Aircraft trajectory sequence convex optimization method based on high-dimensional value function

Abstract

The invention belongs to the technical field of aircraft trajectory planning, and relates to an aircraft trajectory sequence convex optimization method based on a high-dimensional value function, and the method comprises the steps: distributing a target function and a constraint violation degree function in an aircraft trajectory planning problem to a multi-dimensional space, and constructing the high-dimensional value function; a high-dimensional value function is used as an evaluation function of an iterative solution, the iterative solution is solved by adopting a convergence strategy of feasibility first and then optimization, and the convergence strategy is to enable the iterative solution to meet a feasibility sufficient reduction condition first and then enable the iterative solution to meet an optimality sufficient reduction condition; according to the method, the target function and different types of constraint violation degrees can be accurately and separately processed; by constructing a high-dimensional value function and a feasible-first and optimal-second convergence strategy, the convergence performance of the sequence convex optimization method for solving aircraft trajectory planning problems with different types of constraints such as equality constraints, inequality constraints and strong nonlinear constraints is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft trajectory planning, and in particular relates to a convex optimization method for aircraft trajectory sequences based on a high-dimensional value function. Background Art

[0002] In the field of aircraft guidance, real-time trajectory planning is a key challenge in achieving high-precision guidance. Sequential convex optimization methods offer computational efficiency advantages by linearizing the original nonlinear aircraft trajectory planning problem and iteratively solving a convex subproblem of this linearization to obtain the optimal solution. However, this method faces a core challenge: ensuring convergence.

[0003] Traditional methods rely on one-dimensional L1 Penalty function to ensure convergence ( 连续凸化 具有状态约束的非凸最优控制问题[J]。IFAC - 论文在线,2017,50(1):4063 - 4069 However, this method has obvious defects. Its convergence performance is very sensitive to the penalty parameter. When the penalty parameter is too large, the convergence speed will be extremely slow, consuming a lot of computing resources and time. When it is too small, the subproblem may become infeasible, or the algorithm may terminate prematurely and fail to obtain the desired result. These problems greatly limit the sequential convex optimization method ( SCP ) in complex constraint scenarios.

[0004] literature( 用于再入轨迹优化问题的无罚函数顺序凸规划 [J]。《宇航学报》,2024,225 (1): 402 - 417 ) proposed a filter-based sequential convex optimization method that avoids introducing penalty parameters. However, it cannot group violations of different types of constraints, such as equality constraints, inequality constraints, and strong nonlinear constraints. This results in poor convergence performance in complex constraint scenarios, making it unsuitable for practical applications. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a convex optimization method for aircraft trajectory sequences based on a high-dimensional value function.

[0006] In order to achieve the purpose of the present invention, the present invention is implemented by adopting the following technical solutions.

[0007] A convex optimization method for a vehicle trajectory sequence based on a high-dimensional value function comprises the following steps: A convex optimization method for an aircraft trajectory sequence based on a high-dimensional value function, characterized by comprising the following steps: S1. According to the constraint types in the aircraft trajectory planning problem, the constraints in the aircraft trajectory planning problem are divided into subscript set; among which: The subscript sets are denoted as ; S2. Construct the constraint violation degree function of each subscript set obtained in step S1: (1); in, is the total optimization variable in the vehicle trajectory planning problem, For the aircraft trajectory planning problem Constraint Function The violation penalty function is defined as follows: (2); in, and are the subscript sets of equation and inequality constraints in the aircraft trajectory planning problem; S3. The objective function in the aircraft trajectory planning problem And the constraint violation degree function constructed in step S2 , Assigned to dimensional space, constructing high-dimensional value functions: (3); S4, using the high-dimensional value function constructed in step S3 as an evaluation function for finding an iterative solution, and adopting a feasible-first-then-optimal convergence strategy to find an iterative solution, so as to improve the convergence performance of finding an iterative solution; The convergence strategy is to first make the iterative solution satisfy the feasibility sufficient descent condition, and then make the iterative solution satisfy the optimality sufficient descent condition; The feasibility sufficient reduction condition is: (8); (9); in, yes The elements in for No. A quantity, is the total constraint violation degree, is the feasibility full reduction coefficient, Representing high-dimensional value functions No. A quantity, For the The filter set of iterations; The optimality sufficient descent condition is: (13), in, is the decrease in optimality, is the optimality sufficient descent coefficient.

[0008] As a preferred solution of the present invention, the constraint types are classified according to the nonlinearity degree of the constraints.

[0009] As a preferred embodiment of the present invention, the filter set Used to record the value of the iterative solution high-dimensional value function, where the dimension of each element is the same as the dimension of the high-dimensional value function.

[0010] As a preferred solution of the present invention, before the first iteration, the filter set is initialized. , the initial filter set Set to: (4); in, , yes Maximum tolerance value.

