A dual-pulse missile initial guidance method based on pseudospectral method and neural network

Abstract

This invention proposes a dual-pulse missile initial guidance method based on pseudospectral method and neural network, comprising the following steps: Step 1. Establishing a trajectory optimization model; considering only the initial guidance method of the missile in the vertical plane; Step 2. Solving for the optimal trajectory using pseudospectral method; given the corresponding state variables, control variables, and initial time constraints, terminal time constraints, and process constraints; Step 3. Fitting control commands using neural network; fitting them using a BP neural network; Step 4. Fitting the trajectory inclination angle using neural network; Step 5. Suboptimal dual-pulse initial guidance law; obtaining the fitted angle of attack control law and the desired flight trajectory inclination angle, and using the neural network to obtain the desired command and desired trajectory inclination angle based on the current flight state, and performing command control. This invention enables the missile to fly along the optimal trajectory, effectively reducing energy loss during flight. By introducing a trajectory inclination angle feedback term, this method still performs well when there are deviations in the initial launch inclination angle and aerodynamic coefficient. It solves the disadvantage of traditional program guidance, which cannot fully utilize the missile's performance.

Description

Technical Field

[0001] This invention provides a dual-pulse missile initial guidance method based on pseudospectral method and neural network, belonging to the fields of aerospace technology, weapon technology, and guidance and control. Background Technology

[0002] Compared to traditional single-thrust engines, dual-pulse engines can significantly adjust the missile's engagement timing, rationally allocate acceleration and deceleration during flight, and improve the missile's energy utilization efficiency. This technology has been widely applied in missiles. Initial guidance is a crucial part of missile flight, determining mission success. However, traditional initial guidance is mostly programmed, with weak resistance to deviation and difficulty in guaranteeing optimality. The pseudospectral method is a relatively advanced trajectory optimization method, primarily used to solve nonlinear optimal control problems. Neural networks are theoretically capable of fitting any nonlinear function. The optimal control law of the missile's initial guidance phase is highly nonlinear, and neural networks can fit it well. Therefore, it is necessary to improve the initial guidance method to enable the missile to fly with an approximately optimal trajectory, providing good initial conditions for mid-course guidance. Summary of the Invention

[0003] Since the initial guidance phase of a typical dual-pulse missile relies on programmed guidance, which fails to fully utilize the missile's capabilities, this invention optimizes the overall trajectory based on pseudospectral data. Based on the optimization results, a dual-pulse missile initial guidance method using pseudospectral data and neural networks is proposed. This initial guidance method can provide near-optimal control commands according to the missile's current state and launch conditions, offering favorable initial conditions for mid-course guidance.

[0004] This invention provides a dual-pulse missile initial guidance method based on pseudospectral method and neural network, such as... Figure 1 As shown, the specific steps include the following:

[0005] Step 1. Establish a ballistic optimization model

[0006] Since missiles are typically far from their targets at initial launch and experience minimal horizontal motion, this can be ignored during the initial guidance phase. However, in the vertical plane, external conditions such as atmospheric density and gravity change drastically with altitude, significantly impacting the missile's flight trajectory. Therefore, only the initial guidance method in the vertical plane will be considered.

[0007] Figure 2 The forces acting on the missile in the vertical plane are given, and a dynamic model of the missile is established accordingly:

[0008]

[0009] Where r is the horizontal distance, h is the altitude, V is the velocity, γ is the trajectory angle, P is the thrust, α is the angle of attack, L is the lift, D is the drag, m is the mass, and g is the acceleration due to gravity. For a dual-pulse missile, its thrust can be expressed in the following form:

[0010]

[0011]

[0012] Among them, P i This represents the thrust of the i-th segment; For the i-th segment, the mass per second flow rate can be... Perform calculations, I sp For specific impulse; t i Let τ be the duration of the thrust in the i-th segment, and τ be the pulse interval time.

[0013] To ensure the continuity of the control law, let the first derivative of the angle of attack be used as the control variable:

[0014]

[0015] Based on the missile's dynamic model, an optimized model for the missile is given:

[0016]

[0017] Because missiles travel long distances, initial guidance typically only considers predicting the impact point. Therefore, it is necessary to solve for the maximum flight distance of the missile. Let the performance index be:

[0018] minJ = -r(t) f (6)

[0019] Where J is the performance index, tf is the terminal flight time, and r(t) is the terminal flight time. f () represents the terminal flight distance.

