Aerospace vehicle TAEM segment trajectory reconstruction method under actuator fault

Abstract

The invention provides an aerospace vehicle TAEM (end energy management) section trajectory reconstruction method under an actuator fault. In order to solve the problems that in the TAEM section unpowered flight process, due to the fact that an actuator is stuck, a flight path seriously deviates from a nominal path, and guidance requirements are difficult to meet, the torque balancing capacity of the aircraft after the fault is evaluated, the balancing attack angle range of the aircraft is determined, and a feasible flight path is designed in the range so as to ensure that the aircraft can maintain a controllable state. Then, a trajectory optimization problem is converted into an optimal control problem by adopting a convex optimization and pseudo-spectral discrete method, and finally, the optimal control problem is solved by utilizing a primal-dual interior point method to obtain a reconstructed trajectory meeting various constraint conditions. According to the method provided by the invention, on the basis of fully considering the six-degree-of-freedom control capability of the aircraft, a trajectory reconstruction strategy is optimized, the safety and landing capability of the aerospace aircraft in a fault state are improved, and the method has relatively high adaptability and universality.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance, and in particular to a method for optimizing the TAEM segment trajectory of an aerospace aircraft. Background Art

[0002] During the Terminal Area Energy Management (TAEM) phase, the aircraft must achieve transonic flight. This process involves significant changes in dynamic pressure, rapidly changing aerodynamic characteristics, and complex and variable atmospheric disturbances, significantly impacting the aircraft's ability to navigate uncertainties. Furthermore, during this phase, the aircraft's reentry fuel is essentially exhausted, and the aircraft relies primarily on aerodynamic control surfaces as actuators for unpowered trajectory and attitude control. Therefore, their stable and efficient operation is crucial to the safety of the aircraft's return and landing. A malfunction in the control surfaces, such as a jam, can lead to complete failure. Because the aircraft is at a relatively low altitude, the allowable range of adjustment is limited, so a malfunction would severely threaten safe and stable flight and could even result in the destruction of the aircraft and the loss of life.

[0003] To cope with actuator failures that may occur during the TAEM phase and successfully complete the mission, aerospace vehicles must rapidly adjust their guidance and control strategies based on the severity of the failure. For example, they must quickly plan an alternative flight trajectory based on the dynamic characteristics of the failure. This designed trajectory must exhibit excellent tracking performance, and the guidance law must be adaptively adjusted accordingly. Therefore, to achieve high reliability and safety, aerospace vehicle guidance systems must possess the ability to replan trajectories in the presence of failures and uncertainties. Summary of the Invention

[0004] In order to address the problem of actuator jamming failure in the TAEM segment of an aerospace vehicle, improve the successful landing rate of the vehicle, ensure flight safety and reduce costs, the present invention proposes a method for reconstructing the trajectory of the terminal energy management segment of an aerospace vehicle under actuator failure. When a failure occurs during the return process of the vehicle and the flight trajectory seriously deviates from the nominal trajectory, a flyable trajectory can be quickly generated, thereby ensuring that the vehicle guidance system can operate normally, guiding the vehicle to safely reach the landing window, and meeting the landing flight conditions.

[0005] The technical solution is as follows:

[0006] Step 1: Establish a three-degree-of-freedom mathematical model of the aerospace vehicle based on the characteristics of the terminal energy management phase flight mission, taking into account the dynamic pressure, heat flow, control, and initial and terminal constraints during the flight.

[0007] Step 2: Assuming that the fault information has been obtained, evaluate the aircraft's remaining control capability based on the fault information. Determine whether the aircraft can achieve torque trim by considering whether the three-axis torque generated by the control surfaces during flight can be balanced with the three-axis torque generated by the fuselage. Design a mixed-integer linear programming algorithm to calculate the range of trimmable angles of attack for the aircraft in the terminal energy management phase.

[0008] Step 3: Design the optimization index. The performance index can be designed as the maximum lateral distance. Convert the aircraft trajectory optimization problem into the optimal control problem P0.

[0009] Step 4: In order to solve the problem using convex optimization methods, the inequality constraints and equality constraints in step 1 need to be convexly optimized. Here, the sequential linearization approximation method is used to approximate the optimization problem P0 to transform it into problem P1.

