A method for designing an aircraft vertical flight path based on dynamic programming

Abstract

The application belongs to the technical field of aircraft performance design, and particularly relates to a method for designing an aircraft vertical flight path based on dynamic programming. First, fixed tasks are determined by sorting the scenes of the entire flight task, the approximate form of the entire vertical flight path is constructed according to the order, and the entire vertical flight path is decomposed into multiple local vertical flight paths. Then, the cruising altitude and the flight weight are marked, each flight process is divided into multiple stages through the change of the weight. The flight altitude of the aircraft at the beginning of each stage is set as a state, and the state is related to the flight segment. The flight altitude of the aircraft at the beginning of each stage is set as a state, and the state is related to the flight segment: the state value increases for climbing, the value is unchanged for cruising flight, and the value decreases for descending. In this way, the task process is processed into a multi-stage decision problem, and the method of dynamic programming is used to process the optimization problem of the vertical flight path.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aircraft performance design, and particularly relates to a method for designing an aircraft vertical flight path based on dynamic programming. BACKGROUND

[0002] An aircraft is currently a high-efficiency and comfortable long-distance transportation tool in the world. Aircraft flight path design affects the flight mission of the aircraft. Reasonable and optimized flight path design is crucial to reducing the use cost of the aircraft.

[0003] The aircraft flight path design mainly includes two parts: horizontal flight path design and vertical flight path design. The horizontal flight path design refers to the projection of the flight trajectory of the aircraft in the process from the departure airport to the target airport in the ground plane. Ideally, the aircraft flies along the great circle of the earth, and the horizontal flight path distance is the shortest. Usually, the aircraft flies along the navigation points, and the horizontal flight path is basically fixed.

[0004] The vertical flight path design refers to the projection of the flight trajectory of the aircraft in the process from the departure airport to the target airport in the vertical plane, also known as the vertical flight path. For a transport aircraft, the vertical flight path design is to determine the cruising altitude of the aircraft. For the case where the flight path distance is relatively long, the cruising altitude of the aircraft is directly selected as the optimal cruising altitude. For the case where the flight path distance is relatively short, the cruising altitude of the aircraft needs to be selected as a result slightly lower than the optimal cruising altitude.

[0005] For some design scenarios in which certain aircraft need to arrive at a medium or low altitude multiple times during the execution of a task, the traditional aircraft vertical flight path design is not completely applicable. First, the traditional vertical flight path design of a transport aircraft is oriented towards a high vertical flight path, and lacks a task scenario of reducing the cruising altitude during the execution of a transport task. Second, the traditional vertical flight path design of a combat aircraft usually has only one medium or low altitude cruising / operation task segment, and lacks a task scenario of reducing the cruising altitude multiple times during the execution of a task. Finally, the traditional aircraft vertical flight path design is more inclined to performance calculation, and lacks the process of vertical flight path optimization design. Therefore, it is very important to develop an aircraft vertical flight path optimization design method. SUMMARY

[0006] The purpose of the present application is to provide a method for designing an aircraft vertical flight path based on dynamic programming, to solve the problem that the existing transport aircraft flight path design lacks a vertical flight path optimization design process.

[0007] The technical solution of the present application is: a method for designing an aircraft vertical flight path based on dynamic programming, comprising:

[0008] determining the type of the aircraft and the location of the take-off and landing airport, determining the fixed task segments and conditions of the aircraft, and preliminarily constructing the entire vertical flight path according to the sequence of the fixed task segments;

[0009] The whole vertical flight path is split into several local vertical flight paths according to the fixed task segments;

[0010] One of the local vertical flight paths is extracted, state information in the execution of the local vertical flight path is obtained, and the state information is divided into multiple stages; different stages are decided respectively to obtain decision results;

[0011] The state transition equation is used to describe the state relationship between adjacent stages, and the index function with the horizontal flight distance as the index is established according to the state relationship between adjacent stages and the decision results;

[0012] The maximum horizontal flight distance of the index function in each adjacent stage is obtained to form an optimal strategy and an optimal index function corresponding to the local vertical flight path, and the optimal index function is denoted as f k (s k ); then the next local vertical flight path is selected, and the optimization results of the whole vertical flight path are obtained after the optimization of all local vertical flight paths is completed.