[0020] After obtaining the optimal missile flight distance, the predetermined positions are divided into equally spaced areas to predict the impact point based on the missile's closest operational range. At this point, the performance indicators are typically considered as either maximum terminal velocity or minimum flight time. These two cannot be simultaneously achieved. To ensure that the air-to-air missile can effectively balance maximum terminal velocity and minimum flight time, the following performance indicators are given:

[0021] minJ=2t f -V(t f (7)

[0022] Step 2. Solve for the optimal trajectory using the pseudospectral method.

[0023] The pseudospectral method is a method for solving optimal control problems and can be used to solve optimal trajectories. Using the pseudospectral method requires specifying the corresponding state variables, control variables, initial time constraints, terminal time constraints, and process constraints.

[0024] The pseudospectral method can be used to obtain a series of optimal trajectories for a dual-pulse missile. Since the thrust of the dual-pulse missile varies at different times, the missile's flight is divided into multiple segments to obtain the optimal trajectory. The state variables of the missile during flight are shown in the following equation:

[0025] X = [rh V γ α m] T (8)

[0026] The control variables during missile flight are shown below:

[0027]

[0028] The first derivative of the angle of attack is used as a control variable to make the angle of attack of the optimal ballistic trajectory continuous and smooth.

[0029] Since this problem is a multi-stage optimization problem, it is necessary to constrain the final variables of the first stage to be the same as the initial variables of the second stage. The constraint is expressed as follows:

[0030]

[0031] Among them, X link State constraints between different flight segments. The constraint is for the initial moment of the i-th flight segment. For the constraint of the end time of the (i-1)th flight segment, Let i be the initial time of segment i. This represents the end time of the (i-1)th segment. Simultaneously, constraints must be applied to the state variables and control variables.

[0032] Terminal constraints are set as follows:

[0033] X end =[r(t) f )-r PIP h(t f )-h PIP (11)

[0034] Where h(t) f ) represents the terminal flight altitude of the missile, r PIP and h PIP To predict the flight distance and altitude of the impact point.

[0035] Step 3. Use a neural network to fit the control commands.

[0036] The missile's control mechanism exhibits strong nonlinearity, making it difficult to fit using polynomial methods. Therefore, a backpropagation (BP) neural network was used for fitting. Research revealed that the control mechanism correlates with the predicted impact point position r. f The initial launch altitude h0, velocity V0, double pulse interval τ, and current flight time t of the missile are all related, namely:

[0037] α BP =F α (r f ,h0,V0,τ,t) (12)

[0038] Where, α BP The control law for fitting the neural network.

[0039] Step 4. Use a neural network to fit the ballistic inclination angle.

[0040] However, simply using a neural network to fit the control law for guidance is an open-loop guidance system, which has weak resistance to deflection. Therefore, a neural network is also used to fit the trajectory inclination angle. That is:

[0041] γ BP =F γ (r f ,h0,V0,τ,t) (13)

[0042] Step 5. Suboptimal double-pulse initial guidance law

[0043] The fitted angle-of-attack control law and the desired flight trajectory inclination are obtained. Based on the current flight state, a neural network is used to obtain the desired command and the desired trajectory inclination. The following command is used for control:

[0044] α c =α BP +K(γ-γ BP (14)

[0045] Where, α c K is the control coefficient (constant value) for controlling the angle of attack command.

[0046] Thus, the control law proposed in this invention can now be applied in simulations.

[0047] The following summarizes the initial guidance method for dual-pulse missiles based on pseudospectral method and neural network proposed in this invention:

[0048] 1) Establish a ballistic optimization model.

[0049] 2) The pseudospectral method is used to solve the nonlinear optimal trajectory.

[0050] 3) A neural network is used to fit the laws of angle of attack and ballistic inclination.

[0051] 4) Calculate the missile's current angle of attack and trajectory inclination based on the launch conditions and current flight time.

[0052] 5) Calculate the actual control command based on the pre-set guidance coefficients.

[0053] The advantages of this invention are:

[0054] (1) A preliminary guidance method based on pseudospectral method and neural network is proposed, which enables the missile to fly along the optimal trajectory and effectively reduces energy loss during flight.

[0055] (2) By introducing a ballistic tilt angle feedback term, this method can still perform well when there are deviations in the initial launch tilt angle and aerodynamic coefficient.