[0010] Step 5: To ensure the accuracy of the constraints after linear approximation and the convergence of the algorithm, the trust region constraint |X is introduced. k -X k-1 |≤ε, ε is the trust region radius.

[0011] Step 6: Use the Radau pseudo-spectral discretization method to transform the continuous optimal control problem P1 into a discrete optimal control problem P2 that can be numerically solved.

[0012] Step 7: Use the efficient convex optimization algorithm - the primal-dual interior point method to solve the problem and determine whether the angle of attack meets the trimmable angle of attack range. Verify whether the reconstructed angle of attack is within the trimmable range. If not, adjust the angle of attack to α. max And solve again. Furthermore, the three-degree-of-freedom normalized mathematical model of the aircraft described in step 1 is Where x, y, h, V, χ, and γ are the lateral distance, side distance, height, speed, heading angle, and track tilt angle, respectively; σ is the tilt angle; L = qSC L is the lift, D = qSC D is the resistance, where q = 0.5ρV 2 is the dynamic pressure, S is the reference area of the aircraft, ρ is the atmospheric density, C L and C D represents the lift coefficient and drag coefficient. Dynamic pressure constraint: q=0.5ρV 2 ≤q max (2) Heat flow constraints: Q=K Q ρ 0.5 V3.15 ≤Q max (3) In the above formula, K Q is a constant related to the shape and material of the aircraft. The initial and terminal conditions are X(t0)=X0 (4) X(t f )=X f (5) In the above formula, t0, t f are the initial moment and the final moment respectively, X0, X f are the initial state and the final state respectively. Furthermore, the moment balance condition in step 2 is Where, and They represent the roll, pitch and yaw moment coefficients caused by the rudder. The rudder deflection angle satisfies In the formula, δ and Indicates the upper and lower limits of the control surface. Assume δ j,i * is the solution of equation (6). If we can find δ that satisfies equation (6) j,i * , it means that there is enough control force to make the aircraft longitudinally balanced. If formula (6) is not satisfied, it means that it cannot be balanced, and the attack angle range α that meets the balance condition is obtained. * . Furthermore, in step 2, the algorithm flow for iteratively solving the torque balancing condition is as follows: first, a discrete grid of attack angle α and Mach number M is defined based on the flight envelope, and the feasible range of the rudder deflection angle δ is initialized; then, for each grid point (α i ,M j ), calculate the inherent pitch moment coefficient of the fuselage A mixed integer linear programming model is constructed, with the rudder angle δ j,i As the decision variable, the moment balance equation As the core constraint, solve the problem of satisfying the rudder deflection constraint The optimal solution; if there is a feasible solution, record the current angle of attack α i The grid is updated and the balancing state is reached. During the iteration, the convergence is judged by evaluating the balancing deviation d. If d≤10 -3 , then the angle of attack is determined to be trimmable, otherwise it is excluded as an untrimable area; finally, the global trimmable angle of attack range is output. Furthermore, in step 3, the maximum flight lateral distance x fTo optimize the indicators, the optimal control problem P0 is constructed based on the three-degree-of-freedom mathematical model of the aircraft. Its constraints include: the three-degree-of-freedom mathematical model equation of the aircraft, dynamic pressure and heat flow constraints, and terminal state conditions, which can be expressed as: Furthermore, in step 4, if the control quantity σ is directly convexified, high-frequency chattering will occur. A new auxiliary control variable is introduced to decouple the control quantity from the state quantity. The new control quantity is Then the dynamic equation (1) can be rewritten as In the formula, X=[x,y,h,V,χ,γ,σ] T , the state matrices f(X) and B are B=[0 0 0 0 0 0 1] T (12) Then, the dynamic constraint function, dynamic pressure constraint and thermal flow constraint are linearized by sequential linearization approximation. The state variable X = [x, y, h, V, χ, γ, σ] T , at the reference point X k-1 There are: Where c is the right function of equations (2) and (3), h max =[q max ,Q max ] T , transform the aircraft optimal control problem P0 into a convex optimization problem P1: Furthermore, in step 5, after linearizing and approximating the dynamic constraint function, in order to ensure the accuracy of the approximation and the convergence of the algorithm, the trust region constraint of the second-order cone form of the relevant variables |X is introduced k -X k-1 |≤ε, that is: Where x is the lateral distance, y is the lateral distance, h is the height, V is the velocity, χ is the heading angle, γ is the trajectory inclination angle, σ is the roll angle, and the subscripts k and k-1 represent the kth and k-1th iterations, respectively. Furthermore, in step 6, the Radau pseudo-spectral method is used to discretize the optimal control problem P1. For the dynamic model, the Radau pseudo-spectral discretization constraint model is: Where D is the constant differential matrix, X = [x, y, h, V, χ, γ, σ] T are state variables, t0, t f are the starting time and the terminal time, respectively, f is the right function of the dynamic equation (10), N is the number of discrete points, and τ∈(-1,1] is a new independent variable replacing the flight time t; After discretization, the convex optimization problem P1 is transformed into a discrete sequence convex programming problem P2: Furthermore, in step 6, the conversion relationship between τ and t is