[0013] Preferably, the fixed task segments include an aircraft task segment 1, an aircraft task segment 2, and an aircraft task segment 3.

[0014] Preferably, the conditions of the fixed task segments are as follows:

[0015] The condition of the aircraft task segment 1 is determined, which is a distance from the take-off airport XX1, a flight height HH1, and a distance LL1 that the aircraft flies horizontally in the task segment 1.

[0016] The condition of the aircraft task segment 2 is determined, which is a distance from the take-off airport XX2, a flight height HH2, and a distance LL2 that the aircraft flies horizontally in the task segment 2.

[0017] The condition of the aircraft task segment 3 is determined, which is a distance from the take-off airport XX3, a flight height HH3, and a distance LL3 that the aircraft flies horizontally in the task segment 3.

[0018] Preferably, the specific method for constructing the whole vertical flight path is as follows: the weight of each flight segment is preliminarily set according to the data of the task segments and the design parameters of the aircraft.

[0019] Preferably, for a subsonic jet aircraft, the optimal cruising height and cruising speed are evaluated according to the flight weight.

[0020] Preferably, the specific method for splitting the whole vertical flight path is as follows: every two fixed flight segments and the variable flight segment in between form a local vertical flight path, and n fixed flight segments in the air and the take-off and landing segment form n+1 local vertical flight paths.

[0021] Preferably, the route is divided into four partial vertical routes: the first partial vertical route is from the takeoff segment to mission segment 1; the second partial vertical route is from mission segment 1 to mission segment 2; the third partial vertical route is from mission segment 2 to mission segment 3; and the fourth partial vertical route is from mission segment 3 to the landing segment.

[0022] Preferably, the status information includes the cruise altitude markers during mission execution, designated as: H1, H2, H3, ... H m The airport's altitude is marked as H. 机场 The takeoff weights of the aircraft during the mission are marked as: G1, G2, G3, ... G n+1 The flight process is divided into n stages based on the changes in weight.

[0023] Preferably, the aircraft weight corresponding to different stages is weight G. k Weight G k The corresponding state is s k (1≤k≤n+1); when (1≤k≤n), the aircraft is in takeoff mode; when k=n+1, the aircraft is in landing mode; takeoff weight G1~G n Fuel consumption during takeoff under certain conditions is weight-related, ensuring fuel efficiency at G-forces. k >G k+1 Under the condition of (1≤k≤n-1), the weight G at the end of takeoff k >G k+1 '.

[0024] Preferably, the method for dividing the state information into multiple stages is as follows: based on the division of cruising altitude and aircraft weight, the state s of the entire flight process is set. k,j Where 1≤k≤n+1, 1≤j≤m, and state s k,j Information included: Flight altitude equal to H j The flight weight is equal to G. k,j G k,j The aircraft is G k G is the weight at takeoff and when it climbs to the j-th altitude. n+1,j The landing weight of the aircraft is G. n+1 The weight when descending from the j-th altitude; due to the initial climb weight G k >G k+1 According to the performance data patterns, the cruising weight G under the same altitude conditions... k,j >G k+1,j .

[0025] Preferably, the relationship between each state and multiple stages is as follows: an increase in the state value indicates climbing, no change in the value indicates cruise flight, and a decrease in the value indicates descent.

[0026] Preferably, the specific method of making a decision for each stage separately is:

[0027] A set of data marks the cruising altitude during the execution of the task, a set of weight data marks the weight of the aircraft during the execution of the task, each flight process is divided into a plurality of stages by the change of the weight; the flight altitude at which the aircraft is located at the beginning of each stage is set as a state, and the state is related to the flight stage.

[0028] Preferably, the decision result between the states of adjacent stages is determined as: k,j D(s k+1,1 ) = {s k+1,2 , s k+1,m}; the decision result is simplified by combining the law of the vertical air route of the aircraft, i.e. D(s k,j ) = {s k+1,j , s k+1,j+1 , …, s k+1,m}, and then the flight mode of the aircraft from s k,j to s k+1,l (j≤l≤m) is obtained.