[0056] (3) It solves the disadvantage that traditional program guidance cannot fully utilize the missile's performance. Attached Figure Description

[0057] Figure 1 This is a flowchart of a dual-pulse missile initial guidance method based on pseudospectral method and neural network.

[0058] Figure 2 This is a schematic diagram of the force analysis of a missile in a vertical plane.

[0059] Figure 3 It is the pseudo-spectral optimal ballistic curve under the conditions of launch at an altitude of 15km, Mach 1.5, ballistic inclination angle of 0 degrees, and pulse interval of 20s.

[0060] Figure 4 It is the pseudo-spectral optimal velocity curve under the conditions of launch at an altitude of 15km, Mach 1.5, ballistic inclination of 0 degrees, and pulse interval of 20s.

[0061] Figure 5 It is the pseudo-spectral optimal trajectory inclination curve under the conditions of launch at an altitude of 15km, Ma 1.5, a ballistic inclination angle of 0 degrees, and a pulse interval of 20s.

[0062] Figure 6 It is the pseudo-spectral optimal angle of attack curve under the conditions of launch at an altitude of 15km, Ma 1.5, ballistic inclination of 0 degrees, and pulse interval of 20s.

[0063] Figure 7 It is the pseudo-spectral optimal ballistic curve under the following conditions: launch altitude of 15km, Ma1.2, ballistic inclination angle of 0 degrees, pulse interval of 50s, and predicted impact point of 500km:50:1050km.

[0064] Figure 8It is the pseudo-spectral optimal velocity curve under the following conditions: launch altitude of 15km, Ma1.2, ballistic inclination angle of 0 degrees, pulse interval of 50s, and predicted impact point of 500km:50:1050km.

[0065] Figure 9 It is the pseudo-spectral optimal trajectory inclination curve under the following conditions: launch altitude of 15km, Ma1.2, ballistic inclination angle of 0 degrees, pulse interval of 50s, and predicted impact point of 500km:50:1050km.

[0066] Figure 10 It is the pseudo-spectral optimal angle of attack curve under the following conditions: launch altitude of 15km, Ma1.2, ballistic inclination angle of 0 degrees, pulse interval of 50s, and predicted impact point of 500km:50:1050km.

[0067] Figure 11 This is a simulation flowchart of the initial guidance method based on pseudospectral method and neural network.

[0068] Figure 12 This is a comparison chart of the pseudo-spectral optimal result with the uncorrected and corrected results under a simulation example where the initial trajectory tilt angle is deflected by 10 degrees.

[0069] Figure 13 This is a comparison chart of the ballistic trajectory of the pseudo-spectral optimal result with the uncorrected and corrected results under a simulation example where the lift coefficient is skewed by 10%.

[0070] The symbols and codes involved in the above diagram are explained as follows:

[0071] Figure 2 In this context, L represents lift, D represents drag, G represents gravity, P represents thrust, V represents the missile velocity vector, α represents the angle of attack, and γ represents the trajectory inclination angle. The same applies below. Detailed Implementation

[0072] The following will be combined with the appendix Figure 1-12 The invention will be further described in detail with reference to the embodiments.

[0073] Since traditional dual-pulse missiles are all programmed guided, it is difficult to utilize the missile's full performance, and traditional methods perform poorly when the missile is pulled off course. Therefore, this paper proposes to search for the optimal trajectory using a pseudospectral method, and then use a neural network to fit the control commands and flight parameters to construct a suboptimal guidance law with a feedback term.

[0074] The specific implementation of the invention is as follows:

[0075] Step 1: Establish a ballistic optimization model

[0076] Considering the missile's flight in the vertical plane, establish a dynamic model of the missile:

[0077]

[0078] Where r is the horizontal distance, h is the altitude, V is the velocity, γ is the trajectory angle, P is the thrust, α is the angle of attack, L is the lift, and D is the drag.

[0079] For a dual-pulse missile, its thrust can be expressed in the following form:

[0080]

[0081]

[0082] Among them, P i For the i-th segment of thrust, For the i-th segment, the mass per second flow rate can be... t i Let τ be the duration of the thrust in the i-th segment, and τ be the pulse interval time.

[0083] The missile's initial mass is 740 kg. Given specific impulse, thrust at different time intervals, and time intervals:

[0084] I sp =270s (4)

[0085]

[0086]

[0087] In this mission, it is necessary to optimize the missile's flight trajectory. The optimization variable is set as the first derivative of the angle of attack, so that the angle of attack of the optimal trajectory is continuous and smooth. The trajectory optimization model is shown in the following equation:

[0088]

[0089] Where u is the control variable.