Furthermore, in step 7, the solution algorithm process is as follows: first, set the number of pseudo-spectral discrete points N, construct the differential matrix D to discretize the system dynamics equation, and thus transform the trajectory optimization problem in the continuous time domain into a finite-dimensional numerical optimization problem; use the nominal trajectory as the initial reference trajectory X0, and set the trust region radius to construct the initial optimization problem; then, use the primal-dual interior point method to iteratively solve the optimization problem P2 containing system dynamics constraints, path constraints and trust region restrictions, and obtain the kth iterative solution X opt k In each iteration, the attack angle α is detected in real time to see if it exceeds the trim allowable range. If so, it is forced to saturate to the boundary α = α max , and re-solve based on the updated constraints; otherwise, update the aerodynamic parameters and enter the next iteration; in addition, the trust region radius is dynamically adjusted during the iteration process to balance the convergence speed and the stability of the solution; through cyclic iteration until the angle of attack feasibility, constraints and convergence criteria are met, finally, the optimal trajectory that meets the global balancing requirements and its corresponding control sequence are output. Beneficial effects 1. This invention discloses a terminal energy management segment trajectory reconstruction method that considers the residual control capability of an aircraft after an actuator failure. The aircraft's torque balancing capability is considered during the trajectory design phase, thereby improving the flight trajectory tracking performance. 2. The terminal energy management segment trajectory reconstruction method disclosed in this invention utilizes convex optimization theory combined with pseudo-spectral discretization to transform the aircraft trajectory optimization problem into an optimal control problem. It also employs the primal-dual interior point method to solve the problem, improving the algorithm's computational efficiency and ensuring timely updates of flight parameters during flight. 3. The terminal energy management trajectory reconstruction method disclosed in this invention effectively ensures that the aircraft meets the automatic landing window conditions at the end of flight, effectively improving the successful landing rate of the aircraft in the event of a fault, ensuring flight safety, and reducing costs. This method is also universal and can be easily implemented in the guidance systems of other aircraft. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 The range of available angles of attack of an aircraft after a stuck fault occurs according to one embodiment of the present invention; Figure 2 This is a comparison of the lateral distance x change curves under normal and fault conditions of an embodiment of the present invention; Figure 3 1 is a comparison of the lateral distance y change curves under normal and fault conditions of an embodiment of the present invention; Figure 4 This is a comparison of the flight height h change curves under normal and fault conditions of an embodiment of the present invention; Figure 5 This is a comparison of the flight speed V change curves under normal and fault conditions of an embodiment of the present invention; Figure 6 1 is a comparison of the course angle χ change curves under normal and fault conditions according to an embodiment of the present invention; Figure 7 1 is a comparison of the track angle γ change curves under normal and fault conditions of an embodiment of the present invention; Figure 8 1 is a comparison of the change curves of the roll angle σ under normal and fault conditions of an embodiment of the present invention; Figure 9 1 is a comparison of the change curves of the angle of attack α under normal and fault conditions of an embodiment of the present invention; Figure 10 An embodiment of the present invention is a comparison of Mach number Ma change curves under normal and fault conditions; Figure 11 is a flow chart of an embodiment of the present invention. DETAILED DESCRIPTION The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application. like Figure 11As shown, the present invention discloses a method for reconstructing the trajectory of the terminal energy management segment of an aerospace vehicle under the condition of an actuator failure. In order to solve the problem that the flight trajectory seriously deviates from the nominal trajectory and the guidance requirements are difficult to meet due to the actuator jam failure during the unpowered flight of the TAEM segment, the torque balancing capability of the aircraft after the failure is first evaluated, the range of its balancing angle of attack is determined, and a feasible flight trajectory is designed within this range to ensure that the aircraft maintains a controllable state. Then, the trajectory optimization problem is transformed into an optimal control problem by using convex optimization and pseudo-spectral discretization methods. Finally, the original dual interior point method is used to solve the optimal control problem to obtain a reconstructed trajectory that meets various constraints. The method proposed in the present invention optimizes the trajectory reconstruction strategy on the basis of fully considering the six-degree-of-freedom control capability of the aircraft, improves the safety and landing capability of the aerospace vehicle under fault conditions, and has strong adaptability and versatility. Specifically, the following steps are included: Step 1: Establish a three-degree-of-freedom mathematical model of the aerospace vehicle based on