Improved particle swarm optimization algorithm based on the combined power aircraft climbing trajectory optimization method

Abstract

The application discloses a combined power aircraft climbing trajectory optimization method based on an improved particle swarm algorithm, and comprises the following steps: S1, establishing a motion mathematical model of a combined power aircraft climbing section; S2, for the problem of thrust trap existing in a mode switching section, an optimization objective function is constructed, and the optimization objective function comprises a basic cost item and a ballistic inclination angle deviation penalty item; S3, a cubic spline interpolation method is adopted to parameterize an angle of attack-Mach number profile of the aircraft; S4, an improved particle swarm algorithm containing a multiple population cooperative updating mechanism, an adaptive inertia weight strategy and an elite reservation strategy is used to optimize and solve the to-be-optimized variables; and S5, according to the optimal angle of attack sequence obtained by solving, an optimal climbing trajectory overcoming the thrust trap is generated, and the aircraft flight is controlled. The application effectively solves the problems of narrow feasible solution space, large search space and easy numerical divergence caused by considering the thrust trap, and significantly improves the feasibility and safety of mode switching of the aircraft under the weak thrust working condition.

Description

Technical Field

[0001] This invention relates to the field of aerospace vehicle trajectory optimization technology, and more specifically, to a method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm. Background Technology

[0002] Combined-cycle propulsion aircraft (BCCs) are highly susceptible to a "thrust trap" phenomenon during mode switching, where the total thrust is less than the flight drag due to the thrust decay of turbine engines and the difficulty in starting ramjet engines. Current solutions primarily focus on improvements at the engine hardware level, such as using inlet pre-cooling technology or variable geometry inlets, or adding auxiliary power units. However, these methods significantly increase system complexity and weight, making design more difficult. Existing trajectory optimization studies mostly treat mode switching as an instantaneous process, neglecting the impact of the thrust trap, or lacking proactive strategies to address insufficient thrust conditions. Therefore, a trajectory optimization method that overcomes the thrust trap through flight strategies (such as dive acceleration) is urgently needed. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies by providing a method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm.

[0004] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0005] The method for optimizing the climb trajectory of a combined-engine aircraft based on an improved particle swarm optimization algorithm includes the following steps:

[0006] S1: Establish a kinematic mathematical model of the climb phase of the combined-powered aircraft, and divide the climb process into the turbine phase, the mode switching phase, and the ramjet phase;

[0007] S2: To address the thrust trap problem in the mode switching phase, an optimization objective function is constructed. This objective function includes a basic cost term and a trajectory tilt angle deviation penalty term. The trajectory tilt angle deviation penalty term is used to guide the aircraft into a dive when it cannot maintain acceleration; its trigger condition is the real-time monitored velocity differential component. <0;

[0008] S3: The angle-of-attack-Mach number profile of the aircraft is parameterized by cubic spline interpolation, and the angle of attack at several control nodes is selected as the variable to be optimized.

[0009] S4: The improved particle swarm optimization algorithm is used to find the optimal solution for the variable to be optimized. The improved particle swarm optimization algorithm includes multiple swarm collaborative update mechanisms, adaptive inertial weight strategy and elite retention strategy.

[0010] S5: Based on the optimal angle of attack sequence obtained from the solution, generate the optimal climb trajectory to overcome the thrust trap and control the flight of the aircraft.

[0011] To optimize the above technical solution, the specific measures also include:

[0012] In step S1, the motion mathematical model includes the following state equations:

[0013]

[0014] in, For flight speed, For the rate of change of velocity, For flight altitude, For a high rate of change, For the trajectory inclination angle, The rate of change of the trajectory inclination. For the angle of attack, For the mass of the aircraft, For the rate of change of the aircraft's mass, For thrust, As resistance, For lift, It is the acceleration due to gravity. For the purpose of comparison,

[0015] Lift and resistance The calculation formula is:

[0016]

[0017] in, Atmospheric density, For reference area, and These are the lift coefficient and drag coefficient, respectively, and are Mach numbers. and attack angle The function.