[0090] Because missiles travel long distances, initial guidance typically only considers predicting the impact point. Therefore, it is necessary to solve for the maximum flight distance of the missile. Let the performance index be:

[0091] minJ = -r(t) f (8)

[0092] Where J is the performance index, tf is the terminal flight time, and r(t) is the terminal flight time. f () represents the terminal flight distance.

[0093] After obtaining the optimal missile flight distance, the predetermined positions are divided into equally spaced areas to predict the impact point based on the missile's closest operational range. At this point, the performance indicators are typically considered as either maximum terminal velocity or minimum flight time. These two cannot be simultaneously achieved. To ensure that the air-to-air missile can effectively balance maximum terminal velocity and minimum flight time, the following performance indicators are given:

[0094] minJ=2t f -V(t f (9)

[0095] Step 2: Solve for the optimal trajectory using the pseudospectral method

[0096] The pseudospectral method can be used to obtain a series of optimal trajectories for missile flight. Since the thrust of a dual-pulse missile is discontinuous, the missile's flight is divided into multiple segments to obtain the optimal trajectory. The state variables during missile flight are shown in the following equation:

[0097] X = [rh V γ α m] T (10)

[0098] The control variables during missile flight are shown below:

[0099]

[0100] Based on the different forms of propulsion, the problem is divided into four segments. The propulsion for the first and third segments is P1 and P2, respectively, while the second and fourth segments are unpowered gliding segments. Furthermore, the final variable of the first segment is the same as the initial variable of the next segment.

[0101] The initial constraints, terminal constraints, and process constraints of each state variable and control variable are shown in the table below:

[0102]

[0103] The performance index is set as minJ = -r(t) f The system searches for the farthest trajectory of the missile at different pulse intervals to inform subsequent interval division of the predetermined array positions. Figures 3-6 The results show that with an initial altitude of 15km, an initial velocity of 1.5Ma, an initial trajectory inclination of 0 degrees, and a pulse interval of 20s, the optimal range is 1224.07km.

[0104] The performance index is set as minJ = 2t f -V(t f The system searches for the optimal ballistic trajectory for different predetermined positions. Figures 7-10 The results show that with an initial altitude of 15km, an initial velocity of 1.2Ma, an initial trajectory inclination of 0 degrees, a pulse interval of 50s, and a predicted impact point that increases uniformly by 50km from 500km to 1050km.

[0105] Step 3: Solve for optimal control using the pseudospectral fitting method

[0106] The missile's control mechanism exhibits strong nonlinearity, making it difficult to fit using polynomial methods. Therefore, a backpropagation (BP) neural network was used for fitting. Research revealed that the control mechanism correlates with the predicted impact point position r. f The initial launch altitude h0, velocity V0, double pulse interval τ, and current flight time t of the missile are all related, namely:

[0107] α BP =F α (r f ,h0,V0,τ,t) (12)

[0108] Step 4: Fit the ballistic inclination angle using a neural network

[0109] However, simply using a neural network to fit the control law for guidance is an open-loop guidance system, which has weak resistance to deflection. Therefore, a neural network is also used to fit the trajectory inclination angle. That is:

[0110] γ BP =F γ (r f ,h0,V0,τ,t) (13)

[0111] Step 5: Suboptimal double-pulse initial lead law

[0112] The fitted angle-of-attack control law and the desired flight trajectory inclination are obtained. Based on the current flight state, a neural network is used to obtain the desired command and the desired trajectory inclination. The following command is used for control:

[0113] α c =α BP +10(γ-γ BP (14)

[0114] Thus, as Figure 12 (Initial trajectory angle deflected by 10 degrees) and Figure 13 As shown in the figure (lift coefficient deflected by 10%), the results obtained by the method proposed in this invention are basically consistent with the optimal results of the pseudo-spectrum, which demonstrates the effectiveness of this scheme.

[0115] The simulation process for applying this invention is summarized below:

[0116] 1) Calculate the firing parameters (pulse interval time, predicted hit point position).

[0117] 2) Utilize a neural network to output the fitted angle of attack and the fitted trajectory inclination angle based on the launch conditions and the current time.

[0118] 3) Measure the current trajectory inclination angle and output control commands.

