CN113325706B - Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization - Google Patents

Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization Download PDF

Info

Publication number
CN113325706B
CN113325706B CN202110490602.XA CN202110490602A CN113325706B CN 113325706 B CN113325706 B CN 113325706B CN 202110490602 A CN202110490602 A CN 202110490602A CN 113325706 B CN113325706 B CN 113325706B
Authority
CN
China
Prior art keywords
aircraft
hypersonic
population
reentry
constraint
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110490602.XA
Other languages
Chinese (zh)
Other versions
CN113325706A (en
Inventor
蔡光斌
徐慧
杨小冈
徐刚锋
侯明哲
席建祥
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Rocket Force University of Engineering of PLA
Original Assignee
Rocket Force University of Engineering of PLA
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Rocket Force University of Engineering of PLA filed Critical Rocket Force University of Engineering of PLA
Priority to CN202110490602.XA priority Critical patent/CN113325706B/en
Publication of CN113325706A publication Critical patent/CN113325706A/en
Application granted granted Critical
Publication of CN113325706B publication Critical patent/CN113325706B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a hypersonic aircraft reentry trajectory optimization method based on improved control parameterization, which comprises the steps of firstly establishing a hypersonic aircraft reentry trajectory optimization problem model based on path constraint and terminal constraint; then, utilizing time scale transformation and piecewise constant function control quantity approximation strategy in the control parameterization method to discretize the original optimization problem into a parameter selection problem; and then, generating a relatively uniform initialization population in a solution space by using a Tent chaotic sequence, taking the initialization population as an initial population of a particle swarm algorithm, optimizing the dispersed objective function to obtain a better initial guess solution, and solving the problem of the reentry trajectory of the dispersed hypersonic flight vehicle by adopting an interior point method to obtain the reentry trajectory. The method improves the control parameterization method, has higher optimization efficiency, can obtain accurate and safe reentry optimization tracks, and has important reference value for the subsequent exploration of the reentry track optimization problem solution of the hypersonic aircraft.

Description

Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization
Technical Field
The invention relates to the field of a reentry trajectory optimization algorithm of a hypersonic flight vehicle, in particular to a reentry trajectory optimization method of the hypersonic flight vehicle based on improved control parameterization.
Background
The theory related to the hypersonic flight vehicle gradually becomes a research hotspot of all the countries in the aerospace field, a safe and accurate reentry trajectory of the hypersonic flight vehicle is planned quickly, and the premise that the hypersonic flight vehicle completes the flight task smoothly is met.
The difficulty of optimizing the reentry trajectory of the hypersonic flight vehicle is that various path constraints, states and control quantity constraints need to be met while planning a trajectory for completing a flight task, so that the hypersonic flight vehicle can safely and effectively reach a target area. In the field of the reentry trajectory optimization problem of the hypersonic flight vehicle, common optimization algorithms include an analytic method and a numerical method. Due to the complexity of the hypersonic reentry trajectory problem, it is often difficult to solve an analytical solution. The numerical method comprises a direct method and an indirect method, and the direct method has the advantages that the algorithm principle is simple, the understanding is easy, the solving result is easy to fall into the local optimum, and the solving calculation amount is large. The indirect method has the advantages that the solving result meets the optimal necessary condition and the solving precision is high, but the principle derivation is complex and tedious, the dependence degree of the convergence speed on the estimation value of the initial value of the covariance variable is high, the physical significance of the covariance variable is unclear, and a reasonable initial value is difficult to obtain through effective analysis.
