Dual-pulse missile initial guidance method based on pseudo-spectral method and neural network

Abstract

The invention provides a dual-pulse guided missile initial guidance method based on a pseudo-spectral method and a neural network. The dual-pulse guided missile initial guidance method comprises the following steps that 1, a trajectory optimization model is established; only a preliminary guidance method of a missile in a vertical plane is considered; step 2, solving an optimal trajectory by using a pseudo-spectral method; giving a corresponding state quantity, a control quantity, an initial moment constraint, a terminal moment constraint and a process constraint; step 3, fitting a control instruction by using a neural network; a BP neural network is used for fitting; 4, fitting a trajectory inclination angle by using a neural network; step 5, obtaining a suboptimal double-pulse initial guidance law; and obtaining a fitted attack angle control rule and an expected flight trajectory inclination angle, obtaining an expected instruction and an expected trajectory inclination angle by using a neural network according to the current flight state, and performing instruction control. According to the method, the guided missile can fly according to the optimal trajectory, and the energy loss in the flight process is effectively reduced. By introducing a ballistic inclination angle feedback item, the method still can perform well when the initial launching inclination angle and the aerodynamic coefficient have deviations. The disadvantage that all the performance of the guided missile is difficult to give play to through traditional program guidance is solved.

Description

Technical Field

[0001] The invention provides a double-pulse missile primary guidance method based on pseudo-spectral method and neural network, belonging to the fields of aerospace technology, weapon technology and guidance control. Background Art

[0002] Compared with traditional single-thrust engines, dual-pulse engines can greatly adjust the timing of missile engagement, reasonably allocate the acceleration and deceleration process during flight, and improve the energy utilization efficiency of missiles. This technology has been widely used in missiles. Primary guidance is a key link in the flight process of missiles, which is related to the success of the mission. However, traditional primary guidance is mostly program-guided, with weak anti-pulling ability and difficult to guarantee optimality. Pseudo-spectral method is currently a more advanced ballistic optimization method, which is mainly used in solving nonlinear optimal control problems. Neural network is a tool that can theoretically fit any nonlinear function. The optimal control law of the missile's primary guidance stage is extremely nonlinear, and neural network can fit it well. Therefore, it is necessary to improve the primary guidance method so that the missile's primary guidance can fly with an approximate optimal trajectory and provide good initial conditions for mid-range guidance. Summary of the invention

[0003] Since the initial guidance stage of a typical dual-pulse missile is a program guidance, it is difficult to bring out the full performance of the missile. Therefore, the present invention optimizes the overall trajectory according to the pseudo-spectrum, and proposes a dual-pulse missile initial guidance method based on the pseudo-spectrum method and the neural network based on the optimization result. The initial guidance method can give approximately optimal control instructions according to the current state and launch conditions of the missile, and provide good initial conditions for the intermediate guidance.

[0004] The present invention provides a double-pulse missile initial guidance method based on pseudo-spectral method and neural network, such as Figure 1 As shown, the specific steps include:

[0005] Step 1. Build a trajectory optimization model

[0006] Since the missile is usually far away from the target during the initial launch, the horizontal movement is small and can be ignored in the initial guidance stage. In the vertical plane, the missile has a greater impact on the missile's flight trajectory because the atmospheric density, gravity and other external conditions will change dramatically with the height. Therefore, only the initial guidance method of the missile in the vertical plane is considered.

[0007] Figure 2 The force of the missile in the vertical plane is given, and the dynamic model of the missile is established:

[0008]

[0009] Among them, r is the horizontal distance, h is the height, V is the speed, γ is the ballistic inclination, 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 of gravity. For a dual-pulse missile, its thrust can be expressed in the following form:

[0010]

[0011]

[0012] Among them, P i is the thrust of the i-th segment; is the mass flow rate per second of the i-th segment, which can be used Calculate, I sp is the specific impulse; t i is the duration of the thrust in the i-th stage, and τ is the pulse interval time.

[0013] To ensure the continuity of the control law, the first-order derivative of the angle of attack is set as the control quantity:

[0014]

[0015] According to the dynamic model of the missile, the optimization model of the missile is given:

[0016]

[0017] Since the missile has a long flight distance, the initial guidance usually only considers the predicted hit point. Then it is necessary to solve the maximum flight distance of the missile. The performance index is set as:

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

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

[0020] After obtaining the optimal flight distance of the missile, the predetermined positions are divided into equal intervals according to the missile's closest combat distance to predict the hit point. At this time, the performance index is usually considered to be the maximum terminal velocity or the shortest flight time. The two cannot be achieved at the same time. In order to ensure that the air-to-air missile can better take into account the maximum terminal velocity and the shortest flight time, the following performance indicators are given:

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

[0022] Step 2. Use pseudospectral method to solve the optimal trajectory

[0023] Pseudospectral method is a method for solving optimal control and can be used to solve the optimal trajectory. The pseudospectral method requires the corresponding state quantity, control quantity, initial time constraint, terminal time constraint and process constraint.