the characteristics of the terminal energy management phase flight mission, taking into account the dynamic pressure, heat flow, control and terminal constraints during the flight. The normalized mathematical model of the vehicle is Where x, y, h, V, χ, and γ are the lateral distance, side distance, height, speed, heading angle, and track tilt angle, respectively; σ is the tilt angle; L = qSC L is the lift, D = qSC D is the resistance, where q = 0.5ρV 2 is the dynamic pressure, S is the reference area of the aircraft, ρ is the atmospheric density, C L and C D represents the lift coefficient and drag coefficient. Normalization is the process of processing the mathematical model of the aircraft to convert the actual physical quantities into dimensionless or standardized values. The normalization factors of each variable are as follows: Normalization factor for time: R0 is the average radius of the Earth, g0 is the gravitational acceleration at sea level; Normalization factor of position: R0; Normalization factor for speed: Normalization factor of force: g0. Dynamic pressure constraint: q=0.5ρV 2 ≤q max (2) Heat flow constraints: Q=K Q ρ 0.5 V 3.15 ≤Q max (3) In the above formula, KQ is a constant related to the shape and material of the aircraft, q max is the maximum dynamic pressure, Q max is the maximum heat flux density. The initial and terminal conditions are x(t0)=x0 (4) x(t f )=x f (5) In the above formula, t0, t f are the initial moment and the final moment respectively, X0, X f are the initial state and the final state respectively. The initial and terminal conditions are set as shown in Table 1. Table 1 Initial condition and terminal condition settings Where x is the lateral distance, y is the lateral distance, h is the height, V is the velocity, χ is the heading angle, and γ is the track inclination angle. Step 2: Assuming that the fault information has been obtained, evaluate the aircraft's remaining control capability based on the fault information. Determine whether the aircraft can achieve torque trim by considering whether the three-axis torque generated by the control surfaces during flight can be balanced with the three-axis torque generated by the fuselage. Design a mixed-integer linear programming algorithm to calculate the range of trimmable angles of attack for the aircraft in the terminal energy management segment after the fault occurs. Specifically, the core logic of trimming is to achieve torque balance at a specific angle of attack α and Mach number M by adjusting the deflection angle of the control surfaces, thereby maintaining a stable and controllable flight state. In this embodiment, the range of trimmable angles of attack is determined by torque balance, that is, whether the aircraft's control surfaces can generate sufficient torque to offset the imbalance of aerodynamic forces, especially the torque on the pitch, roll, and yaw axes. The trimming logic is implemented using a mixed integer linear programming algorithm: Step 2.1, define the variable grid: divide the angle of attack interval according to the flight envelope, divide the discrete values of the Mach number according to the flight speed in the TAEM segment, and define the deflection range of each control surface. Step 2.2, for each attack angle α i and Mach number M j , solve for the rudder surface deflection angle δ j,i , to satisfy the equilibrium equation: Where, and are the roll, pitch and yaw moment coefficients caused by the control surfaces, is the pitching moment generated by the fuselage. If a combination of rudder deflection angles that satisfies the equilibrium equation can be found, it means that there is sufficient control force to make the aircraft longitudinally balanced and there is excess control capability; otherwise, it means that it cannot be balanced, and the angle of attack range α that satisfies the balance condition is obtained. * . In step 2.3, the rudder angle is used as the decision variable, constraints are added to the rudder angle, and iterative calculation is performed with minimizing the trim deviation as the objective function. The constraints are expressed as: In the formula, δ and Indicates the upper and lower limits of the control surface. The iterative calculation process is as follows: first, a discrete grid of attack angle α and Mach number M is defined based on the flight envelope, and the feasible range of the rudder deflection angle δ is initialized; then, for each grid point (α i ,M j ), calculate the pitching moment coefficient generated by the fuselage A mixed integer linear programming model is constructed, with the rudder angle δ j,i As the decision variable, the moment balance equation As the core constraint, solve the problem of satisfying the rudder deflection constraint The optimal solution. If there is a feasible solution, record the current angle of attack α i The system then updates the mesh to a trimmable state. During the iteration process, convergence is determined by evaluating the trim deviation d. If d ≤ 0.001, the angle of attack is considered trimmable; otherwise, it is excluded from the untrimable region. Finally, the global trimmable angle of attack range is output. In this embodiment, the trim deviation is calculated as follows: Figure 1 As shown in the figure, within the Mach number range of 0.3 to 4, the trimmable angle of attack is limited to a certain range for high Mach numbers, with a maximum value of 16°. This angle of attack further decreases as the Mach number decreases. When the Mach number decreases below 1.5, the trimmable angle of attack begins to increase, and when the Mach number decreases below 1, the trimmable angle of attack expands to the full range. The reconstructed flight trajectory should satisfy this angle of attack constraint. Step 3: Design