Aircraft collaborative optimal mid-guidance method based on singular perturbation theory
Through two-time scale decomposition and boundary layer controller optimization based on singular perturbation theory, the problem of large energy loss in coordinated medium guidance of multiple vehicles is solved, and the optimal medium guidance and efficient fuel utilization of the aircraft are achieved.
Patent Information
- Application Number
- CN202510278209.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-10
- Publication Date
- 2025-07-08
AI Technical Summary
The existing multi-aircraft coordination medium-guided method attaches importance to formation convergence and ignores synergistic optimization, resulting in large energy losses and high fuel consumption, reducing the endurance and cruise radius of multi-aircraft.
Based on the singular perturbation theory, the dynamic equations of the aircraft are divided into fast-changing and slow-changing variables, and a two-time scale system is constructed. The slow-changing and fast-changing systems are obtained by lowering the order, and the minimum energy controller of the left and right boundary layers is set to optimize the control amount of the aircraft to achieve optimal medium-guided guidance.
The calculation process is simplified, guidance accuracy is improved, energy consumption is reduced, the optimal intermediate guidance of the aircraft is achieved, and fuel utilization and endurance is improved.
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Figure CN120276459A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a cooperative optimal mid-course guidance method for aircraft based on singular perturbation theory, belonging to the field of flight control technology. Background Art
[0002] Existing cooperative mid-course guidance methods for multiple aircraft mostly focus on the convergence and maintenance of formation, and rarely focus on the optimality of cooperative mid-course guidance, which easily leads to large energy losses and high fuel consumption in the mid-course guidance of multiple aircraft, directly reducing the endurance and cruise radius of multiple aircraft.
[0003] Therefore, it is necessary to conduct a more in-depth study on the existing cooperative guidance and interception methods to solve the above problems. Summary of the Invention
[0004] In order to overcome the above problems, in-depth research has been carried out, and a cooperative optimal mid-course guidance method for aircraft based on singular perturbation theory is proposed, including the following steps:
[0005] S1. Establish the dynamic equation of the aircraft, and classify the variables into fast-varying variables and slow-varying variables according to the variable change rate therein;
[0006] S2. Based on the dynamic equation of the aircraft, construct a two-time-scale system;
[0007] Based on the slow-varying variable time scale, reduce the order of the two-time-scale system to obtain a slow-varying system;
[0008] Based on the fast-varying variable time scale, reduce the order of the two-time-scale system to obtain a fast-varying system;
[0009] S3. Based on the slow-varying system, obtain the control quantity of the aircraft in the slow-varying state;
[0010] Based on the fast-varying system, set a left boundary layer minimum energy controller and a right boundary layer minimum energy controller to obtain the control quantity of the aircraft in the fast-varying state;
[0011] S4. Control the aircraft with the obtained control quantity to realize the flight of the aircraft during the mid-course guidance.
[0012] In a preferred embodiment, in S1, the dynamic equation of the aircraft is expressed as:
[0013]
[0014] r i (t f,i ) = 0
[0015]
[0016] Among them, the subscript i represents the i-th aircraft, and r i is the relative line-of-sight distance between the i-th aircraft and the target point; q i is the line-of-sight angle of the i-th aircraft relative to the target point; θ i is the flight path angle of the i-th aircraft. The variable with subscript f represents its value at the end time, and T i is the thrust received by the i-th aircraft; D i is the drag force received by the i-th aircraft; g is the acceleration due to gravity; m is the mass of the aircraft; x i is the range of the i-th aircraft; y i is the flight altitude of the i-th aircraft; n yi is the overload of the i-th aircraft, which is the control variable; E i is the specific energy of the i-th aircraft, and V i represents the speed of the i-th aircraft.
[0017] In a preferred embodiment, the fast-varying variables are the flight altitude and the flight path angle; the slow-varying variables are the specific energy and the range.
[0018] In a preferred embodiment, in S2, the two-time-scale system is expressed as:
[0019]
[0020] Among them, ε is a small parameter.
[0021] In a preferred embodiment, the slow-varying system is expressed as:
[0022]
[0023] Among them, the subscript 0 represents the state of the slow-varying system.