[0024] The pseudo-spectral method can be used to obtain a series of optimal trajectories for the dual-pulse missile. Since the thrust of the dual-pulse missile is different at different times, the flight of the missile is divided into multiple segments to obtain the optimal trajectory. The state quantity of the missile during flight is shown in the following formula:

[0025] X=[rh V γ α m] T (8)

[0026] The control quantities of the missile during flight are as follows:

[0027]

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

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

[0030]

[0031] Among them, X link is the state constraint between different flight segments, is the constraint at the initial time of the i-th flight segment, is the constraint at the end time of the i-1th flight segment, is the initial moment of the i-th segment, is the end time of the i-1th segment. At the same time, constraints should be imposed on the state variables and control variables.

[0032] The terminal constraints are set as:

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

[0034] Among them, h(t f ) is 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 neural network to fit control instructions

[0036] From the control law of the missile, it shows strong nonlinearity, and the polynomial method is difficult to fit it, so the BP neural network is used to fit it. Through research, it is found that the control law and the predicted hit point position r f , the missile's initial launch height h0, speed V0, double pulse interval τ, and current flight time t are related, namely:

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

[0038] Among them, α BP The control law fitted by the neural network.

[0039] Step 4. Use neural network to fit the trajectory inclination

[0040] However, simply using the control law fitted by the neural network for guidance is an open-loop guidance with weak anti-pulling ability. Therefore, the neural network is also used to fit the trajectory inclination. That is:

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

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

[0043] Get the fitted angle of attack control law and the expected flight trajectory inclination angle, use the neural network to get the expected instructions and expected trajectory inclination angle according to the current flight state, and use the following instructions for control:

[0044] α c =α BP +K(γ-γ BP ) (14)

[0045] Among them, α c is the control angle of attack command, K is the control coefficient (constant).

[0046] So far, the control law proposed in the present invention has been able to be applied in simulation.

[0047] The following summarizes a dual-pulse missile initial guidance method based on pseudo-spectral method and neural network proposed by the present invention:

[0048] 1) Establish a trajectory optimization model.

[0049] 2) Use pseudo-spectral method to solve nonlinear optimal trajectory.

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

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

[0052] 5) According to the guidance coefficients set in advance, the actual control instructions are calculated.

[0053] The advantages of the present invention are:

[0054] (1) A preliminary guidance method based on pseudo-spectral method and neural network is proposed, which can make the missile fly along the optimal trajectory and effectively reduce the energy loss during the flight.

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

[0056] (3) It solves the disadvantage that traditional program guidance cannot fully utilize the missile's performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the primary guidance method of dual-pulse missile based on pseudo-spectral method and neural network.

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

[0059] Figure 3 It is the pseudo-spectrum optimal trajectory curve under the launch conditions of 15km altitude, 1.5Ma, 0 degree ballistic inclination, and 20s pulse interval.

[0060] Figure 4 It is the pseudo-spectrum optimal velocity curve under the launch conditions of 15km altitude, 1.5Ma, 0 degree ballistic inclination, and 20s pulse interval.

[0061] Figure 5 It is the pseudo-spectrum optimal ballistic inclination curve under the launch conditions of 15km altitude, 1.5Ma, 0 degree ballistic inclination, and 20s pulse interval.

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

[0063] Figure 7 It is the pseudo-spectrum optimal trajectory curve under the launch conditions of 15km altitude, 1.2Ma, 0 degree ballistic inclination, 50s pulse interval, and predicted impact point of 500km:50:1050km.

[0064] Figure 8It is the pseudo-spectrum optimal velocity curve under the launch conditions of 15km altitude, 1.2Ma, 0 degree ballistic inclination, 50s pulse interval, and predicted impact point of 500km:50:1050km.

[0065] Fig. 9 It is the pseudo-spectrum optimal ballistic inclination curve under the conditions of launch altitude of 15km, 1.2Ma, 0 degree ballistic inclination, pulse interval of 50s, and predicted impact point of 500km:50:1050km.

[0066] Fig.10 It is the pseudo-spectrum optimal angle of attack curve under the launch conditions of 15km altitude, 1.2Ma, 0 degree ballistic inclination, 50s pulse interval, and predicted impact point of 500km:50:1050km.

[0067] Fig.11 It is a simulation flow chart of the primary guidance method based on pseudo-spectral method and neural network.

[0068] Fig.12 This is a trajectory comparison chart of the pseudo-spectrum optimal result and the non-corrected and corrected results in a simulation example where the initial trajectory inclination is pulled 10 degrees.