[0029] Preferably, the flight mode of the aircraft from s k,j to s k+1,l (j≤l≤m) is: first, climbing from H j to H l , and then cruising from G k,l to G k+1,l ; the flight mode of the aircraft from s k,j to s n+1,l (l≤j≤m) is: first, cruising from G k,j to G n+1,l , and then descending from H j to H l .

[0030] Preferably, the state relationship of each adjacent stage is: according to the altitude and weight information contained in each state, and in combination with the state design in the whole endurance process, a state transition equation of the aircraft from s k,j to s k+1,l (j≤l≤m) is obtained.

[0031] Preferably, the state transition equation is:

[0032]

[0033] where G climb (G k , H j ) is the calculation of the take-off of the aircraft with G k as the take-off weight and climbing to H jWeight at the height; G decline (G k+1 , H l ) is the weight at the height H l , and G k+1 is the landing weight.

[0034] Preferably, the index function in terms of horizontal flight distance is:

[0035] L (k,j) = L (k,j) (s k,j , u k,j ), G climb (G k+1 , H l ) > G decline (G n+1 , H l )

[0036] L (k,j) = L (k,j) (s k,j , u k,j ) + L decline , G climb (G k+1 , H l ) < G decline (G n+1 , H l )

[0037]

[0038] L k,n = L (k,j),n + L climb,(k,j)

[0039] where L (k,j) (s k,j , u k,j ) represents the flight distance at the kth stage and the jth height state s k,j , taking the decision u k,j ;

[0040] L decline,j is the horizontal flight distance when the aircraft descends from the jth height to the airport airspace;

[0041] L (k,j),n (s k,j , p k,n ) represents the flight distance of the rear sub-process when the kth stage and the jth height state s k,j is taken, and the strategy p k,n , and L k,n (s k , pk,n represents the state at the kth stage k adopting policy p k,n the flight distance of the rear sub-process, L climb,(k,j) represents the initial state s k the horizontal flight distance when taking off and climbing to the jth height.

[0042] Preferably, for a given state s k , the index function value changes with the policy, and different policies can result in different index function values.

[0043] Preferably, the relationship between the optimal index function and the index function is:

[0044]

[0045] where opt represents taking the optimal value, and the terminal condition is f n+1 (s n+1 ) = 0.

[0046] The method for designing the vertical flight path of the aircraft based on dynamic programming provided by the present application divides each flight process into multiple stages through the change in weight. The flight height at which the aircraft is located at the beginning of each stage is set as the state, and the state is related to the flight segment: the state value increases for climbing, the value remains unchanged for cruising, and the value decreases for descending. In this way, the task process is processed into a multi-stage decision problem, and the no-effect condition is obviously satisfied, and the dynamic programming method is used to process the optimization problem of the vertical flight path. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions provided by the present application, the drawings will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application.

[0048] Figure 1 is a schematic diagram of the overall process of the present application;

[0049] Figure 2 is a schematic diagram of the task scene of the aircraft performing the low-altitude task multiple times according to the present application;

[0050] Figure 3 is a schematic diagram of the entire vertical flight path constructed in the order according to the present application;

[0051] Figure 4 is a schematic diagram of the state setting of the vertical flight path of the aircraft according to the present application. DETAILED DESCRIPTION

[0052] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments of the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.

[0053] A method for designing a vertical flight path of an aircraft based on dynamic programming, comprising the following steps: Figure 1

[0054] Step S100, determining the type of the aircraft and the location of the take-off and landing airports, and determining each fixed mission segment and condition of the aircraft.

[0055] In a specific example, the type of the aircraft is a subsonic jet.

[0056] Preferably, the take-off airport and the landing airport are XX4 apart.

[0057] As shown in Figure 2 Each fixed mission segment includes aircraft mission segment 1, aircraft mission segment 2 and aircraft mission segment 3.