optimization indicators. The performance indicators can be designed as the maximum lateral distance of flight x f , i.e. minJ=-x f ; Based on the three-degree-of-freedom mathematical model of the aircraft, the optimal control problem P0 is constructed. Its constraints include: the three-degree-of-freedom mathematical model equation of the aircraft disclosed in step 1, dynamic pressure and heat flow constraints, and initial and terminal state conditions, thereby converting the aircraft trajectory optimization problem into the optimal control problem P0, Step 4: In order to solve the problem using the convex optimization method, the inequality constraints and equality constraints in step 1 need to be convexly optimized. If the control quantity σ is directly convexified, high-frequency chattering will occur. Introduce a new auxiliary control variable to decouple the control quantity from the state quantity. Let the new control quantity be Then the dynamic equation (1) can be rewritten as In the formula, X=[x,y,h,V,χ,γ,σ] T , the state matrices f(X) and B are B=[0 0 0 0 0 0 1] T (12) Then the sequential linearization approximation method is used to approximate the optimization problem P0 into problem P1. The terminal constraint function and performance index function in the constraints disclosed in step 3 are convex, but the dynamic constraint function, dynamic pressure constraint and thermal flow constraint are non-convex. Therefore, in step 4, the sequential linearization method is used for linear approximation processing. At the reference point X k-1 There are: Where c is the right function of the dynamic pressure constraint in equation (2) and the heat flow constraint in equation (3), h max =[q max ,Q max ] T . Convert the aircraft optimal control problem P0 into a convex optimization problem P1: Step 5: To ensure the accuracy of the constraints after linear approximation and the convergence of the algorithm, the trust region constraint |X is introduced. k -X k-1 |≤ε, where ε is the trust region radius. By limiting the amplitude of the control correction in each iteration, the linearized model is ensured to be sufficiently accurate in the current local area, thereby improving the stability and convergence of the algorithm. Expressed as: The trust region constraint in this example is specifically ε = [10000, 10000, 10000, 50, 20π / 180, 20π / 180, 20π / 180] T . Step 6: Use the Radau pseudo-spectral discretization method to transform the continuous optimal control problem into a discrete optimal control problem that can be solved numerically. Since the convex optimization problem P1 still describes a continuous optimal control problem, in order to obtain the numerical solution of problem P1, it is necessary to discretize the problem first. For the dynamic model, its Radau pseudo-spectral discretization constraint model is: Where D is the constant differential matrix, X = [x, y, h, V, χ, γ, σ] T are state variables, t0, t f are the starting time and the terminal time respectively, f is the right function of the dynamic equation (10), N is the number of discrete points, τ∈(-1,1] is the new independent variable replacing the flight time t, and its conversion relationship with t is: After discretization, the convex optimization problem P1 is transformed into a discrete sequence convex programming problem P2: In this example, the number of pseudo-spectral discrete points N is set to 30, and the nominal trajectory is selected as the initial guess value. In the trajectory discretization strategy, this application adopts the Radau pseudospectral method (LGR collocation), which has the following advantages compared with the Gauss pseudospectral method (LG collocation) that is more commonly used in the prior art: First, the collocation set of the Radau pseudospectral method is asymmetrically distributed in the interval [-1,1), and at the end point τ N+1 = 1, forming N+1 nodes (the Gauss method uses N nodes). This feature expands the dimension of its differential matrix D to N×(N+1), unlike the N×N matrix structure of the Gauss method. Secondly, the [-1, 1) interval configuration better matches the boundary conditions of the terminal energy management segment, which requires "strict initial constraints and fixed terminal states," significantly improving the numerical stability of online trajectory reconstruction. Finally, for smooth optimal control problems, the Radau method not only offers higher approximation accuracy, but also outperforms the Gauss method in terms of covariance variable convergence, providing reliable mathematical support for rapid trajectory generation under fault conditions. Step 7: Use the original dual interior point method to solve P2, obtain the reconstructed trajectory, and verify whether the angle of attack is within the trimmable range. If not, adjust the angle of attack to α max And solve again. The specific solution algorithm process is as follows: First, the number of pseudo-spectral discrete points N is set, and the differential matrix D is constructed to discretize the system dynamics equation, thereby converting the trajectory optimization problem in the continuous time domain into a finite-dimensional numerical optimization problem; the nominal trajectory is used as the initial reference trajectory X0, and the trust region radius is set to construct the initial optimization problem; then, the primal-dual interior point method is used to iteratively solve the optimization problem P2 containing system dynamics constraints, path constraints and trust region restrictions, and the kth iterative solution X0 is obtained. opt k In each iteration, the attack angle α is detected in real time to see if it exceeds the trim allowable range. If so, it is forced to saturate to the boundary α = α max , and re-solve