[0069] Fig.13 It is a trajectory comparison chart of the pseudo-spectrum optimal result and the non-corrected and corrected results under the simulation example of a 10% deviation in lift coefficient.

[0070] In the above figure, the symbols and codes involved are explained as follows:

[0071] Figure 2 In the equation, L is lift, D is drag, G is gravity, P is thrust, V is missile velocity vector, α is angle of attack, and γ is ballistic inclination, and the same below. DETAILED DESCRIPTION

[0072] The following will be combined with the attached Figure 1-12 The present invention is further described in detail with reference to the accompanying drawings and implementation examples.

[0073] Since traditional dual-pulse missiles are all program-guided, it is difficult to bring out the full performance of the missile, and the traditional method performs poorly in the case of deviation. Therefore, the pseudo-spectral method is used to search for the optimal trajectory, and then the neural network is used to fit the control instructions and flight parameters to construct a suboptimal guidance law with feedback terms.

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

[0075] Step 1: Build a trajectory optimization model

[0076] Considering the flight of a missile in a vertical plane, the dynamic model of the missile is established:

[0077]

[0078] Among them, r is the horizontal distance, h is the height, V is the speed, γ is the ballistic inclination, P is the thrust, α is the angle of attack, L is the lift, and D is the drag.

[0079] For dual-pulse missiles, the thrust can be expressed as follows:

[0080]

[0081]

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

[0083] The initial mass of the missile is 740kg. Given the specific impulse, thrust in different time periods, and time in different time periods:

[0084] I sp =270s (4)

[0085]

[0086]

[0087] In this mission, the flight trajectory of the missile needs to be optimized. The optimization variable is set as the first-order 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 as follows:

[0088]

[0089] Among them, u is the control quantity.

[0090] Since the missile has a long flight distance, the initial guidance usually only considers the predicted hit point. Then it is necessary to solve the maximum flight distance of the missile. The performance index is set as:

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

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

[0093] After obtaining the optimal flight distance of the missile, the predetermined positions are divided into equal intervals according to the missile's closest combat distance to predict the hit point. At this time, the performance index is usually considered to be the maximum terminal velocity or the shortest flight time. The two cannot be achieved at the same time. In order to ensure that the air-to-air missile can better take into account the maximum terminal velocity and the shortest flight time, the following performance indicators are given:

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

[0095] Step 2: Use pseudo-spectral method to solve the optimal trajectory

[0096] The pseudo-spectral method can be used to obtain a series of optimal trajectories for missile flight. Since the thrust of the dual-pulse missile is discontinuous, the flight of the missile is divided into multiple segments to obtain the optimal trajectory. The state quantity of the missile during flight is shown in the following formula:

[0097] X=[rh V γ α m] T (10)

[0098] The control quantities of the missile during flight are as follows:

[0099]

[0100] According to the different forms of power, the problem is divided into four sections. The power of the first and third sections is P1 and P2 respectively, and the second and fourth sections are unpowered gliding sections. The terminal variables of the first section are the same as the initial variables of the second section.

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

[0102]

[0103] Set the performance index as minJ = -r(t f ), search for the missile's farthest trajectory at different pulse intervals, so as to divide the predetermined positions into intervals later. Figure 3-Figure 6 The results showed an initial altitude of 15km, an initial velocity of 1.5Ma, an initial ballistic inclination of 0 degrees, a pulse interval of 20s, and an optimal range of 1224.07km.

[0104] Set the performance index to minJ = 2t f -V(t f ), search for the optimal trajectory results for different predetermined positions, Figure 7-10 The results show an initial altitude of 15km, an initial velocity of 1.2Ma, an initial ballistic 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: Fitting pseudo-spectral method to solve optimal control

[0106] From the control law of the missile, it shows strong nonlinearity, and the polynomial method is difficult to fit it, so the BP neural network is used to fit it. Through research, it is found that the control law and the predicted hit point position r f , the missile's initial launch height h0, speed V0, double pulse interval τ, and current flight time t are related, namely:

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

[0108] Step 4: Use a neural network to fit the trajectory inclination

[0109] However, simply using the control law fitted by the neural network for guidance is an open-loop guidance with weak anti-pulling ability. Therefore, the neural network is also used to fit the trajectory inclination. That is:

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

[0111] Step 5: Suboptimal Double Pulse Initial Guidance Law

[0112] Get the fitted angle of attack control law and the expected flight trajectory inclination angle, use the neural network to get the expected instructions and expected trajectory inclination angle according to the current flight state, and use the following instructions for control:

[0113] α c =α BP +10(γ-γ BP ) (14)

[0114] So far, if Fig.12 (The initial trajectory angle is 10 degrees off) Fig.13 (lift coefficient is pulled off by 10%), the result obtained by the method proposed by the present invention is basically consistent with the optimal result of the pseudo spectrum, which illustrates the effectiveness of the present solution.