In recent years, because of the advantages of simple principle, easy solution and realization, a Control Parameterization Method (CPM) in the optimization field is introduced into the research of hypersonic track optimization problems, and the Control parameterization method mainly uses time scale transformation and piecewise constant function Control quantity approximation to disperse the original problem and convert the optimization problem into a parameter selection problem, thereby solving the problem by using common nonlinear programming methods such as an interior point method and the like. However, the control parameterization method is sensitive to initial values, and different initial value selections have great influence on optimization solving speed and accuracy.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide a hypersonic aircraft reentry trajectory optimization method based on improved control parameterization, and aiming at the problem of initial value sensitivity in the control parameterization method, a control parameterization algorithm is improved, so that the hypersonic aircraft reentry trajectory optimization problem can be solved more efficiently, and an accurate and safe reentry optimization trajectory is finally obtained.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the hypersonic aircraft reentry trajectory optimization method based on improved control parameterization is characterized by comprising the following steps of,
s1: establishing a hypersonic glide vehicle reentry trajectory optimization problem model based on conventional path constraint and terminal constraint;
s2: performing model conversion on the problem model established in the step S1 by using a time scale change strategy in control parameterization;
s3: performing approximate representation on the control quantity in the problem model converted in the step S2 by using a fine segmentation constant function to obtain a discrete problem description model, and converting the hypersonic glide vehicle reentry trajectory optimization problem into a nonlinear programming problem;
s4: processing the constraint in the nonlinear programming problem in the step S3 by using a penalty method, and further converting the original problem model into a constraint-free optimization problem;
s5: and solving the unconstrained optimization problem obtained in the step S4 by utilizing nonlinear programming to obtain the reentry optimization trajectory of the hypersonic glide vehicle meeting the path constraint and the terminal constraint.
Further, the specific operation of step S1 includes the following steps,
s101: establishing a dynamic equation of reentry of the hypersonic glide aircraft
Figure BDA0003052343630000021
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000022
representing the state quantity, r is the earth center distance of the aircraft, V is the earth relative speed of the aircraft, psi and gamma are the heading angle and track angle of the aircraft, theta and gamma, respectively
Figure BDA0003052343630000023
Respectively, the longitude and latitude at which the aircraft is located; m and g are the mass of the aircraft and the gravitational acceleration of the current geocentric distance, respectively; u ═ α, σ] T Representing two control quantities, wherein sigma and alpha respectively refer to a sideslip angle and an attack angle of the aircraft;
D＝ρV 2 S ref C D p V ═ L and/2 2 S ref C L The/2 respectively refers to the aerodynamic drag and the lift of the aircraft in the flight process, wherein rho is the air density of the aircraft at the current altitude, and S ref Is the reference cross-sectional area of the aircraft, C L And C D Aerodynamic parameters relating to the angle of attack α and mach number of the aircraft, respectively;
s102: mathematical model for establishing conventional path constraint
Figure BDA0003052343630000031
Wherein the content of the first and second substances,
Figure BDA0003052343630000034
n and
Figure BDA0003052343630000035
respectively representing heat flow rate constraint, overload constraint and dynamic pressure constraint;
Figure BDA0003052343630000036
n max and
Figure BDA0003052343630000037
maximum values of heat flow rate, overload and dynamic pressure during the flight of the aircraft, respectively, and a heat flow rate constant K Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 )；
S103: the mathematical model of the conventional path constraint in step S102 is denoted as
Figure BDA0003052343630000032
S104: building (C.E.)Mathematical model of vertical terminal constraint
Figure BDA0003052343630000033
In the formula, r f And gamma f Respectively, at terminal time t f Then, the expected terminal time values of the earth center distance and the track angle; Δ r and Δ γ denote at the terminal time t f The earth center distance r and the track angle gamma are relative to r f And gamma f The allowable offset of (d);
s105: establishing an objective function J (u) ═ V (t) f )-V f In the formula, V (t) f ) Is the velocity value of the terminal moment, V f The expected value of the terminal time speed is obtained;
s106: combining the step S101 to the step S105, describing a hypersonic glide vehicle reentry trajectory optimization problem model as follows:
Figure BDA0003052343630000041
further, the specific operation of step S2 includes the following steps,