[0024] In a preferred embodiment, the fast-varying system is expressed as:
[0025]
[0026] In a preferred embodiment, the fast-varying system is feedback linearized, and the feedback-linearized fast-varying system is expressed as:
[0027]
[0028] Among them, ω is the state variable of the fast-varying system, v is the control variable of the fast-varying system, v, A represents the state matrix, and B represents the input matrix.
[0029] In a preferred embodiment, in S3, in the slow-varying state, the aircraft flies at n yiThe state of = 1 is the control quantity, and cruise flight is performed at the optimal altitude.
[0030] In a preferred embodiment, the quadratic performance J of the left boundary fast-varying system L is expressed as:
[0031]
[0032] where τ L represents the left boundary fast-varying time scale, Q is the state weighting matrix used to quantify the importance of different variables, and q 11 , q 12 , q 21 , q 22 are the elements in the state weighting matrix, representing the weights between system states respectively, R is the control weighting matrix used to quantify the importance of control inputs, and the superscript T represents transpose;
[0033] The left boundary layer minimum energy controller is expressed as:
[0034]
[0035] where represents the Lyapunov matrix.
[0036] In a preferred embodiment, the right boundary layer minimum energy controller is expressed as:
[0037]
[0038] HW + WH T + BB T = 0
[0039] where is the stable state of the system during the slow-varying process, and ω f is the end state of the system.
[0040] The beneficial effects of the present invention include:
[0041] (1) By introducing small parameters to approximate the dynamic equation, the high-order system can be reduced in order, thereby simplifying the solution process, reducing the computational amount, and improving the control response speed;
[0042] (2) Connecting the boundary conditions with the reduced-order system and correcting the reduced-order solution improve the guidance accuracy and reduce the energy consumption. Brief Description of the Drawings
[0043] Figure 1 Shows a schematic flow diagram of a cooperative optimal mid-course guidance method for an aircraft based on singular perturbation theory according to a preferred embodiment of the present invention;
[0044] Figure 2 Show the comparison chart of flight trajectories in Example 1 and Comparative Example 1;
[0045] Figure 3 Show the comparison chart of speed curves in Example 1 and Comparative Example 1;
[0046] Figure 4 Show the comparison chart of overload curves in Example 1 and Comparative Example 1;
[0047] Figure 5 Show the comparison chart of track angle curves in Example 1 and Comparative Example 1;
[0048] Figure 6 Show the flight trajectory diagrams of different aircraft in Example 2;
[0049] Figure 7 Show the speed curve diagrams of different aircraft in Example 2;
[0050] Figure 8 Show the overload curve diagrams of different aircraft in Example 2. Detailed implementation manners
[0051] The present invention will be further described in detail below with reference to the drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become more clearly defined.
[0052] The special term "exemplary" herein means "serving as an example, embodiment, or illustration". Any embodiment described herein as "exemplary" does not necessarily have to be construed as superior or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.
[0053] A cooperative optimal mid-course guidance method for aircraft based on singular perturbation theory provided by the present invention, as Figure 1 shown, includes the following steps:
[0054] S1. Establish the dynamic equation of the aircraft, and classify the variables into fast-varying variables and slow-varying variables according to the variable change rate therein;
[0055] S2. Based on the dynamic equation of the aircraft, construct a two-time-scale system;
[0056] Based on the time scale of the slow-varying variables, reduce the order of the two-time-scale system to obtain a slow-varying system;
[0057] Based on the time scale of the fast-varying variables, reduce the order of the two-time-scale system to obtain a fast-varying system;
[0058] S3. Based on the slow-varying system, obtain the control quantity of the aircraft in the slow-varying state;
[0059] Based on the fast-varying system, a left boundary layer minimum energy controller and a right boundary layer minimum energy controller are set to obtain the control quantity of the aircraft in the fast-varying state;
[0060] S4. Use the obtained control quantity to control the aircraft to realize the flight of the aircraft during the mid-course guidance process.
[0061] In S1, the dynamic equation of the aircraft is expressed as:
[0062]
[0063] r i (t f,i ) = 0
[0064]
[0065] Among them, the subscript i represents the i-th aircraft, and r i is the relative line-of-sight distance between the i-th aircraft and the target point; q i is the line-of-sight angle of the i-th aircraft relative to the target point; θ i is the flight path angle of the i-th aircraft. The variable with the subscript f represents its value at the end time, and T i is the thrust received by the i-th aircraft; D i is the drag received by the i-th aircraft; g is the acceleration due to gravity; m is the mass of the aircraft; x i is the range of the i-th aircraft; y i is the flight altitude of the i-th aircraft; n yi is the overload of the i-th aircraft, which is the control quantity; E i is the specific energy of the i-th aircraft, and V i represents the speed of the i-th aircraft.