[0115] The simulation process of applying the present invention is summarized below:

[0116] 1) Calculate the launch parameters (pulse interval time, predicted impact point location).

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

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

[0119] 4) Use the fourth-order to fifth-order Runge-Kutta algorithm to perform dynamic simulation on the differential equation of the missile, determine whether the missile has been ignited, and stop the simulation; otherwise, jump back to 2) to continue the calculation.

[0120] In summary, through the above process, the method of the present invention, i.e., a primary guidance method for a dual-pulse missile based on pseudospectral method and neural network, can be used to enable the missile to fly in a suboptimal trajectory. The example verified that the method of the present invention can still complete the boost in the form of the optimal trajectory when the initial trajectory inclination angle and aerodynamic coefficient are pulled off.

Claims

1. A dual-pulse missile initial guidance method based on pseudo-spectral method and neural network, characterized in that: The steps include: Step 1. Establish a trajectory optimization model; only consider the initial guidance method of the missile in the vertical plane; Step 2. Use pseudo-spectral method to solve the optimal trajectory; give the corresponding state quantity, control quantity, initial time constraint, terminal time constraint and process constraint; Step 3. Use the neural network to fit the control command; use the BP neural network to fit it; Step 4. Use neural network to fit the trajectory inclination; Step 5. Suboptimal dual-pulse initial guidance law; obtain the fitted angle of attack control law and the desired flight trajectory inclination, use the neural network to obtain the desired command and the desired trajectory inclination according to the current flight state, and perform command control.

2. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 1 is characterized in that: In step 1, the dynamic model of the missile is established: Among them, r is the horizontal distance, h is the height, V is the velocity, γ is the ballistic inclination, 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.

3. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 2 is characterized in that: For dual-pulse missiles, the thrust is expressed as follows: Among them, P i is the thrust of the i-th segment; is the mass flow rate of the i-th segment, Calculate, I sp is the specific impulse; t i is the duration of the i-th thrust, and τ is the pulse interval.

4. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 3 is characterized in that: To ensure the continuity of the control law, the first-order derivative of the angle of attack is set as the control quantity: According to the dynamic model of the missile, the optimization model of the missile is given:

5. The method for primary guidance of a double-pulse missile based on pseudo-spectral method and neural network according to claim 4 is characterized in that: Since the missile flies a long distance, the initial guidance only considers the predicted hit point, and the maximum distance of the missile flight needs to be solved. The performance index is set as: minJ=-r(t f ) (6) Among them, J is the performance index, t f is the terminal flight time, r(t f ) is the terminal flight distance.

6. A dual-pulse missile primary guidance method based on pseudo-spectral 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 according to the missile's closest combat distance to predict the hit point; at this time, the performance index is considered to be the maximum terminal speed or the shortest flight time; the two cannot be achieved at the same time, so the following performance index is given: minJ=2t f -V(t f ) (7).

7. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 1 is characterized in that: In step 2, the pseudo-spectral method is used to obtain a series of optimal trajectories of the dual-pulse missile. Since the thrust of the dual-pulse missile is different at different times, the flight of the missile is divided into multiple segments to obtain the optimal trajectory; the state quantity of the missile during flight is shown in the following formula: X=[rh V γ a m] T (8) The control quantities of the missile during flight are as follows: The first-order derivative of the angle of attack is used as the control variable to make the angle of attack of the optimal trajectory continuous and smooth. It is necessary to constrain the terminal variables of the previous segment to be the same as the initial variables of the next segment; the constraint is expressed as follows: Among them, X link is the state constraint between different flight segments, is the constraint at the initial time of the i-th flight segment, is the constraint at the end time of the i-1th flight segment, is the initial moment of the i-th segment, is the end moment of the i-1th segment; at the same time, constraints should be imposed on the state variables and control variables; The terminal constraints are set as: X end =[r(t f )-r PIP h(t f )-h PIP ] (11) Among them, h(t f ) is the terminal flight altitude of the missile, r PIP and h PIP To predict the flight distance and altitude of the impact point.

8. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 1 is characterized in that: In step 3, the control law and the predicted hit point position r f , the missile's initial launch height h0, speed V0, double pulse interval τ, and current flight time t are related, namely: a BP =F α (r f ,h0,V0,τ,t) (12) Among them, α BP The control law fitted by the neural network.

9. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 1 is characterized in that: In step 4, a neural network is used to fit the trajectory inclination; that is: c BP =F γ (r f ,h0,V0,τ,t) (13).

10. The double-pulse missile primary guidance method based on pseudo-spectral method and neural network according to claim 1, characterized in that: In step 5, the following instructions are used for control: a c =a BP +K(γ-γ BP ) (14) Among them, α c is the control angle of attack command, K is the control coefficient, which is a constant.

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