s201: according to the time scale change strategy, the time scale [0, t ] of the whole problem is divided f ]Mapping to [0, 1]Time scale change strategy is recorded as
Figure BDA0003052343630000045
In the formula, t is equal to [0, t ∈ [ ] f ]，s∈[0，1]；
S202: after the time scale changes, the problem of optimizing the reentry trajectory of the hypersonic gliding aircraft is converted into
Figure BDA0003052343630000042
Further, the specific operation of step S3 includes the following steps,
s301: using a fine piecewise constant function
Figure BDA0003052343630000043
Figure BDA0003052343630000044
Approximating the control quantity in the hypersonic glide vehicle reentry trajectory optimization problem model in the step S2; wherein l represents s ∈ [0, 1 ]]Divided into l segments, k denoting the k segment, u i (s) represents the ith control quantity, τ i，k An approximation constant representing a k-th segment; s is an element of [ s ] k-1 ，s k ) Represents a span segment;
s302: after the controlled variable is approximated by a piecewise constant function, a discrete form of the reentry trajectory optimization problem of the hypersonic aerocraft is obtained,
Figure BDA0003052343630000051
further, the specific operation of step S4 includes the following steps,
s401: by using
Figure BDA0003052343630000052
Figure BDA0003052343630000053
The constraint in the nonlinear programming problem in step S3 is processed in the form of a penalty method of (1), 2, …, l;
s402: according to the processing method in step S401, the question P is processed 2 To the target function form of
Figure BDA0003052343630000054
S403: after the constraints in the nonlinear programming problem in the step S3 are processed, the reentry trajectory optimization problem of the original hypersonic velocity aircraft can be converted into an unconstrained optimization problem
Figure BDA0003052343630000055
Further, the specific operation of step S5 includes the following steps,
s501: generating a Tent chaotic sequence, and mapping the chaotic sequence to a solution space to obtain an initial population of the PSO particle swarm algorithm;
s502: using the initial population obtained in the step S501 and a particle swarm algorithm to preliminarily solve the unconstrained optimization problem of the reentry trajectory optimization of the hypersonic flight vehicle obtained in the step S4 to obtain a better initial guess solution of an objective function;
s503: and (4) solving the unconstrained optimization problem obtained in the step (S4) by using the initial guess solution obtained in the step (S502) by adopting an interior point method to obtain an optimal solution.
Further, the specific operation of step S501 includes the following steps,
s5011: assuming that the population scale is N and the solution space dimension is M, generating a chaos sequence p (p) by using Tent chaos mapping i ，i＝1，2，3，…，N}，p i ＝[p i1 ，p i2 ，p i3 ，…，p iM ]Wherein p is i Can be represented by Tent chaos mapping formula
Figure BDA0003052343630000061
To obtain the compound, wherein M is 1, 2, 3 … M;
s5012: mapping the chaotic sequence p to a solution space to obtain a population
Figure BDA0003052343630000062
The corresponding individual in the population is
Figure BDA0003052343630000063
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000064
is calculated by the formula
Figure BDA0003052343630000065
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000066
is a population X 1 The value in the m-dimension of the ith individual, l m Is the value lower bound of the mth dimension of a certain body, u m Is the value upper bound, p, of the mth dimension of a certain body im Is the value in the m-dimension of the ith sequence in the chaotic sequence p.
Further, the specific operation of step S502 includes,
s5021: group of people
Figure BDA0003052343630000067
As an initial population of the particle swarm algorithm, a problem P is set 3 Taking the target function as a fitness function, substituting the positions of the particles of the initial population into the fitness function, and calculating the fitness values of all the particles in the initial population;
s5022: sorting the fitness values of all the particles from good to bad to obtain the position of the particle corresponding to the optimal fitness of the contemporary population and recording the position as g best Historical optimum position is noted as p best ；
S5023: updating the speed and the position of each particle in the population in a v mode i+1 ＝ω×v i +c 1 ×rand 1 ×(p best -x i )+c 2 ×rand 2 ×(g best -x i )，x i+1 ＝x i +v i Wherein v is velocity; x is a position; rand 1 And rand 2 Is two [0, 1 ]]A random number of (c); omega is a weight factor which changes linearly; c. C 1 And c 2 As a learning factor, c 1 ＝c 2 ＝2；
S5024: substituting the updated particle speed and position into a fitness function to calculate a fitness value, and repeating the step S5022;
s5025: judging whether the particle position corresponding to the optimal fitness of the contemporary population obtained in the step S5024 meets the optimization ending condition, if so, turning to the step S5026, and if not, turning to the step S5023;
s5026: and after the optimization is finished, outputting an optimal position and an optimal objective function value, wherein the output particle position corresponding to the optimal fitness of the population is an initial guess solution in the track optimization problem.