[0018] The expression for the objective function J in step S2 is:

[0019]

[0020] in, , This is the height at the end of the turbine section. It is the expected height at the end of the turbine stage. , For terminal height, It is the expected terminal height. As the triggering factor for the ballistic tilt guidance mechanism, when the velocity infinitesimal component... When all values ​​are greater than 0, When a velocity differential appears When <0 is less than 0, , These correspond to the weighting coefficients of the cost term. This is the cost term for the deviation of the ballistic inclination angle.

[0021] Ballistic inclination deviation cost The calculation formula is:

[0022]

[0023] in, The number of sampling points. For the first The actual trajectory inclination angle at each sampling point For the first The expected trajectory inclination angle at each sampling point, the expected trajectory inclination angle Designed in the form of a sine function, its expression is:

[0024]

[0025] in, The maximum dive angle is set, with a value ranging from -10° to -2°. The current flight Mach number, , It is divided into the starting Mach number and the ending Mach number of the mode switching segment.

[0026] In step S2, the thrust trap problem is simulated by constructing a thrust model, and the thrust model measures the thrust during the mode switching phase. The calculation formula is:

[0027]

[0028] in, For the final thrust of the turbine stage, This is the initial thrust of the stamping section. The coefficient characterizing the degree of thrust trapping is adjusted by... The value is set such that the available thrust during the mode switching phase is less than or close to the flight drag to simulate the thrust trap problem.

[0029] The specific method for step S3 is as follows:

[0030] Select Mach number nodes Each node corresponds to an angle of attack value to be optimized. For any Mach number Angle of attack Determined by a cubic polynomial,

[0031]

[0032] in, These are the interpolation coefficients.

[0033] Step S4, which uses the improved particle swarm optimization algorithm to find the optimal solution for the variable to be optimized, specifically includes the following steps:

[0034] 1) Encode the sequence of the angle-of-attack control nodes of the aircraft in all stages into particle position vectors, initialize the particle velocity, individual optimal position, subgroup optimal position, global optimal position and elite particle pool, and divide the initial population into multiple independent subgroups;

[0035] 2) Dynamically update the inertia weight based on the current iteration number and the maximum iteration number, so that the inertia weight decreases from the initial weight to the final weight, in order to achieve a balance between global search and local search;

[0036] The inertial weights satisfy:

[0037]

[0038] Where w(k) is the inertia weight in the k-th iteration, w_max and w_min are the initial and final inertia weights, respectively, k is the current iteration number, and k_max is the maximum iteration number.

[0039] 3) In the corresponding optimization dimension subspace, multiple populations combine the individual optimal position, the subgroup optimal position and the global optimal position to iteratively and collaboratively update the velocity and position of particles, and after a preset iteration period, exchange optimal solution information between subgroups to update the subgroup optimal position and the global optimal position.

[0040] The particle velocity and position satisfy the following conditions respectively:

[0041]

[0042]

[0043] in, and Let be the current position and velocity of the i-th particle in the d-th dimension at the k-th iteration. Let be the optimal position for the i-th particle. This represents the optimal position for the corresponding subgroup. The component of the globally optimal position in the d-th dimension. As a learning factor, for Random numbers within the interval.

[0044] 4) Perform boundary constraint processing on the updated particles, and substitute the angle of attack control nodes corresponding to the particle positions into cubic spline interpolation to construct a continuous angle of attack-Mach number profile.

[0045] 5) Substitute the continuous angle of attack-Mach number profile into the combined-power aircraft motion mathematical model established in step S1, and solve the flight state variables of the turbine section, mode switching section and ramjet section respectively.

[0046] 6) Substitute the obtained flight state variables into the optimization objective function in step S2 to calculate the fitness value, and update and retain the elite particle pool after each iteration. Inject the current global best solution individual into the next round of population by replacing the particle with the worst fitness.

[0047] 7) Repeat steps 3) to 6) until the maximum number of iterations is reached or the termination condition is met. Output the angle of attack at each Mach number control node that minimizes the objective function, and determine the optimal angle of attack-Mach number profile accordingly.