based on the updated constraints; otherwise, update the aerodynamic parameters and enter the next iteration; in addition, the trust region radius is dynamically adjusted during the iteration process to balance the convergence speed and the stability of the solution; through cyclic iteration until the angle of attack feasibility, constraints and convergence criteria are met, finally, the optimal trajectory that meets the global balancing requirements and its corresponding control sequence are output. This application addresses the trajectory reconstruction problem of the terminal energy management section of a faulty aircraft by proposing an innovative method that integrates convex optimization with six-degree-of-freedom control capability assessment. This method uses convex optimization to directly solve the global optimal solution, transforming the trajectory reconstruction problem after an actuator failure into a mathematical programming problem with deterministic convergence. By introducing angle-of-attack trim constraints (as shown in steps 2 and 7), a fault-adaptive trajectory optimization model is established, overcoming the limitations of traditional local optimization, which is prone to suboptimal solutions, while achieving a deep integration of control capability constraints and trajectory generation. In this embodiment, the solution obtained by the original dual interior point method is as follows: Figures 2 to 10 shown. Figure 2 and Figure 3 The lateral distance of the aircraft is shown. The results show that the lateral distance of the aircraft under normal flight conditions is smaller than the lateral distance after the fault. This phenomenon occurs because the average flight speed of the aircraft under fault conditions is higher than the average flight speed under normal conditions. Figure 5 The flight speed change curve shown further verifies this point. In addition, when the initial heading angle is set to 0, the aircraft must maintain the heading angle at 0 in order to obtain the maximum lateral distance under normal circumstances. Figure 6 The nominal trajectory heading angle in is always 0. Therefore, Figure 3 The lateral distance y in is always 0 and remains constant. from Figure 4 and Figure 5The changes in altitude and speed shown indicate that the post-fault trajectory is less smooth than the nominal trajectory. This change is an inevitable consequence of the fault. However, using the trajectory reconstruction method designed in this invention, the aircraft's flight parameters during the terminal energy management phase still meet the landing window requirements, validating the effectiveness of the proposed method. Figure 7 The curve of track inclination changes is shown. As can be seen from the figure, the track inclination changes greatly during the flight, but it always remains within the range allowed by the aircraft. Figure 8 Figure 2 is the roll angle change curve. Under normal conditions, the aircraft does not need to change the heading angle, so the roll angle is 0. However, under fault conditions, the rolling angle is approximately 6.4° due to the continuous change in the heading angle. Figure 9 The angle of attack curve shows that the reconstructed trajectory's angle of attack is significantly lower than that of the nominal trajectory. This change is primarily due to the aircraft's reduced trimming capability after the fault, significantly reducing the available angle of attack range. To maintain the aircraft's controllability, the angle of attack range after the fault is limited to the available range. at last, Figure 10 The Mach number evolution of the aircraft was described. The results show that under nominal flight conditions, the aircraft can rapidly transition from supersonic to subsonic speeds, a characteristic that contributes to trajectory smoothness and improves flight safety. However, under reconfigured trajectory conditions, the performance of this transition process degrades, primarily due to actuator failure. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense. The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure, characterized in that: The following steps are involved: Step 1: Establish a three-degree-of-freedom mathematical model of the aerospace vehicle based on the terminal energy management phase flight mission, including dynamic pressure, thermal flow, control, and initial and terminal constraints; Step 2: Obtain fault information and evaluate the aircraft's residual control capability. The aircraft's ability to achieve torque trim is determined by balancing the three-axis torques generated by the control surfaces with those generated by the fuselage during flight. A mixed-integer linear programming algorithm is designed to calculate the range of trimmable angles of attack for the aircraft during the terminal energy management phase. Step 3: Using the maximum lateral distance of flight as the optimization index, the aircraft trajectory optimization problem is transformed into the optimal control problem P0; Step 4: Convex optimization processes the constraints in step 1 and uses sequential linearization approximation to transform the optimization problem P0 into a convex optimization problem P1; Step 5: Introduce trust region constraint |X k -X k-1 |≤ε, where ε is the trust region radius to ensure linearization accuracy and solution efficiency; Step 6: Use the Radau pseudo-spectral discretization method to transform the continuous P1 into a discrete optimal control problem P2 that can be numerically solved; Step 7: Use the original dual interior point method to solve P2, obtain the reconstructed trajectory, and verify whether the reconstructed angle of attack is within the trimmable range. If not, adjust the angle of attack to α max And solve again.

2. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 1 is characterized in that: In step 1, the three-degree-of-freedom mathematical model of the aircraft is: Where x, y, h, V, χ, and γ are the lateral distance, side distance, height, speed, heading angle, and track tilt angle, respectively; σ is the tilt angle; L = qSC L is the lift, D = qSC D is the resistance, where q = 0.5ρV 2 is the dynamic pressure, S is the reference area of the aircraft, ρ is the atmospheric density, C L and C D represents the lift coefficient and drag coefficient; Dynamic pressure constraint: q=0.5ρV 2 ≤q max (2) Heat flow constraints: Q=K Q ρ 0.5 V 3.15 ≤Q max (3) In the above formula, K Q is a constant related to the shape and material of the aircraft; The initial and terminal conditions are X(t0)=X0 (4) X(t f )=X f (5) In the above formula, t0, t f are the initial moment and the final moment respectively, X0, X f are the initial state and the final state respectively.

3. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 2, characterized in that: In step 2, the torque balance condition is: Where, and They represent the roll, pitch and yaw moment coefficients caused by the rudder respectively; the rudder deflection angle satisfies In the formula, δ and Indicates the upper and lower limits of the control surface.

4. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 3 is characterized in that: In step 2, the torque balancing process is solved iteratively: first, a discrete grid of attack angle α and Mach number M is defined based on the flight envelope, and the feasible range of the rudder deflection angle δ is initialized; then, for each grid point (α i ,M j ), calculate the pitching moment coefficient generated by the fuselage A mixed integer linear programming model is constructed, with the rudder angle δ j,i As the decision variable, the moment balance equation As the core constraint, solve the problem of satisfying the rudder deflection constraint The optimal solution; if there is a feasible solution, record the current angle of attack α i The grid is updated and the balancing state is reached. During the iteration, the convergence is judged by evaluating the balancing deviation d. If d≤10 -3 , then the angle of attack is determined to be trimmable, otherwise it is excluded as an untrimable area; finally, the global trimmable angle of attack range is output.

5. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 2, characterized in that: In step 3, the maximum lateral flight distance x f To optimize the indicators, the optimal control problem P0 is constructed based on the three-degree-of-freedom mathematical model of the aircraft. Its constraints include: the three-degree-of-freedom mathematical model equation of the aircraft, dynamic pressure and heat flow constraints, and terminal state conditions, which can be expressed as:

6. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 2, characterized in that: In step 4, if the control quantity σ is directly convexified, high-frequency chattering will occur. A new auxiliary control variable is introduced to decouple the control quantity from the state quantity. The new control quantity is Then the dynamic equation (1) can be rewritten as In the formula, X=[x,y,h,V,χ,γ,σ] T , the state matrices f(X) and B are B＝[0 0 0 0 0 0 1] T (12) Then, the dynamic constraint function, dynamic pressure constraint and thermal flow constraint are linearized by sequential linearization approximation. The state variables are k-1 There are: Where c is the right function of equations (2) and (3), h max =[q max ,Q max ] T , transform the aircraft optimal control problem P0 into a convex optimization problem P1:

7. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 6, characterized in that: In step 5, after linearizing and approximating the dynamic constraint function, in order to ensure the accuracy of the approximation and the convergence of the algorithm, the trust region constraint of the second-order cone form of the relevant variables |X k -X k-1 |≤ε, that is: Where x is the lateral distance, y is the lateral distance, h is the height, V is the velocity, χ is the heading angle, γ is the trajectory inclination angle, σ is the roll angle, and the subscripts k and k-1 represent the kth and k-1th iterations, respectively.

8. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 7, characterized in that: In step 6, the Radau pseudo-spectral method is used to discretize the optimal control problem P1. For the dynamic model, the Radau pseudo-spectral discretization constraint model is: Where D is the constant differential matrix, X = [x, y, h, V, χ, γ, σ] T are state variables, t0, t f are the starting time and the terminal time, respectively, f is the right function of the dynamic equation (13), N is the number of discrete points, and τ∈[-1,1) is a new independent variable replacing the flight time t; After discretization, the convex optimization problem P1 is transformed into a discrete sequence convex programming problem P2:

9. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to claim 8, characterized in that: In step 6, the conversion relationship between τ and t is 10. The method for reconstructing the TAEM segment trajectory of an aerospace vehicle under actuator failure according to any one of claims 1 to 9, characterized in that: In step 7, the solution algorithm flow is as follows: first, set the number of pseudo-spectral discretization points N, and construct the differential matrix D to discretize the system dynamics equation, thereby converting the trajectory optimization problem in the continuous time domain into a finite-dimensional numerical optimization problem; The nominal trajectory is used as the initial reference trajectory X0, and the trust region radius is set to construct the initial optimization problem; then, the primal-dual interior point method is used to iteratively solve the optimization problem P2 containing system dynamics constraints, path constraints and trust region constraints to obtain the kth iterative solution X opt k ; In each iteration, the attack angle α is detected in real time to see if it exceeds the trim allowable range. If so, it is forced to saturate to the boundary α = α max , and re-solve based on the updated constraints; otherwise, the aerodynamic parameters are updated and the next iteration is entered; in addition, the trust region radius is dynamically adjusted during the iteration process to balance the convergence speed and the stability of the solution; Through cyclic iteration until the angle of attack feasibility, constraints and convergence criteria are met, the optimal trajectory that meets the global balancing requirements and its corresponding control sequence are finally output.

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