The invention has the beneficial effects that:
1. according to the invention, an initial population which is uniformly distributed in a solution space is obtained by a Tent chaotic mapping population initialization method, the problem that initial population individuals generated by a traditional initial population initialization method are not uniformly distributed in the solution space is solved, and a foundation is laid for finding an optimal solution in the solution space by utilizing a PSO optimization method subsequently.
2. The method greatly improves the problem that the initial value of the control parameterization method is extremely sensitive by combining the improved PSO optimization algorithm with the control parameterization method, obtains a good effect on the hypersonic velocity reentry trajectory optimization problem, can obtain an accurate and safe reentry optimization trajectory, and has important reference value in the subsequent exploration of solving the hypersonic velocity reentry trajectory optimization problem.
Drawings
FIG. 1 is a flow chart of a hypersonic aircraft reentry trajectory optimization method of the present invention;
FIG. 2 is a comparison of reentry trajectory heights of hypersonic flight vehicles obtained by two methods in simulation experiments according to the present invention with time;
FIG. 3 is a comparison of reentry trajectory speed of the hypersonic flight vehicle obtained by two methods in simulation experiments according to the present invention with time;
FIG. 4 is a comparison of the reentry trajectory track angle of the hypersonic flight vehicle obtained by two methods in the simulation experiment of the present invention with time;
FIG. 5 is a comparison of the reentry trajectory path constraints of the hypersonic flight vehicle obtained by two methods in the simulation experiment of the present invention over time.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following description will be made with reference to the accompanying drawings and embodiments.
As shown in fig. 1, the hypersonic aircraft reentry trajectory optimization method based on improved control parameterization comprises the following steps,
s1: establishing a hypersonic glide aircraft reentry trajectory optimization problem model based on conventional path constraint and terminal constraint;
in particular, the method comprises the following steps of,
s101: establishing a dynamic equation of reentry of the hypersonic glide aircraft
Figure BDA0003052343630000081
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000083
representing the state quantity, r is the earth center distance of the aircraft, V is the earth relative speed of the aircraft, psi and gamma are the heading angle and track angle of the aircraft, theta and gamma, respectively
Figure BDA0003052343630000084
Respectively, the longitude and latitude at which the aircraft is located; m and g are the mass of the aircraft and the gravitational acceleration of the current geocentric distance, respectively; u ═ α, σ] T Representing two control quantities, wherein sigma and alpha respectively refer to a sideslip angle and an attack angle of the aircraft; d ═ ρ V 2 S ref C D P V ═ L and/2 2 S ref C L The/2 respectively refers to the aerodynamic resistance and the lift force of the aircraft in the flight process, wherein rho is the air density of the aircraft at the current height, S ref Is the reference cross-sectional area of the aircraft, C L And C D Aerodynamic parameters relating to the angle of attack α and mach number of the aircraft, respectively;
s102: mathematical model for establishing conventional path constraint
Figure BDA0003052343630000082
Wherein the content of the first and second substances,
Figure BDA0003052343630000085
n and
Figure BDA0003052343630000086
respectively representing heat flow rate constraint, overload constraint and dynamic pressure constraint;
Figure BDA0003052343630000094
n max and
Figure BDA0003052343630000095
maximum values of heat flow rate, overload and dynamic pressure during the flight of the aircraft, respectively, and a heat flow rate constant K Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 )；
S103: the mathematical model of the conventional path constraint in step S102 is recorded as
Figure BDA0003052343630000091
S104: mathematical model for establishing terminal constraint
Figure BDA0003052343630000092
In the formula, r f And gamma f Respectively, at terminal time t f Then, the expected terminal time values of the earth center distance and the track angle; delta r And Δ γ Respectively, at terminal time t f The earth center distance r and the track angle gamma are relative to r f And gamma f The allowable offset of (a) is a very small positive value;