[0058] The condition of each fixed mission segment is:

[0059] The condition of the aircraft mission segment 1 is XX1 apart from the take-off airport, HH1 in flight height, and LL1 in the distance of the aircraft flying straight in the mission segment 1.

[0060] The condition of the aircraft mission segment 2 is XX2 apart from the take-off airport, HH2 in flight height, and LL2 in the distance of the aircraft flying straight in the mission segment 2.

[0061] The condition of the aircraft mission segment 3 is XX3 apart from the take-off airport, HH3 in flight height, and LL3 in the distance of the aircraft flying straight in the mission segment 3.

[0062] Step S200, preliminarily constructing the entire vertical flight path according to the sequence of each fixed mission segment.

[0063] As shown in Figure 3 Specifically, the weight of each flight segment is preliminarily set according to the data of the mission segment and the design parameters of the aircraft. For a subsonic jet, the optimal cruising height and cruising speed can be evaluated according to the flight weight. The optimal cruising height is temporarily used to fill the blank between the mission segments.

[0064] Step S300, splitting the entire vertical flight path according to each fixed mission segment to form a plurality of local vertical flight paths.

[0065] ​The specific method is as follows: every two fixed flight segments and the intermediate variable flight segment form a local vertical route, and n fixed flight segments in the air and take-off and landing segments together form n+1 local vertical routes.

[0066] It is divided into four partial vertical routes: the first partial vertical route is from the takeoff segment to mission segment 1; the second partial vertical route is from mission segment 1 to mission segment 2; the third partial vertical route is from mission segment 2 to mission segment 3; and the fourth partial vertical route is from mission segment 3 to the landing segment.

[0067] This constructs a multi-stage decision problem that adheres to the principle of no aftereffects. That is, given the state of a certain stage, the development of the process after that stage is unaffected by the states of previous stages. When the states of all stages are determined, the entire process is determined. Dynamic programming is used to handle the performance optimization problem of the entire vertical flight path.

[0068] Step S400: Extract one of the local vertical routes, obtain the state information of the local vertical routes during the execution of the task, and divide the state information into multiple stages; make decisions for different stages separately to obtain decision results.

[0069] like Figure 4 The status information includes the cruise altitude markers during mission execution, designated as (H1, H2, H3, ... H...). m The airport's altitude is marked as H. 机场 .

[0070] The takeoff weight of the aircraft during the mission is marked as (G1, G2, G3, ... G... n+1 The flight process is divided into n stages by the change in weight.

[0071] The aircraft weight corresponding to different stages is weight G. k Weight G k The corresponding state is s k (1≤k≤n+1). When (1≤k≤n), the aircraft is in takeoff mode; when k=n+1, the aircraft is in landing mode. Takeoff weight G1~G n Fuel consumption during takeoff under certain conditions is weight-related, ensuring fuel efficiency at G-forces. k >G k+1 Under the condition of (1≤k≤n-1), the weight G at the end of takeoff k >G k+1 '.

[0072] The method for dividing state information into multiple stages is as follows: based on the cruise altitude and aircraft weight, the state s of the entire flight process is set. k,j Where 1≤k≤n+1, 1≤j≤m, and state s k,jThe information contained: flight altitude is equal to H j , flight weight is equal to G k,j . k,j G k is the weight of the aircraft taking off with a takeoff weight of G n+1,j and climbing to the jth altitude, G n+1 is the weight of the aircraft descending from the jth altitude with a landing weight of G k ' > G k+1 ', according to the performance data law, the cruise weight G k,j at the same altitude condition is greater than G k+1,j .

[0073] The relationship between each state and multiple stages is that the state value increases for climbing, the value does not change for cruise flight, and the value decreases for descending. In this way, the task process is processed into a multi-stage decision problem, and the no-effect obviously meets. Therefore, the dynamic programming method can be used to process the optimization problem of the task performance.

[0074] The specific method for making decisions for different stages is:

[0075] A set of data is used to mark the cruising altitude in the execution of the task process, and a set of weight data is used to mark the weight of the aircraft in the execution of the task process. Each flight process is divided into multiple stages through the change of the weight. The flight altitude of the aircraft at the beginning of each stage is set as the state, and the state is related to the flight stage.