[0048] The multi-group collaborative update mechanism specifically includes the following steps:

[0049] (i) Divide the initial population into at least two independent subgroups, and each subgroup conducts independent search in a different optimization dimension subspace;

[0050] (ii) Each subgroup updates the particle state based on the optimal position of its own subgroup, the optimal position of the subgroup, and the global optimal position;

[0051] (iii) When the preset collaborative update cycle is reached, the current optimal solution of each subgroup and the global optimal solution are exchanged between the subgroups;

[0052] (iv) Update the optimal position of each subgroup and the global optimal position based on the information exchange results, and continue subsequent iterative optimization.

[0053] The present invention has the following beneficial effects:

[0054] 1. This invention introduces a trajectory inclination deviation cost term into the optimization objective function and establishes a triggering mechanism based on real-time monitoring of velocity differential components. This enables the activation of a gravity-assisted acceleration strategy when the aircraft enters a thrust-deficient state. This strategy guides the aircraft to perform a "dive-first, pull-up" maneuver, converting gravitational potential energy into kinetic energy to compensate for the thrust deficit during mode switching, thereby improving the feasibility of the aircraft completing mode switching under weak thrust conditions.

[0055] 2. This invention constructs a comprehensive objective function that includes a turbine end altitude deviation term, a terminal altitude deviation term, and a trajectory tilt angle deviation cost term. This transforms the thrust trap avoidance and dive acceleration flight strategy into a quantifiable optimization index, which helps to reduce the search blind zone and lower the risk of numerical divergence in the trajectory solution process.

[0056] 3. The improved particle swarm optimization algorithm proposed in this invention employs a multi-population collaborative update mechanism, an adaptive inertia weight strategy, and an elite retention strategy. By dividing the original population into multiple independent subpopulations and periodically exchanging information, population diversity and global search capability are enhanced; by dynamically adjusting the inertia weight with the number of iterations, a balance between global and local search can be achieved; and by updating and retaining the elite particle pool, the stability and convergence reliability of the algorithm are improved. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the improved particle swarm optimization algorithm and trajectory optimization process in this invention.

[0058] Figure 2 This is a schematic diagram of the thrust-drag characteristic curve of the combined-powered aircraft in an embodiment of the present invention.

[0059] Figure 3 This is a thrust-resistance characteristic curve of the mode switching segment under different thrust depression degrees in the embodiments of the present invention.

[0060] Figure 4 These are flight characteristic curves under different dive degrees in embodiments of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this application clearer, the application is described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0062] Obviously, the accompanying drawings described below are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar scenarios based on these drawings without any inventive effort. Furthermore, it is understood that although the efforts made in this development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, any changes to design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as insufficient disclosure of the content of this application.

[0063] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment that is mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0064] like Figure 1 As shown: The trajectory optimization method for this combined-powered aircraft includes the following steps:

[0065] S1: Establish a kinematic mathematical model of the climb phase of the combined-powered aircraft.

[0066] The climb process of the combined-powered aircraft is divided into three stages: the turbine stage, the mode switching stage, and the ramjet stage. Assuming the aircraft moves in a vertical plane and neglecting the effects of Earth's rotation and curvature, the motion equations of the aircraft's point mass are established as follows:

[0067]

[0068] in, For flight speed, For the rate of change of velocity, For flight altitude, For a high rate of change, For the trajectory inclination angle, The rate of change of the trajectory inclination. For the angle of attack, For the mass of the aircraft, For the rate of change of the aircraft's mass, For thrust, As resistance, For lift, It is the acceleration due to gravity. For the purpose of comparison,

[0069] Lift and resistance The calculation formula is:

[0070]

[0071] in, Atmospheric density, For reference area, and These are the lift coefficient and drag coefficient, respectively, and are Mach numbers. and attack angle The function.

[0072] S2: To address the thrust trap problem in the mode switching segment, an optimization objective function is constructed.