[0011] As a preferred solution of the present invention, the specific implementation process of step S4 includes the following steps: S41. Solve the iterative solution The convex subproblem at , where Indicates the number of iterations; If the convex subproblem is infeasible, then Add to filter set In, that is (5); in, and Respectively and The filter set of iterations; Then, feasibility recovery is used, that is, iteratively solving the convex subproblem with the objective function of minimizing the degree of constraint violation to obtain a new iterative solution , so that the iterative solution The convex subproblem at is feasible, and then enters the next iteration; If the convex subproblem is feasible, check the optimal solution of the convex subproblem, that is, the iteration direction , does it satisfy the following iteration stopping conditions: (6); (7); in, yes The total constraint violation degree, is the absolute value of the objective function of the convex subproblem, for exist The gradient at is the feasibility error tolerance, is the optimality error tolerance; If conditions (6) and (7) are satisfied at the same time, the iterative solution is stopped and Output as the optimal solution; otherwise, check the iterative solution and iteration direction The following feasibility sufficient reduction conditions are met: (8); (9); in, yes The elements in for No. A quantity, is the total constraint violation degree, is the feasibility full reduction coefficient, Representing high-dimensional value functions No. A quantity, For the The filter set of iterations; if and If conditions (8) and (9) are not met, the trust region in the convex subproblem is reduced. ,Right now (10); in, To reduce the scale; Then, continue solving the convex subproblem until and Satisfy conditions (8)-(9); S42, note is the estimated drop in optimality; check Are the following conditions met? (11); If condition (11) is met, then according to formula (5) Add to the filter set and reduce the trust region in the subproblem according to formula (10) , update the iterative solution according to the following formula (12) and enter the next iteration; (12); If condition (11) is not met, check Whether the following optimality sufficient descent conditions are met: (13); in, is the actual optimality reduction, is the optimality sufficient descent coefficient; If condition (13) is met, the iterative solution is updated according to formula (12) and the next iteration is entered; otherwise, the trust region in the convex subproblem is reduced. ,Right now , then returns to step S41.

[0012] Beneficial effects Compared with the existing technology, the present invention can accurately and separately process the objective function and different types of constraint violation degrees; By constructing a high-dimensional value function and designing a reasonable iterative solution process, the present invention effectively improves the convergence performance of the sequential convex optimization method in solving trajectory planning problems with different types of constraints, such as equality constraints, inequality constraints, and strong nonlinear constraints, providing more reliable technical support for trajectory planning of aircraft in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flowchart of the iterative solution in the present invention; Figure 2 A comparison diagram of simulation results between the total constraint violation degree between the one-dimensional L1 penalty function and the two-dimensional value function and the three-dimensional value function of the present invention; Figure 3 A comparison diagram of simulation results between the absolute value of the objective function of the convex subproblem of the one-dimensional L1 penalty function, the two-dimensional value function, and the three-dimensional value function of the present invention; DETAILED DESCRIPTION

[0014] The present invention will be further described with reference to the embodiments and the accompanying drawings.

[0015] As an embodiment of the present invention, Figure 1 As shown, taking the minimum longitudinal reentry trajectory planning problem of a certain aircraft as an example, the convex optimization method of aircraft trajectory sequence based on high-dimensional value function described in the present invention is further explained. In this embodiment, the aircraft model is selected as the publicly available 乘员探索飞行器 Aircraft ( 再入制导 用于低升阻比航天器的具有扩展射程能力[D]。马萨诸塞州 理工学院,2006 ); For the setting of the objective function and constraints in the reentry trajectory planning problem, please refer to the public literature ( 基于混合阶软信赖域的顺序凸规划 用于再入轨迹优化[J]。《空间研究进展》,2024,73 (6): 3195-3208 ).

[0016] The specific implementation steps are as follows: S1. According to the degree of nonlinearity of the constraints, the constraints of the trajectory planning problem are divided into two categories, namely The first category is the motion equation constraint of the distance from the center of the earth, and the second category is other constraints except the motion equation constraint of the distance from the center of the earth. The subscript sets of the corresponding constraints are and ; S2. Construction and Function of the degree of constraint violation in a set: (14); (15); S3. Constructing high-dimensional value functions: (16); in, Represents the terminal longitudinal variable in the spacecraft minimum longitudinal reentry trajectory planning problem, included in the total optimization variable , is the objective function of the minimum longitudinal reentry trajectory planning problem; S4. Set the filters together Initialize to a filter set : (17); S5. Find iterative solution The convex subproblem at , where: Indicates the number of iterations; If the convex subproblem is infeasible, then Add to the filter set, then perform feasibility recovery to obtain a new iterative solution , so that the new iterative solution The convex subproblem at is feasible, and then enters the next iteration; If the convex subproblem is feasible, check the optimal solution of the subproblem, that is, the iteration direction , whether the following iteration stopping conditions are met: (18); (19); If conditions (18) and (19) are satisfied at the same time, the iterative solution is stopped and Output as the optimal solution; otherwise, check the iterative solution and iteration direction Whether the following two feasibility sufficient reduction conditions are met: (20); (twenty one); if and If conditions (20) and (21) are not met, then the trust region in the convex subproblem is reduced. ; Then continue solving subproblems until and Satisfy conditions (20) and (21); S6. Inspection Are the following conditions met? (twenty two); If condition (22) is met, then Add to the filter set and reduce the trust region in the convex subproblem , update iterative solution And enter the next iteration; If condition (22) is not met, check Are the following conditions met? (twenty three); If condition (23) is met, the iterative solution is updated and enter the next iteration; otherwise, reduce the trust region in the convex subproblem ,Right now , then returns to step S5.