[0076] In this way, the task process is processed into a multi-stage decision problem, and the no-effect obviously meets, and the dynamic programming method is used to process the optimization problem of the vertical route.

[0077] Then the decision results between adjacent stages of each state are determined, which are D(s k,j ) = {s k+1,1 , s k+1,2 , …, s k+1,m}. In combination with the law of the vertical route of the aircraft, the decision result is simplified, that is, D(s k,j ) = {s k+1,j , s k+1,j+1 , …, s k+1,m}, and then the flight mode of the aircraft running from s k,j to s k+1,l (j≤l≤m) is obtained.

[0078] The flight mode of the aircraft running from s k,j to s k+1,l (j≤l≤m) is: first, climb from H j to H l , and then cruise from G k,l to Gk+1,l ; the airplane flies from s k,j to s n+1,l (j≤j≤m) in the following way: first from G k,j to G n+1,l , then from H j to H l .

[0079] In step S500, the state relationship of each adjacent stage is described using a state transition equation, and an index function with horizontal flight distance as an index is established according to the state relationship of each adjacent stage and the decision result.

[0080] The state relationship of each adjacent stage is specifically: according to the height and weight information contained in each state, in combination with the state design in the entire endurance process, a state transition equation of the airplane from s k,j to s k+1,l (j≤l≤m) is obtained.

[0081] The state transition equation is:

[0082]

[0083] where G climb (G k , H j ) is the weight of the airplane taking off at G k and climbing to H j height, G decline (G k+1 , H l ) is the descent weight of the airplane descending from H l height to the airport and landing at G k+1 , and △G is the weight step.

[0084] The index function is a quantitative index for measuring the pros and cons of the process, which is a quantitative function defined on the entire process and all subsequent sub-processes.

[0085] The index function with horizontal flight distance as an index is:

[0086] L (k,j) = L (k,j) (s k,j , u k,j ), G climb (G k+1 , H l ) > G decline (G n+1 , H l ) (2)

[0087] L (k,j) = L (k,j) (sk,j ,u k,j )+L decline ,G climb (G k+1 ,H l )≤G decline (G n+1 ,H l ) (3)

[0088]

[0089] L k,n =L (k,j),n +L climb,(k,j) (5)

[0090] wherein, L (k,j) (s k,j , u k,j ) represents the horizontal flight distance of the aircraft at the kth stage when the jth altitude state is s k,j and the decision u k,j is taken,

[0091] L decline,j is the horizontal flight distance of the aircraft from the jth altitude to the airport.

[0092] L (k,j),n (s k,j , p k,n ) represents the flight distance of the rear sub-process when the jth altitude state is s k,j at the kth stage and the strategy p k,n is taken, and L k,n (s k , p k,n ) represents the flight distance of the rear sub-process when the state is s k at the kth stage and the strategy p k,n is taken,

[0093] L climb,(k,j) represents the horizontal flight distance when the initial state is s k takes off and climbs to the jth altitude.

[0094] For a given state s k , the index function value changes with the strategy, and different strategies can result in different index function values.

[0095] Step S600, the maximum value of the horizontal flight distance of the index function in each adjacent stage is obtained, the optimal strategy and the optimal index function corresponding to the local vertical flight path are formed, and the optimal index function is denoted as f k (s k ); and then the next local vertical flight path is selected, and until the optimization of all local vertical flight paths is completed, the optimization result of the entire vertical flight path is obtained.

[0096] Preferably, the relationship between the optimal index function and the index function is:

[0097] f k (s k )=opt uk∈Dk(sk) {L climb,(k,j) +L (k,j) +f k+1 (s k+1 )},k=n,n-1,...,1 (6)

[0098] where opt denotes taking the optimal value, and the terminal condition is f n+1 (s n+1 )=0.

[0099] The names involved in this paper are as follows:

[0100] Flight mission scenario - the specific requirements of the flight mission proposed by the customer, such as requiring the aircraft to take off from airport No. 1, fly at 5 km altitude and Ma 0.50 for 50 min at 300 km away, fly at 3 km altitude and Ma 0.40 for 40 min at 1000 km away, and finally land at airport No. 2.