[0066] In the dynamic equation, r i (t f,i ) = 0 ensures that each aircraft successfully reaches the target point position.
[0067] Furthermore, the specific energy of the i-th aircraft is expressed as:
[0068]
[0069] In S1, the fast-varying variables are the flight altitude and the flight path angle; the slow-varying variables are the specific energy and the range.
[0070] Since the aircraft will fly for a long time and distance during the mid-course guidance section, it is desired that the aircraft can minimize the energy consumption during the mid-course guidance section, so as to meet the demand for the initial energy in the terminal guidance section. Select the maximum energy of the i-th aircraft at the end of the mid-course guidance section as the performance index, that is, take the performance index as:
[0071] J = max[E i (t f )]
[0072] The inventors found that when the flight distance is relatively long, the minimum-energy flight trajectory of the aircraft always includes a cruise segment at the optimal altitude. Since air resistance decreases with increasing altitude, the optimal altitude for the aircraft to cruise is often relatively high. Therefore, in the initial stage, it is necessary to control the overload of the aircraft to climb to the optimal cruise altitude, and at the end of the flight, it is also necessary to control the overload of the aircraft to reach the target point from the optimal cruise altitude to meet the terminal constraints. The overload of the aircraft only changes significantly at the beginning and end of the flight trajectory, and is close to the steady state during the remaining flight time, that is: n y ≈ 1, θ ≈ 0. Based on the above findings, according to the characteristics of the minimum-energy trajectory of the aircraft, in the present invention, the flight altitude and the track angle are used as fast-varying variables, and the specific energy and the range are used as slow-varying variables.
[0073] In S2, the two-time-scale system is expressed as:
[0074]
[0075] where ε is a small parameter.
[0076] Due to the highly nonlinear characteristics of the aircraft dynamics system, this two-point boundary value problem usually cannot be solved by analytical methods. In the present invention, inspired by the singular perturbation theory, by introducing a small parameter to approximate the dynamic equations, the high-order system can be reduced in order, thereby simplifying the system and the subsequent solution process.
[0077] Furthermore, when the system is measured by the slow-varying time scale t, the system is a slow-varying system at this time, and the dynamic terms of the altitude and the track angle and disappear, and the fast-varying variables θ i and y i quickly reach the steady state, and the fast-varying state is in the equilibrium state. In this state, the i-th aircraft enters the optimal altitude cruise, that is, when ε = 0, n yi0 = 1, θ i0 = 0, and the reduced-order slow-varying system is obtained:
[0078]
[0079] where the subscript 0 represents the state of the slow-varying system.
[0080] In the slow-varying state, the aircraft will cruise at the optimal altitude with the state of n yi = 1.
[0081] According to the present invention, before the aircraft enters the cruise phase, it is necessary to control the aircraft to climb from the initial position to the optimal cruise altitude, and this phase is the left boundary layer phase; similarly, after the aircraft ends the cruise phase, it is necessary to control the aircraft to descend from the optimal cruise altitude to the terminal target point to meet the terminal constraints, and this phase is the right boundary layer. The motion state of the aircraft in the left and right boundary layers is a fast-varying state. During this state process, the slow-varying variables are in a steady state, and the fast-varying variables play a dominant role.
[0082] The fast time scale τ is expressed as:
[0083]
[0084] where t is the slow time scale, t * represents the boundary time, t * = t0 or t * = t f , t0 represents the initial time of the aircraft at the initial position, t f represents the end time of the aircraft reaching the target point.
[0085] The fast system is expressed as:
[0086]
[0087] Preferably, the fast system is also feedback linearized, and let
[0088]
[0089] The nonlinear transformation is designed as:
[0090] ω = Φ(η) = [y i V i sinθ i T
[0091] The nonlinear feedback is designed as:
[0092]
[0093] Then the fast system after feedback linearization is expressed as:
[0094]
[0095] where ω is the state variable of the fast system, v is the control variable of the fast system, v, A represents the state matrix, and B represents the input matrix.