[0119] 4) Use the fourth- to fifth-order Runge-Kutta algorithm to perform dynamic simulation of the missile's differential equations, determine whether the missile has finished ignition, and stop the simulation; otherwise, jump back to 2) to continue the calculation.

[0120] In summary, the above process allows the missile to fly along a suboptimal trajectory using the method of this invention, namely, a dual-pulse missile initial guidance method based on pseudospectral method and neural network. Numerical examples verify that the method of this invention can still achieve a boost in the optimal trajectory even under initial trajectory tilt and aerodynamic coefficient deviation.

Claims

1. A dual-pulse missile initial guidance method based on pseudospectral method and neural network, characterized in that, Includes the following steps: Step 1. Establish a ballistic optimization model; only consider the initial guidance method of the missile in the vertical plane; Step 2. Solve for the optimal trajectory using the pseudospectral method; given the corresponding state variables, control variables, initial time constraints, terminal time constraints, and process constraints; Step 3. Fit the control command using a neural network; fit it using a BP neural network. Step 4. Use a neural network to fit the ballistic inclination angle; Step 5. Suboptimal double-pulse initial guidance law; obtain the fitted angle of attack control law and the desired flight trajectory inclination angle, and use a neural network to obtain the desired command and desired trajectory inclination angle based on the current flight state, and perform command control; In step 3, the control law and the predicted hit point position r f Initial launch altitude h0, velocity V0, and double pulse interval of the missile. It is related to the current flight time t, that is: Where, α BP The control law for neural network fitting; In step 4, a neural network is used to fit the ballistic inclination angle; that is: In step 5, the following instructions are used for control: a c =a BP +K(γ-γ BP ) (3) Where, α c To control the angle of attack command, K is the control coefficient, which is a constant.

2. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 1, characterized in that: In step 1, a dynamic model of the missile is established: Where r is the horizontal distance, h is the altitude, V is the velocity, γ is the trajectory angle, P is the thrust, α is the angle of attack, L is the lift, D is the drag, m is the mass, and g is the gravitational acceleration.

3. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 2, characterized in that: For a dual-pulse missile, its thrust manifests in the following form: Among them, P i This represents the thrust of the i-th segment; Let the mass per second flow rate of the i-th segment be denoted by . Perform calculations, I sp For specific impulse; t i Let i be the duration of the thrust segment. This is the interval between the two pulses.

4. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 3, characterized in that: To ensure the continuity of the control law, let the first derivative of the angle of attack be used as the control variable: Based on the missile's dynamic model, an optimized model for the missile is given:

5. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 4, characterized in that: Because the missile travels a long distance, the initial guidance only considers predicting the impact point; therefore, it is necessary to solve for the maximum flight distance of the missile. Let the performance index be: minJ=-r(t f ) (9) Where J is the performance index, t f For the terminal flight time, r(t) f () represents the terminal flight distance.

6. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 5, characterized in that: After obtaining the optimal flight distance of the missile, the predetermined positions are divided into equal intervals to predict the impact point based on the missile's closest operational distance. At this point, the performance indicators are considered as either maximum terminal velocity or minimum flight time; since both cannot be achieved simultaneously, the following performance indicators are given: minJ=2t f -V(t f ) (10).

7. The initial guidance method for a dual-pulse missile based on pseudospectral method and neural network according to claim 1, characterized in that: In step 2, a series of optimal trajectories for the dual-pulse missile flight are obtained using the pseudospectral method. Since the thrust of the dual-pulse missile varies at different times, the missile's flight is divided into multiple segments to obtain the optimal trajectory. The state variables of the missile during flight are shown in the following equation: X=[rh V γ a m] T (11) The control variables during missile flight are shown below: The first derivative of the angle of attack is used as a control variable to make the angle of attack of the optimal ballistic trajectory continuous and smooth. The constraint requires that the final variable of the preceding segment be the same as the initial variable of the following segment; the constraint is expressed as follows: Among them, X link State constraints between different flight segments. The constraint is for the initial moment of the i-th flight segment. The constraint is the time limit at the end of the (i-1)th flight segment. Let i be the initial time of segment i. This is the end time of the (i-1)th segment; at the same time, constraints must be imposed on the state variables and control variables; Terminal constraints are set as follows: X end =[r(t f )-r PIP h(t f )-h PIP ] (14) Where h(t) f ) represents the terminal flight altitude of the missile, r PIP and h PIP To predict the flight distance and altitude of the impact point.

Images