s105: establishing an objective function J (u) ═ V (t) f )-V f In the formula, V (t) f ) As the velocity value of the terminal time, V f The expected value of the terminal time speed is obtained;
s106: combining the step S101 to the step S105, describing a hypersonic glide vehicle reentry trajectory optimization problem model as follows:
Figure BDA0003052343630000093
s2: performing model conversion on the problem model established in the step S1 by using a time scale change strategy in control parameterization;
specifically, S201: according to the time scale change strategy, the time scale [0, t ] of the whole problem is divided f ]Mapping to [0, 1]Time scale change strategy is noted
Figure BDA0003052343630000096
Wherein t is [0, t ] f ]，s∈[0，1]；
S202: after the time scale changes, the reentry trajectory optimization problem of the hypersonic gliding aircraft is converted into
Figure BDA0003052343630000101
S3: performing approximate representation on the control quantity in the problem model converted in the step S2 by using a fine segmentation constant function to obtain a discrete problem description model, and converting the hypersonic glide vehicle reentry trajectory optimization problem into a nonlinear programming problem;
in particular, the method comprises the following steps of,
s301: using a fine piecewise constant function
Figure BDA0003052343630000102
Figure BDA0003052343630000103
Approximating the control quantity in the hypersonic glide vehicle reentry trajectory optimization problem model in the step S2; wherein l represents s ∈ [0, 1 ]]Divided into l segments, k representing the k-th segment, u i (s) represents the ith control quantity, τ i，k An approximation constant representing a k-th segment; s is an element of [ s ] k-1 ，s k ) Represents a span segment;
s302: after the controlled variable is approximated by a piecewise constant function, a discrete form of the reentry trajectory optimization problem of the hypersonic aerocraft is obtained,
Figure BDA0003052343630000104
s4: processing the constraint in the nonlinear programming problem in the step S3 by using a penalty method, and further converting the original problem model into a constraint-free optimization problem;
in particular, the method comprises the following steps of,
s401: by using
Figure BDA0003052343630000111
Figure BDA0003052343630000112
The penalty method of (1) deals with the constraint in the nonlinear programming problem in step S3, where k is 1, 2, …, l;
s402: according to the processing method in step S401, the question P is processed 2 To the target function form of
Figure BDA0003052343630000113
S403: after the constraints in the nonlinear programming problem in the step S3 are processed, the reentry trajectory optimization problem of the original hypersonic velocity aircraft can be converted into an unconstrained optimization problem
Figure BDA0003052343630000114
Therefore, the original track optimization problem is converted into a parameter selection problem, and the parameter selection problem can be solved.
S5: solving the unconstrained optimization problem obtained in the step S4 by utilizing nonlinear programming to obtain the reentry optimization trajectory of the hypersonic glide vehicle meeting the path constraint and the terminal constraint.
In particular, the method comprises the following steps of,
s501: generating a Tent chaotic sequence, and mapping the chaotic sequence to a solution space to obtain an initial population of the PSO particle swarm algorithm;
assuming that the population scale is N and the solution space dimension is M, and generating a chaotic sequence p (p) by using Tent chaotic mapping i ，i＝1，2，3，…，N}，p i ＝[p i1 ，p i2 ，p i3 ，…，p iM ]Wherein p is i Can be represented by Tent chaos mapping formula
Figure BDA0003052343630000121
To obtain the compound, wherein M is 1, 2, 3 … M;
mapping the chaotic sequence p to a solution space to obtain a population
Figure BDA0003052343630000122
The corresponding individual in the population is
Figure BDA0003052343630000123
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000124
is calculated by the formula
Figure BDA0003052343630000125
In the formula (I), the compound is shown in the specification,
Figure BDA0003052343630000126
is a population X 1 The value in the m-dimension of the ith individual, l m Is the value lower bound of the mth dimension of a certain body, u m Is the value upper bound, p, of the mth dimension of a certain body im Is the value in the m-dimension of the ith sequence in the chaotic sequence p.