[0096] The state matrix A and the input matrix B satisfy:
[0097]
[0098] In S3, according to the slow - varying system, in the slow - varying state, that is, during the cruise flight at the optimal altitude, the aircraft will use n yi = 1 as the control variable and conduct cruise flight at the optimal altitude.
[0099] According to the fast - varying system, in the left - hand boundary layer stage, that is, when the aircraft climbs from the initial position to the optimal cruise altitude and the system reaches the steady - state, that is, when n yi0 = 1, θ i0 = 0, y i0 = y op , there exists:
[0100] ω S = [y op , 0] T , v S = 0
[0101] where the subscript S represents the quantity in the left - hand boundary layer steady - state, that is, ω S represents the state quantity in the left - hand boundary layer steady - state, v S represents the control quantity in the left - hand boundary layer steady - state; y op represents the optimal cruise altitude.
[0102] Combining with the fast - varying system after feedback linearization, the left - hand boundary fast - varying system can be obtained:
[0103]
[0104] ω L = ω - ω S , v L = v - v S
[0105] where ω L represents the left - hand boundary layer state quantity, v L represents the left - hand boundary layer control quantity.
[0106] Furthermore, taking the quadratic performance of the left - hand boundary fast - varying system as an index, a left - hand boundary layer minimum - energy controller is constructed.
[0107] The quadratic performance J L of the left - hand boundary fast - varying system is expressed as:
[0108]
[0109] where τ L represents the left - hand boundary fast - varying time scale, Q is the state - weighting matrix used to quantify the importance of different variables, q 11 , q 12 , q 21 , q 22is an element in the state weighting matrix, representing the weights between system states respectively. R is the control weighting matrix, used to quantify the importance of control inputs, and the superscript T represents transpose.
[0110] The left boundary layer minimum energy controller is expressed as:
[0111]
[0112] where, represents the Lyapunov matrix.
[0113] By solving the controller, the left boundary layer control quantity is obtained:
[0114] v L (τ L ) = K(ω - ω S ) = k L1 (y i - y op ) + k L2 V i sin(θ i ).
[0115] where, k L1 、k L2 are adjustable parameters.
[0116] According to the fast - varying system, in the right boundary layer stage, that is, the stage of descending from the optimal cruise altitude to the terminal target point, combining with the fast - varying system after feedback linearization, the right - hand boundary fast - varying system can be obtained:
[0117]
[0118] H = A + BK′
[0119]
[0120] where, ω R represents the left boundary layer state quantity, v R represents the left boundary layer control quantity, H is an intermediate variable, K′ is an adjustable gain value, τ R represents the fast - varying time scale of the right boundary layer.
[0121] Based on the right - hand boundary fast - varying system, applying the optimal control theory, the right boundary layer minimum energy controller is obtained, expressed as:
[0122]
[0123] HW + WH T + BB T = 0
[0124] where, is the stable state of the system during the slow-varying process, ω f is the end state of the system.
[0125] Furthermore, ω f = [y f V if sin(θ if )] T
[0126] where V if represents the end velocity of the i-th aircraft, and θ if represents the end track angle of the i-th aircraft.
[0127] Solve the minimum energy controller for the right boundary layer to obtain the right boundary layer control quantity:
[0128]
[0129] where k R1 , k R2 are adjustable parameters.
[0130] In S4, during the left boundary layer stage, based on the left boundary layer control quantity, according to v = v S + v L obtain the overload command n yi of the aircraft at this time:
[0131]
[0132] where k L1 , k L2 are adjustable parameters.
[0133] The aircraft flies from the initial state to the optimal cruise altitude under this command;
[0134] During the optimal cruise altitude stage, the aircraft will fly with the command n yi = 1.
[0135] In the right boundary layer stage, based on the right boundary layer control quantity, according to v = v L + v S + v R obtain the overload command n yi of the aircraft at this time:
[0136]
[0137] where t go is the remaining flight time.
[0138] The aircraft flies from the optimal cruise altitude to the end target point under this command.
[0139] Preferably, the remaining flight time is estimated and obtained by the following method:
[0140]
[0141] where V ir is an intermediate variable.