[0101] Altitude - the altitude at which the aircraft flies

[0102] Speed - the flight speed of the aircraft

[0103] Flight segment - the specific flight process of the aircraft in a certain period of time according to the requirements. The flight mission segments involved in this paper include: takeoff segment, climb segment, cruise segment, mission segment, descent segment, and landing segment.

[0104] Takeoff segment - the process of the aircraft taking off from the airport and leaving the ground to the initial climb.

[0105] Climb segment - the process of the aircraft increasing the flight altitude.

[0106] Cruise segment - the process of the aircraft flying long distances, with little change in altitude and speed during the cruise process.

[0107] Mission segment - the specific requirements of the aircraft to perform the flight mission, generally at a given location, altitude, and speed, flying for a certain period of time, or performing material loading and unloading operations.

[0108] Descent segment - the process of the aircraft reducing the flight altitude.

[0109] Endurance segment - the process of the aircraft continuously flying in the air, including the climb segment, cruise segment, mission segment, and descent segment.

[0110] Landing segment - the process of the aircraft descending from the end to landing on the ground.

[0111] Fixed flight segments - In the context of a flight mission, some flight segments are fixed, including the takeoff segment, the landing segment, and each mission segment.

[0112] Variable flight segments - In the context of a flight mission, some flight segments are variable, including the climb segment, the cruise segment, and the descent segment. Variable flight segments are the objects of vertical route optimization design.

[0113] Vertical route - Refers to the projection of the flight trajectory in the vertical plane during the process of the aircraft from the departure airport to the target airport. The vertical route is the acceptance of the customer flight mission.

[0114] Local vertical route - Refers to the vertical route composed of two adjacent fixed flight segments and the variable flight segment between them. n fixed flight segments and takeoff and landing segments together form n+1 local vertical routes, and all local vertical routes form the entire vertical route.

[0115] Dynamic programming - A branch of operations research, is a mathematical method for solving multi-stage decision-making optimization process. The term dynamic programming in this paper refers to Chen Baolin's "Optimization Theory and Algorithm (2nd Edition)" published by Tsinghua University Press in October 2005

[0116] Stage - A term of dynamic programming, is the natural division of the entire vertical route, this paper divides the stage by the takeoff weight of the aircraft.

[0117] State - A term of dynamic programming, the natural state or objective condition at the beginning of each stage in the entire process is called state.

[0118] Decision - A term of dynamic programming, after the state of a stage is determined, different choices can be made, thereby evolving to a certain state of the next stage.

[0119] Strategy - A term of dynamic programming, a sequence composed of decisions is called a strategy. Starting from the initial state s1, a sequence composed of decisions u k (s k )(k=1,2,...,n) is called the overall process strategy, and the inspection strategy is generally denoted as p 1,n (s1).

[0120] State transition equation - A term of dynamic programming, if the state s k of the kth stage and the decision u k are given, then the state s k+1 of the k+1th stage is determined, s k+1 and s k , u k exist a functional relationship, denoted as s k+1= T(s k u k ), which is called the state transition equation.

[0121] Index function - a term in dynamic programming, the index function is a quantitative index to measure the pros and cons of the process, which is a quantitative function defined on the whole process and all the post-process.

[0122] Optimal strategy - a term in dynamic programming, the optimal strategy is the strategy p k,n (s k , p k,n ) that reaches the optimal value of the index function V k,n ※ called the optimal strategy in the kth post-process, the strategy p 1,n (s1, p 1,n ) that reaches the optimal value of the index function V 1,n ※ called the optimal strategy in the whole process, simply referred to as the optimal strategy.

[0123] Finally, it needs to be explained that: the present application discloses the embodiment in the drawing, only relates to the structure involved in the present disclosure embodiment, other structures can refer to the usual design, in the case of no conflict, the same embodiment and different embodiments of the present application can be combined with each other;

[0124] Finally: the above only for the preferred embodiment of the present application, and not for limiting the present application, any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application, should be included in the protection scope of the present application.

