missile and the target were the same as those in constraint 1 above. The simulation results are shown in Table 3 below. Figures 4a-4e .

[0161] Table 3. Simulation results comparing three guidance laws

[0162]

[0163] As can be seen from Table 3, the miss distance, hit time, line-of-sight angle error, and convergence time of the guidance law proposed in this invention are all smaller than those of the other two. Figure 4a This is a comparison diagram of missile interception trajectories provided in an embodiment of the present invention. Figure 4b This is a comparison diagram of the pitch and yaw plane line-of-sight angles provided in an embodiment of the present invention. Figure 4c This is a comparison diagram of pitch and yaw plane line-of-sight angular rates provided in an embodiment of the present invention. Figure 4d This is a comparison diagram of pitch and yaw plane sliding modes provided in an embodiment of the present invention. Figure 4e This is a comparison diagram of line-of-sight normal pitch and yaw acceleration provided in an embodiment of the present invention. For example... Figure 4a As shown, the guidance law proposed in this invention has a smoother trajectory and a shorter hit time, combined with... Figures 4a-4d The guidance law used in this invention has a faster convergence speed for the sliding surface, line-of-sight angle, and line-of-sight angle rate. See further details. Figure 4e The rapid convergence of the guidance law in this invention results in a shorter duration of saturation acceleration, thus reducing energy loss.

[0164] As can be seen from the above embodiments, the beneficial effects of the present invention are as follows:

[0165] This invention provides an adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment. It employs a segmented, fast-converging sliding mode surface. In the design of the sliding mode surface and the reaching law, a variable exponent term is used instead of a constant exponent term in the traditional fixed-time convergence system. This avoids singularities while improving the system's convergence speed, and allows for setting the upper bound of the convergence time. Furthermore, this invention utilizes an RBF neural network observer to estimate the target's unknown acceleration, compensating for the coupling between the pitch and yaw channels of the guidance system, accelerating the convergence speed. Moreover, its parameter configuration is simple and it exhibits strong adaptability.

[0166] In the description of this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0167] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for adaptive fast sliding mode guidance of air-to-air missiles in a simulated environment, characterized in that, include: A relative motion model of the missile target is established in the line-of-sight coordinate system, and a three-dimensional guidance model of the missile is established based on the relative motion model of the missile target. Based on the missile's three-dimensional guidance model, line-of-sight normal pitch guidance law and line-of-sight normal yaw guidance law are designed respectively. Design the line-of-sight normal pitch guidance law according to the following steps: Constructing a fixed-time nonsingular fast terminal sliding surface ; Based on the fixed-time non-singular fast terminal sliding surface design, the approach law of the line-of-sight normal pitch direction is used. Based on the missile's three-dimensional guidance model and the fixed-time non-singular fast terminal sliding surface And the approach law of the line-of-sight normal pitch direction, and design the line-of-sight normal pitch guidance law; Fixed-time non-singular fast terminal sliding surface for: ； ； In the formula, , For state variables; ， ， ， ， , , , Both are constants and , , , , , , For symbolic functions, It is a positive constant less than 1; The approximation law for the line-of-sight normal pitch direction is: ； In the formula, , , , , , , Both are constants and , , , , , Indicates the relative distance between the missile and the target; After estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, the obtained first estimated value is substituted into the line-of-sight normal pitch guidance law. Then, the parameters to be estimated in the line-of-sight normal yaw guidance law are estimated using a second radial basis function (RBF) neural network, and the obtained second estimated value is substituted into the line-of-sight normal yaw guidance law to obtain a fixed-time non-singular fast terminal sliding mode guidance law with angle constraints.

2. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 1, characterized in that, The relative motion model of the missile target is as follows: ； In the formula, Indicates the relative distance between the missile and the target. , They are respectively The first and second derivatives, , These represent the missile's line-of-sight tilt angle and line-of-sight deflection angle, respectively. , , These represent the tangential, normal pitch, and normal yaw components of the missile's acceleration in the line-of-sight coordinate system, respectively. , , These represent the tangential, pitch, and yaw components of the target acceleration in the line-of-sight coordinate system, respectively. , They are respectively and The first derivative.

3. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 2, characterized in that, The missile's three-dimensional guidance model is as follows: ； In the formula, , , and All are state variables, where, , , , , , These represent the missile's desired pitch line-of-sight angle and desired yaw line-of-sight angle, respectively.

4. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 3, characterized in that, The line-of-sight normal pitch guidance law is as follows: ； In the formula, This indicates the normal pitch disturbance caused by the target maneuver that needs to be estimated. express The derivative of .

5. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 3, characterized in that, Design the line-of-sight normal yaw guidance law according to the following steps: Constructing a fixed-time nonsingular fast terminal sliding surface : ； ； In the formula, ， ， ， ， , , , Both are constants and , , , , , , For symbolic functions, It is a positive constant less than 1; Based on the aforementioned fixed-time non-singular fast terminal sliding surface design, the approach law for the line-of-sight normal yaw direction is as follows: ； In the formula, , , , , , , Both are constants and , , , , ; Based on the missile's three-dimensional guidance model and the fixed-time non-singular fast terminal sliding surface And based on the approach law of the line-of-sight normal yaw direction, design the line-of-sight normal yaw guidance law: ； In the formula, This represents the normal yaw disturbance caused by the target maneuver that needs to be estimated. express The derivative of .

6. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 1, characterized in that, The step of estimating the parameters to be estimated in the line-of-sight normal pitch guidance law using a pre-trained first radial basis function (RBF) neural network, and then substituting the obtained first estimated value into the line-of-sight normal pitch guidance law, includes: Fixed-time nonsingular fast terminal sliding surface and its first derivative By inputting a pre-trained first radial basis function (RBF) neural network, the normal pitch component of the target acceleration in the line-of-sight coordinate system is estimated. ; Based on the estimated target acceleration in the normal pitch direction component in the line-of-sight coordinate system Calculate the normal pitch disturbance caused by the target's maneuver. ; The calculated normal pitch disturbance caused by the target maneuver Substituting the line-of-sight normal pitch guidance law into the given law, we obtain the line-of-sight normal pitch guidance law.

7. The adaptive fast sliding mode guidance method for air-to-air missiles in a simulated environment according to claim 6, characterized in that, The step of estimating the parameters to be estimated in the line-of-sight normal yaw guidance law using a second radial basis function (RBF) neural network, and substituting the obtained second estimated value into the line-of-sight normal yaw guidance law, includes: Fixed-time nonsingular fast terminal sliding surface and its first derivative By inputting a pre-trained second radial basis function (RBF) neural network, the normal yaw component of the target acceleration in the line-of-sight coordinate system is estimated. ; Based on the estimated normal yaw component of the target acceleration in the line-of-sight coordinate system Calculate the normal yaw interference caused by the target maneuver. ; The calculated normal yaw interference caused by the target maneuver Substituting the line-of-sight normal yaw guidance law into the above, a line-of-sight normal yaw direction guidance law is generated.

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