[0142] Embodiment
[0143] Embodiment 1
[0144] Conduct a cooperative optimal mid-course guidance simulation experiment, including the following steps:
[0145] S1. Establish the dynamic equation of the aircraft, and classify the variables into fast-changing variables and slow-changing variables according to the variable change rate therein;
[0146] S2. Based on the dynamic equation of the aircraft, construct a two-time-scale system;
[0147] Based on the slow-changing variable time scale, reduce the order of the two-time-scale system to obtain a slow-changing system;
[0148] Based on the fast-changing variable time scale, reduce the order of the two-time-scale system to obtain a fast-changing system;
[0149] S3. Based on the slow-changing system, obtain the control amount of the aircraft under the slow-changing state;
[0150] Based on the fast-changing system, set the left boundary layer minimum energy controller and the right boundary layer minimum energy controller, and obtain the control amount of the aircraft under the fast-changing state;
[0151] S4. Control the aircraft with the obtained control amount to realize the flight of the aircraft during the mid-course guidance process.
[0152] In S1, the dynamic equation of the aircraft is expressed as:
[0153]
[0154] r i (t f,i ) = 0
[0155]
[0156] In S2, the two-time-scale system is expressed as:
[0157]
[0158] The slow-changing system is:
[0159]
[0160] The fast-varying system after feedback linearization is expressed as:
[0161]
[0162] In S3, in the slow-varying state, the aircraft will use the state with n yi = 1 as the control variable and perform cruise flight at the optimal altitude.
[0163] The left boundary layer minimum energy controller is expressed as:
[0164]
[0165] Solve the controller to obtain the left boundary layer control variable:
[0166] v L (τ L ) = K(ω - ω S ) = k L1 (y i - y op ) + k L2 V i sin(θ i )
[0167] The right boundary layer minimum energy controller is expressed as:
[0168]
[0169] HW + WH T + BB T = 0
[0170] Solve the controller to obtain the right boundary layer control variable:
[0171]
[0172] In S4, in the left boundary layer stage, based on the left boundary layer control variable, obtain the overload command n yi :
[0173]
[0174] In the optimal cruise altitude stage, the aircraft will fly with the command of n yi = 1.
[0175] In the right boundary layer stage, based on the right boundary layer control variable, according to v = v L + v S + v R obtain the overload command n yi :
[0176]
[0177] During the simulation process, a single aircraft is set for simulation, and the simulation conditions are as follows:
[0178] (1) The initial position coordinates of the aircraft are (0 km, 13 km).
[0179] (2) The target point coordinates of the aircraft are (400 km, 11 km).
[0180] (3) The initial track angle is 20°, and the initial speed of the aircraft is 300 m / s.
[0181] (4) The maximum altitude of the aircraft is 30 km.
[0182] (5) The adjustable parameters are set as follows:
[0183] k L1 =-0.0105, k L2 =-0.2, k R1 =-0.00405, k R2 =-0.2
[0184] Example 2
[0185] The same experiment as in Example 1 is carried out, except that three aircraft are used for simulation, and the simulation conditions are as follows:
[0186] (1) The initial position coordinates of the three aircraft are respectively: Missile-a aircraft (0 km, 13 km), Missile-b aircraft (20 km, 13 km), Missile-c aircraft (40 km, 13 km);
[0187] (2) The initial speeds of the three aircraft are all set to 300 m / s;
[0188] (3) The target point positions of the three aircraft are all set to (500 km, 11 km);
[0189] (4) The adjustable parameters are set as follows:
[0190] k L1 =-0.0105, k L2 =-0.2, k R1 =-0.0042, k R2 =-0.2
[0191] Comparative Example 1
[0192] The same experiment as in Example 1 is carried out, except that the guidance law is obtained by using the GPOPS optimization software.
[0193] Experimental Example 1
[0194] Comparing the results in Example 1 and Comparative Example 1, as Figures 2 - 5 shown.
[0195] Among them, Figure 2 shows a comparison chart of flight trajectories, Figure 3 shows a comparison chart of speed curves, Figure 4 shows a comparison chart of overload curves, Figure 5 shows a comparison chart of track angle curves.
[0196] From Figures 2 - 5 it can be seen that the methods in Example 1 and Comparative Example 1 can both enable the aircraft to accurately reach the target point and meet the terminal position constraint conditions; however, the terminal speed obtained by the method in Example 1 is higher than the global optimal solution obtained in Comparative Example 1, with less energy consumption, improving the fuel utilization rate and achieving the optimal terminal speed.