Claims

1. A method for designing an aircraft's vertical flight path based on dynamic programming, characterized in that, include: Determine the aircraft type and the location of the take-off and landing airports, and determine the fixed mission segments and conditions for each aircraft; construct the entire vertical route in the preliminary stage based on the sequence of each fixed mission segment. The entire vertical route is divided into several local vertical routes based on each fixed task segment; Extract a local vertical flight path, obtain the state information of the local vertical flight path during the execution of the task, and divide the state information into multiple stages; make decisions for different stages separately to obtain the decision results; The state transition equation is used to describe the state relationship between adjacent stages, and an index function with horizontal flight distance as the indicator is established based on the state relationship between adjacent stages and the decision results. The maximum horizontal flight distance of the index function within each adjacent stage is obtained to form the optimal strategy and optimal index function for the corresponding local vertical path. The optimal index function is denoted as f. k (s k Then select the next local vertical route, and continue until all local vertical routes have been optimized, and then obtain the optimization result of the entire vertical route. The state transition equation is: Among them G climb (G k H j ) is the calculation of the aircraft in G k Take off at takeoff weight and climb to H j Weight at height; G decline (G k+1 H l ) is the calculation of the aircraft from H l Descend to the airport and take G k+1 Let G be the descent weight under the condition of landing weight, and ΔG be the weight step size.

2. The method for designing aircraft vertical routes based on dynamic programming as described in claim 1, characterized in that: Each fixed mission segment includes aircraft mission segment 1, aircraft mission segment 2, and aircraft mission segment 3.

3. The method for designing aircraft vertical routes based on dynamic programming as described in claim 2, characterized in that, The conditions for each fixed task segment are: The conditions for mission segment 1 are determined as follows: distance from the takeoff airport XX1, flight altitude HH1, and the distance the aircraft flies at level within mission segment 1 is LL1. The conditions for mission segment 2 are determined as follows: distance from the takeoff airport XX2, flight altitude HH2, and the distance the aircraft flies at level in mission segment 2 is LL2. The conditions for mission segment 3 are determined as follows: distance from the takeoff airport XX3, flight altitude HH3, and the distance the aircraft flies at level within mission segment 3 is LL3.

4. The method for designing aircraft vertical routes based on dynamic programming as described in claim 1, characterized in that: The specific method for constructing the entire vertical flight path is as follows: based on the data of the mission segment and the design parameters of the aircraft, the weight of each flight segment is initially determined.

5. The method for designing aircraft vertical routes based on dynamic programming as described in claim 4, characterized in that: For subsonic jet aircraft, the optimal cruise altitude and cruise speed are determined based on flight weight.

6. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 1, characterized in that, The specific method for dividing the entire vertical route is as follows: every two fixed flight segments and the intermediate variable flight segment form a local vertical route, and n fixed flight segments in the air and take-off and landing segments together form n+1 local vertical routes.

7. The method for designing aircraft vertical routes based on dynamic programming as described in claim 6, characterized in that: It is divided into four partial vertical routes: the first partial vertical route is from the takeoff segment to mission segment 1; the second partial vertical route is from mission segment 1 to mission segment 2; the third partial vertical route is from mission segment 2 to mission segment 3; and the fourth partial vertical route is from mission segment 3 to the landing segment.

8. The method for designing aircraft vertical routes based on dynamic programming as described in claim 1, characterized in that, Status information includes the cruise altitude markers during mission execution, designated as: H1, H2, H3, ... H m The airport's altitude is marked as H. 机场 The takeoff weights of the aircraft during the mission are marked as: G1, G2, G3, ... G n+1 The flight process is divided into n stages based on the changes in weight.

9. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 8, characterized in that: The aircraft weight corresponding to different stages is weight G. k Weight G k The corresponding state is s k (1≤k≤n+1); when (1≤k≤n), the aircraft is in takeoff mode; when k=n+1, the aircraft is in landing mode; takeoff weight G1~G n Fuel consumption during takeoff under certain conditions is weight-related, ensuring fuel efficiency at G-forces. k >G k+1 Under the condition of (1≤k≤n-1), the weight G at the end of takeoff k >G k+1 '.

10. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 9, characterized in that: The method for dividing state information into multiple stages is as follows: based on the cruise altitude and aircraft weight, the state s of the entire flight process is set. k,j Where 1≤k≤n+1, 1≤j≤m, and state s k,j Information included: Flight altitude equal to H j The flight weight is equal to G. k,j G k,j The aircraft is G k G is the weight at takeoff and when it climbs to the j-th altitude. n+1,j The landing weight of the aircraft is G. n+1 The weight when descending from the j-th altitude; due to the initial climb weight G k >G k+1 According to the performance data patterns, the cruising weight G under the same altitude conditions... k,j >G k+1,j .

11. The method for designing aircraft vertical routes based on dynamic programming as described in claim 1, characterized in that, The relationship between each state and multiple stages is as follows: an increase in the state value indicates climbing, no change in the value indicates cruise flight, and a decrease in the value indicates descent.

12. The method for designing aircraft vertical routes based on dynamic programming as described in claim 1, characterized in that, The specific methods for making decisions at different stages are as follows: A set of data is used to mark the cruising altitude during the mission, and a set of weight data is used to mark the aircraft's weight during the mission. By measuring the changes in weight, each flight process is divided into multiple stages. The flight altitude at the beginning of each stage is set as the state, and a relationship is established between the state and the flight stage.

13. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 10, characterized in that: The decision outcome between states in adjacent stages is determined as: D(s) k,j )={s k+1,1 s k+1,2 , ..., s k+1,m }; Combining the characteristics of the aircraft's vertical flight path, the decision result is simplified, i.e., D(s k,j )={s k+1,j s k+1,j+1 , ..., s k+1,m }, and then the plane was found to be from s k,j Run to s k+1,l Flight mode (j≤l≤m).

14. The method for designing aircraft vertical routes based on dynamic programming as described in claim 13, characterized in that, The plane from s k,j Run to s k+1,l The flight path for (j≤l≤m) is as follows: First from H j Climb to H l Then from G k,l Cruise to G k+1,l The plane from s k,j Run to s n+1,l The flight pattern for (l≤j≤m) is as follows: First, from G... k,j Cruise to G n+1,l Then from H j Descending to H l .

15. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 1, characterized in that: The specific state relationships between adjacent stages are as follows: Based on the altitude and weight information contained in each state, combined with the state design throughout the entire flight process, the aircraft's state relationships from stage s are obtained. k,j Run to s k+1,l The state transition equation for (j≤l≤m).

16. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 1, characterized in that, The index function, which uses horizontal flight distance as an indicator, is: L (k,j) =L (k,j) (s k,j ,u k,j ),G climb (G k+1 ,H l )>G decline (G n+1 ,H l ) L (k,j) =L (k,j) (s k,j ,u k,j )+L decline ,G climb (G k+1 ,H l )≤G decline (G n+1 ,H l ) L k,n =L (k,j),n +L climb,(k,j) Among them, L (k,j) (s k,j u k,j ) indicates that the state at height j in stage k is s k,j Make a decision k,j Flight distance at time k; L decline,j It is the horizontal flight distance of the aircraft as it descends from altitude j to the airspace above the airport; L (k,j),n (s k,j p k,n ) indicates that the state at height j in stage k is s k,j Adopt strategy p k,n At that time, the flight distance of the subsequent subprocess is denoted by L. k,n (s k p k,n ) indicates that the state is s in the k-th stage. k Adopt strategy p k,n At that time, the flight distance of the later subprocess, L climb,(k,j) Indicates the initial state as s k The horizontal flight distance when taking off and climbing to altitude j.

17. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 16, characterized in that: For a given state s k The value of the indicator function changes with the strategy; different strategies can yield different indicator function values.

18. The method for designing an aircraft's vertical flight path based on dynamic programming as described in claim 16, characterized in that: The relationship between the optimal index function and the index function is as follows: Where opt represents taking the optimal value, and the terminal condition is f. n+1 (s n+1 ) = 0.

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