[0073] According to the thrust-drag characteristic curve of hypersonic vehicles, the main reason for the thrust trap problem during mode switching is the decrease in thrust. During mode transition, the turbine engine operates at a high Mach number, the inlet becomes unstable, the temperature and pressure are too high, and the engine efficiency is low. Furthermore, the turbine engine is gradually shutting down, further reducing thrust. Simultaneously, if the incoming Mach number does not reach the ramjet engine's starting Mach number, the ramjet engine has difficulty starting and cannot provide sufficient thrust. Although the formation mechanism of the thrust trap problem is complex, its impact on mode switching is only manifested as insufficient net thrust from the combined engines, preventing the vehicle from accelerating to the ramjet engine's operating Mach number, thus causing mode switching failure. Therefore, by designing a thrust model for the mode switching segment, a thrust dip is created during the mode switching segment, and the degree of thrust dip is controlled by a coefficient.

[0074]

[0075] in, For the final thrust of the turbine stage, This is the initial thrust of the stamping section. The coefficient characterizing the degree of thrust trapping is adjusted by... The value is set such that the available thrust during the mode switching phase is less than or close to the flight drag to simulate the thrust trap problem.

[0076] To overcome thrust trapping, a trajectory tilt deviation penalty term was designed. First, the differential velocity components of the aircraft were calculated in real time. .

[0077] 1. When When the thrust is sufficient to maintain acceleration, the guiding mechanism is not triggered in the objective function.

[0078] 2. When When this occurs, it indicates that the target has fallen into a thrust trap. At this point, the guidance mechanism is activated, and the overall objective function is adjusted accordingly. Add a ballistic tilt angle deviation cost term to the middle , The calculation formula is as follows:

[0079]

[0080] in, For the first The actual trajectory inclination angle at each feature point Let this be the desired trajectory inclination angle. The desired trajectory inclination angle is designed as a sine function to guide the aircraft to first dive and then pull up.

[0081]

[0082] in This is the maximum dive angle.

[0083] The expression for the objective function J is:

[0084]

[0085] in, , This is the height at the end of the turbine section. , For terminal height, This is the trigger factor for the ballistic tilt guidance mechanism; when all velocity differential components are greater than 0, When the velocity differential is less than 0, , These correspond to the weighting coefficients of the cost terms.

[0086] S3: Optimize variable parameterization

[0087] Angle-of-attack Mach number profiles are used as control variables. To transform the infinite-dimensional optimal control problem into a finite-dimensional parameter optimization problem, cubic spline interpolation is employed. Mach number nodes Each node corresponds to an angle of attack value to be optimized. For any Mach number Angle of attack It is determined by a cubic polynomial.

[0088]

[0089] in, These are the interpolation coefficients.

[0090] S4: Solve using an improved particle swarm optimization algorithm, such as Figure 1 As shown, the improved particle swarm optimization algorithm and trajectory optimization process includes the following:

[0091] First, the angle-of-attack control node sequence obtained in step S3 is encoded into a particle position vector. The particle velocity, individual optimal position, subgroup optimal position, global optimal position, and elite particle pool are initialized, and the initial population is divided into multiple independent subgroups.

[0092] Secondly, the inertia weight is dynamically adjusted based on the current iteration number and the maximum iteration number, so that the inertia weight decreases from the initial weight to the final weight. In the corresponding optimization dimension subspace, multiple populations combine the individual optimal position, the subgroup optimal position and the global optimal position to iteratively and collaboratively update the velocity and position of particles. After a preset iteration period, the optimal solution information between subgroups is exchanged to update the subgroup optimal position and the global optimal position.

[0093] Multi-group iterative collaborative updates include the following steps:

[0094] (i) Divide the initial population into at least two independent subgroups, and each subgroup conducts independent search in a different optimization dimension subspace;

[0095] (ii) Each subgroup updates the particle state based on the optimal position of its own subgroup, the optimal position of the subgroup, and the global optimal position;

[0096] (iii) When the preset collaborative update cycle is reached, the current optimal solution of each subgroup and the global optimal solution are exchanged between the subgroups;

[0097] (iv) Update the optimal position of each subgroup and the global optimal position based on the information exchange results, and continue subsequent iterative optimization.