[0197] The guidance comparison results between Example 1 and Comparative Example 1 are shown in Table 1.
[0198] Table 1
[0199]
[0200] From Table 1, it can be seen that the method in Example 1 takes less calculation time and requires less computing power, enabling the method in Example 1 to achieve real-time calculation and planning.
[0201] Experimental Example 2 analyzes the simulation results in Example 2, as Figures 6 - 8 shown.
[0202] Among them, Figure 6 shows the flight trajectory diagrams of different aircraft, Figure 7 shows the speed curve diagrams of different aircraft, Figure 8 shows the overload curve diagrams of different aircraft.
[0203] From Figures 6 - 8 it can be seen that all three aircraft can accurately reach the target point, meet the terminal position constraint, and the three aircraft can achieve less energy loss in the mid-course guidance section and the optimal terminal speed, and can enter the terminal guidance section at a relatively high speed. Therefore, it shows that the method in Example 2 can effectively reduce the energy loss in the mid-course guidance section of multi-aircraft cooperation, improve the fuel utilization rate, and achieve the optimal terminal speed.
[0204] The present invention has been described above in combination with preferred embodiments, but these embodiments are only exemplary and only serve an illustrative purpose. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.
Claims
1. A cooperative optimal mid-course guidance method for aircraft based on singular perturbation theory, characterized in that, It includes the following steps: S1. Establish the dynamic equation of the aircraft, and classify the variables into fast-varying variables and slow-varying variables according to the variable change rate therein; S2. Based on the dynamic equation of the aircraft, construct a two-time-scale system; Based on the slow-varying variable time scale, reduce the order of the two-time-scale system to obtain a slow-varying system; Based on the fast-varying variable time scale, reduce the order of the two-time-scale system to obtain a fast-varying system; S3. Based on the slow-varying system, obtain the control quantity of the aircraft in the slow-varying state; Based on the fast-varying system, set the left boundary layer minimum energy controller and the right boundary layer minimum energy controller, and obtain the control quantity of the aircraft in the fast-varying state; S4. Use the obtained control quantity to control the aircraft to realize the flight of the aircraft during the mid-course guidance process.
2. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein in S1, the dynamic equation of the aircraft is expressed as: r i (t f,i )＝0 Among them, the subscript i represents the i-th aircraft, and r i is the relative line-of-sight distance between the i-th aircraft and the target point; q i is the line-of-sight angle of the i-th aircraft relative to the target point; θ i is the track angle of the i-th aircraft. The variable with the subscript f represents its value at the end moment, T i is the thrust received by the i-th aircraft; D i is the drag force received by the i-th aircraft; g is the acceleration due to gravity; m is the mass of the aircraft; x i is the range of the i-th aircraft; y i is the flight altitude of the i-th aircraft; n yi is the overload of the i-th aircraft, which is the control variable; E i is the specific energy of the i-th aircraft, and V i represents the speed of the i-th aircraft.
3. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein the fast-varying variables are flight altitude and track angle; the slow-varying variables are specific energy and range.
4. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein in S2, the two-time-scale system is expressed as: where ε is a small parameter.
5. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein the slow-varying system is expressed as: where the subscript 0 represents the state of the slow-varying system.
6. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein the fast-varying system is expressed as:
7. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 6, wherein perform feedback linearization on the fast-varying system, and the feedback-linearized fast-varying system is expressed as: where ω is the state quantity of the fast-varying system, v is the control quantity of the fast-varying system, v, A represents the state matrix, and B represents the input matrix.
8. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein In S3, in the slow-varying state, the aircraft uses the state with n yi = 1 as the control variable and conducts cruise flight at the optimal altitude.
9. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein The quadratic performance J of the left boundary fast-varying system L is expressed as: Among them, τ L represents the left boundary fast-changing time scale, Q is the state weighting matrix, and q 11 , q 12 , q 21 , q 22 are the elements in the state weighting matrix, R is the control weighting matrix, and the superscript T represents the transpose; the left boundary layer minimum energy controller is expressed as: where P represents the Lyapunov matrix.
10. The cooperative optimal mid-course guidance method for an aircraft based on the singular perturbation theory according to claim 1, wherein the right boundary layer minimum energy controller is expressed as: HW+WH T +BB T =0 Among them, is the stable state of the system during the slow-varying process, ω f is the end state of the system.