[0017] In order to fully verify the effectiveness of the method of the present invention, the method of the present invention is compared with the sequential convex optimization method based on a one-dimensional penalty function and the sequential convex optimization method based on a two-dimensional value function. Figures 2 to 3 The simulation results clearly show that the sequential convex optimization method based on the one-dimensional L1 penalty function showed no signs of convergence after 50 iterations; the iterations based on the two-dimensional value function converged in 21 iterations; and the iterations based on the three-dimensional value function of the present invention converged in only 11 iterations. This comparison fully demonstrates that the proposed algorithm can significantly improve the convergence speed of sequential convex optimization methods and has important value in practical applications.

[0018] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A convex optimization method for aircraft trajectory sequences based on high-dimensional value functions, characterized by: The steps include: S1. According to the constraint types in the aircraft trajectory planning problem, the constraints in the aircraft trajectory planning problem are divided into subscript set; among which: The subscript sets are denoted as ; S2. Construct the constraint violation degree function of each subscript set obtained in step S1: (1)； in, is the total optimization variable in the vehicle trajectory planning problem, For the aircraft trajectory planning problem Constraint Function The violation penalty function is defined as follows: (2)； in, and They are the subscript sets of equation and inequality constraints in the vehicle trajectory planning problem, respectively; S3. The objective function in the aircraft trajectory planning problem And the constraint violation degree function constructed in step S2 , Assign to dimensional space, constructing high-dimensional value function: (3)； S4, using the high-dimensional value function constructed in step S3 as the evaluation function of the iterative solution, and adopting the feasible first and then optimal convergence strategy to perform iterative solution to improve the convergence performance of the iterative solution; The convergence strategy is to first make the iterative solution satisfy the feasibility sufficient descent condition, and then make the iterative solution satisfy the optimality sufficient descent condition; The feasibility sufficient reduction condition is: (8)； (9)； in, yes The elements in for No. Quantity, is the total constraint violation degree, is the feasibility sufficient reduction coefficient, Representing high-dimensional value functions No. Quantity, For the The filter set of iterations; The optimality sufficient descent condition is: (13), in, is the decrease in optimality, is the optimality sufficient descent coefficient.

2. The method for convex optimization of aircraft trajectory sequences based on high-dimensional value functions according to claim 1, characterized in that: The constraint types are categorized according to the degree of nonlinearity of the constraint.

3. The method for convex optimization of aircraft trajectory sequences based on high-dimensional value functions according to claim 1, characterized in that: The filter set Used to record the value of the iterative solution high-dimensional value function, where the dimension of each element is the same as the dimension of the high-dimensional value function.

4. The method for convex optimization of aircraft trajectory sequences based on high-dimensional value functions according to claim 3, characterized in that: Before the first iteration, initialize the filter set , the initial filter set Set to: (4)； in, , yes Maximum tolerance value.

5. The method for convex optimization of aircraft trajectory sequence based on high-dimensional value function according to claim 1, characterized in that: The specific process of step S4 includes the following steps: S41. Solving iterative solutions The convex subproblem at , where Indicates the number of iterations; If the convex subproblem is infeasible, then Add to filter set In (5)； in, and Respectively and The filter set of iterations; Then, feasibility recovery is used, that is, iteratively solving the convex subproblem with the objective function of minimizing the degree of constraint violation to obtain a new iterative solution , so that the new iterative solution The convex subproblem at is feasible, and then proceed to the next iteration; If the convex subproblem is feasible, check the optimal solution of the convex subproblem, that is, the iteration direction , whether the following iteration stop conditions are met: (6)； (7)； in, yes The total constraint violation degree, is the absolute value of the objective function of the convex subproblem, for exist The gradient at is the feasibility error tolerance, is the optimality error tolerance; If conditions (6) and (7) are satisfied at the same time, the iterative solution is stopped and Output as the optimal solution; otherwise, check the iterative solution and iteration direction The following feasibility reduction conditions are met: (8)； (9)； in, yes The elements in for No. Quantity, is the total constraint violation degree, is the feasibility sufficient reduction coefficient, Representing high-dimensional value functions No. Quantity, For the The filter set of iterations; if and If conditions (8) and (9) are not met, the trust region in the convex subproblem is reduced. ,Right now （10）； in, To reduce the scale; Then, continue solving the convex subproblem until and Satisfy conditions (8) and (9); S42, remember is the estimated decrease in optimality; check Are the following conditions met? （11）； If condition (11) is met, then according to formula (5) Add to the filter set and reduce the trust region in the convex subproblem according to formula (10) , update the iterative solution according to the following formula (12) and enter the next iteration; （12）； If condition (11) is not met, check Whether the following optimality sufficient descent conditions are met: （13）； in, is the actual optimality reduction, is the optimality sufficient descent coefficient; If condition (13) is met, the iterative solution is updated according to formula (12) and the next iteration is entered; otherwise, the trust region in the convex subproblem is reduced. ,Right now , then returns to step S41.

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