[0098] The formula for updating inertia weights is:

[0099]

[0100] The particle velocity and position update formulas are as follows:

[0101]

[0102]

[0103] Where w(k) is the inertia weight of the kth iteration, w_max and w_min are the initial inertia weight and the final inertia weight, respectively, k is the current iteration number, and k_max is the maximum iteration number; and Let be the current position and velocity of the i-th particle in the d-th dimension at the k-th iteration. Let be the optimal position for the i-th particle. This represents the optimal position for the corresponding subgroup. The component of the globally optimal position in the d-th dimension. As a learning factor, for Random numbers within the interval.

[0104] Then, boundary constraint processing is performed on the updated particles, and the angle of attack control node corresponding to the particle position is substituted into cubic spline interpolation to construct a continuous angle of attack-Mach number profile. The angle of attack-Mach number profile is then substituted into the motion mathematical model established in step S1 to solve the flight state variables of the turbine section, mode switching section and ramjet section, and the fitness value is calculated according to the optimization objective function in step S2.

[0105] Finally, after each iteration, the elite particle pool is updated and retained, and in the next population update, the current global best solution individual is injected into the population by replacing the particle with the worst fitness; the above iterative process is repeated until the maximum number of iterations is reached or the preset termination condition is met.

[0106] S5: Based on the optimal angle of attack sequence obtained from the solution, generate the optimal climb trajectory to overcome the thrust trap and control the flight of the aircraft.

[0107] In an example of the present invention, different thrust trapping degree coefficients are selected. , and obtained Figure 3 The thrust characteristic curves of the mode switching segment under different thrust trapping degrees are shown. It can be seen that the thrust model designed in this invention can simulate the thrust trapping problem caused by thrust trapping, and the thrust trapping degree coefficient... It can also effectively control the degree of thrust trapping.

[0108] like Figure 4 As shown, it can be observed that the ballistic tilt guidance mechanism used to implement the gravity-assisted acceleration strategy is triggered when the aircraft cannot accelerate, resulting in the optimized trajectory exhibiting obvious dive-acceleration characteristics under insufficient net thrust.

[0109] In summary, this invention can solve the thrust trap problem of combined-powered aircraft by optimizing flight strategies without changing the engine hardware design.

[0110] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm, characterized in that, Includes the following steps: S1: Establish a kinematic mathematical model of the climb phase of the combined-powered aircraft, and divide the climb process into the turbine phase, the mode switching phase, and the ramjet phase; S2: To address the thrust trap problem during mode switching, an optimization objective function is constructed. This objective function includes a basic cost term and a trajectory tilt angle deviation penalty term. The trajectory tilt angle deviation penalty term is used to guide the aircraft into a dive when it cannot maintain acceleration; its triggering condition is the real-time monitored velocity differential component. <0; S3: The angle-of-attack-Mach number profile of the aircraft is parameterized by cubic spline interpolation, and the angle of attack at several control nodes is selected as the variable to be optimized. S4: The improved particle swarm optimization algorithm is used to find the optimal solution for the variable to be optimized. The improved particle swarm optimization algorithm includes a multi-swarm collaborative update mechanism, an adaptive inertial weight strategy, and an elite retention strategy. S5: Based on the optimal angle of attack sequence obtained from the solution, generate the optimal climb trajectory to overcome the thrust trap and control the flight of the aircraft.

2. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, In step S1, the motion mathematical model includes the following state equations: ； in, For flight speed, For the rate of change of velocity, For flight altitude, For a high rate of change, For the trajectory inclination angle, The rate of change of the trajectory inclination. For the angle of attack, For the mass of the aircraft, For the rate of change of the aircraft's mass, For thrust, As resistance, For lift, It is the acceleration due to gravity. For the purpose of comparison, Lift and resistance The calculation formula is: ； in, Atmospheric density, For reference area, and These are the lift coefficient and drag coefficient, respectively, and are Mach numbers. and attack angle The function.

3. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, The expression for the optimization objective function J in step S2 is: ； in, , This is the height at the end of the turbine section. It is the expected height at the end of the turbine section. , For terminal height, It is the expected terminal height. As the triggering factor for the ballistic tilt guidance mechanism, when the velocity infinitesimal component... When all values ​​are greater than 0, When a velocity differential appears When <0 is less than 0, , These correspond to the weighting coefficients of the cost term. This is the cost term for the deviation of the ballistic inclination angle.

4. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 3, characterized in that, The cost of the ballistic tilt angle deviation The calculation formula is: ； in, The number of sampling points. For the first The actual trajectory inclination angle at each sampling point For the first The expected trajectory inclination angle at each sampling point, the expected trajectory inclination angle Designed in the form of a sine function, its expression is: ； in, The maximum dive angle is set, with a value ranging from -10° to -2°. The current flight Mach number, , It is divided into the starting Mach number and the ending Mach number of the mode switching segment.

5. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 4, characterized in that, In step S2, the thrust trap problem is simulated by constructing a thrust model, wherein the thrust model measures the thrust during the mode switching phase. The calculation formula is: ； in, For the final thrust of the turbine stage, This is the initial thrust of the stamping section. The coefficient characterizing the degree of thrust trapping is adjusted by... The value is set such that the available thrust during the mode switching phase is less than or close to the flight drag to simulate the thrust trap problem.

6. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, The specific method for step S3 is as follows: Select Mach number nodes Each node corresponds to an angle of attack value to be optimized. For any Mach number Angle of attack Determined by a cubic polynomial, ； in, These are the interpolation coefficients.

7. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 1, characterized in that, Step S4, which uses the improved particle swarm optimization algorithm to find the optimal solution for the variable to be optimized, specifically includes the following steps: 1) Encode the sequence of the angle-of-attack control nodes of the aircraft in all stages into particle position vectors, initialize the particle velocity, individual optimal position, subgroup optimal position, global optimal position and elite particle pool, and divide the initial population into multiple independent subgroups; 2) Dynamically update the inertia weight based on the current iteration number and the maximum iteration number, so that the inertia weight decreases from the initial weight to the final weight, in order to adjust the global search capability and local search capability of the particle; The inertial weights satisfy: ； Where w(k) is the inertia weight in the k-th iteration, w_max and w_min are the initial and final inertia weights, respectively, k is the current iteration number, and k_max is the maximum iteration number. 3) In the corresponding optimization dimension subspace, multiple populations combine the individual optimal position, the subgroup optimal position and the global optimal position to iteratively and collaboratively update the velocity and position of particles, and after a preset iteration period, exchange optimal solution information between subgroups to update the subgroup optimal position and the global optimal position. The particle velocity and position satisfy the following conditions respectively: ； ； in, and Let be the current position and velocity of the i-th particle in the d-th dimension at the k-th iteration. Let be the optimal position for the i-th particle. This represents the optimal position for the corresponding subgroup. The component of the globally optimal position in the d-th dimension. As a learning factor, for Random numbers within the interval 4) Perform boundary constraint processing on the updated particles, and substitute the angle of attack control node corresponding to the particle position into cubic spline interpolation to construct a continuous angle of attack-Mach number profile. Then substitute it into the combined power aircraft motion mathematical model established in step S1 to solve the flight state variables of the turbine section, mode switching section and ramjet section. 5) Substitute the obtained flight state variables into the optimization objective function described in step S2 to calculate the fitness value, and update and retain the elite particle pool after each iteration. Inject the current global optimal solution individual into the next round of population by replacing the particle with the worst fitness. 6) Repeat steps 3) to 5) until the maximum number of iterations is reached or the preset termination condition is met. Output the angle of attack at each Mach number control node that minimizes the objective function, and determine the optimal angle of attack-Mach number profile accordingly.

8. The method for optimizing the climb trajectory of a combined-powered aircraft based on an improved particle swarm optimization algorithm according to claim 7, characterized in that, The multi-group collaborative update mechanism in step S4 specifically includes the following steps: (i) Divide the initial population into at least two independent subgroups, and each subgroup conducts independent search in a different optimization dimension subspace; (ii) Each subgroup updates the particle state based on the optimal position of its own subgroup, the optimal position of the subgroup, and the global optimal position; (iii) When the preset collaborative update cycle is reached, the current optimal solution of each subgroup and the global optimal solution are exchanged between the subgroups; (iv) Update the optimal position of each subgroup and the global optimal position based on the information exchange results, and continue subsequent iterative optimization.

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