S502: using the initial population obtained in the step S501 and a particle swarm algorithm to preliminarily solve the unconstrained optimization problem of the reentry trajectory optimization of the hypersonic flight vehicle obtained in the step S4 to obtain a better initial guess solution of an objective function;
specifically, S5021: the population is
Figure BDA0003052343630000127
As an initial population of the particle swarm algorithm, a problem P is set 3 Taking the target function as a fitness function, substituting the positions of the particles of the initial population into the fitness function, and calculating the fitness values of all the particles in the initial population;
s5022: sorting the fitness values of all the particles from good to bad to obtain the position of the particle corresponding to the optimal fitness of the contemporary population and recording the position as g best Historical optimum position is noted as p best ；
S5023: updating the speed and the position of each particle in the population in a v mode i+1 ＝ω×v i +c 1 ×rand 1 ×(p best -x i )+c 2 ×rand 2 ×(g best -x i )，x i+1 ＝x i +v i Wherein v is velocity; x is a position; rand 1 And rand 2 Is two [0, 1 ]]A random number of (c); omega is a weight factor which changes linearly; c. C 1 And c 2 As a learning factor, c 1 ＝c 2 ＝2；
S5024: substituting the updated particle speed and position into a fitness function to calculate a fitness value, and repeating the step S5022;
s5025: judging whether the particle position corresponding to the optimal fitness of the contemporary population obtained in the step S5024 meets the optimization ending condition, if so, turning to the step S5026, and if not, turning to the step S5023;
s5026: and after the optimization is finished, outputting an optimal position and an optimal objective function value, wherein the output particle position corresponding to the optimal fitness of the population is an initial guess solution in the track optimization problem.
S503: and (4) solving the unconstrained optimization problem obtained in the step (S4) by using the initial guess solution obtained in the step (S502) by adopting an interior point method to obtain an optimal solution.
Simulation experiment:
by adopting a CAV-H hypersonic aerocraft model and using the improved control parameterization hypersonic aerocraft reentry track optimization method provided by the invention, a hypersonic reentry track optimization simulation experiment is carried out.
CAV-H hypersonic aerocraft cross-sectional area is 0.484m 2 907.2kg in mass; and setting a reentry trajectory optimization simulation task of the hypersonic aircraft, wherein detailed parameters are shown in a table 1.
TABLE 1 hypersonic aircraft reentry trajectory optimization task parameters
Figure BDA0003052343630000131
The trajectory optimization is carried out by using the hypersonic aircraft reentry trajectory optimization method based on improved control parameterization, meanwhile, the reentry trajectory obtained by using the original control parameterization method (without improving initial value selection) for solution is used as comparison, and the result is shown in the attached figures 2-5. In fig. 2-5, PSOCPM represents a reentry trajectory obtained by the hypersonic flight vehicle reentry trajectory optimization method based on improved control parameterization proposed in the present invention, and CPM represents a reentry trajectory obtained by the original control parameterization method.
As can be seen from fig. 2, the reentry trajectory height variation obtained by the PSOCPM algorithm provided by the present invention has smaller jitter and relatively smoother trajectory compared to the height variation obtained by the CPM method.
As can be seen from the attached figure 3, the reentry trajectory speed change obtained by the PSOCPM algorithm provided by the invention is smoother compared with the speed change obtained by the CPM method, and has a certain reference value for aircraft control.
As can be seen from fig. 4, the reentry trajectory track angle change obtained by the PSOCPM algorithm provided by the present invention is more stable and has less jitter than the track angle change obtained by the CPM method.
As can be seen from the attached figure 5, the three path constraint changes of the reentry trajectory obtained by the PSOCPM algorithm provided by the invention are smaller than those obtained by the CPM method, and do not exceed the maximum value of the path constraint, so that the safety of the hypersonic aircraft in the flight process can be ensured.
In conclusion, the hypersonic aircraft reentry trajectory optimization method based on improved control parameterization can achieve safe and accurate optimization effects.
The foregoing shows and describes the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. The hypersonic aircraft reentry trajectory optimization method based on improved control parameterization is characterized by comprising the following steps of,
s1: establishing a hypersonic glide vehicle reentry trajectory optimization problem model based on conventional path constraint and terminal constraint;
s2: performing model conversion on the problem model established in the step S1 by using a time scale change strategy in control parameterization;
s3: performing approximate representation on the control quantity in the problem model converted in the step S2 by using a fine segmentation constant function to obtain a discrete problem description model, and converting the hypersonic glide vehicle reentry trajectory optimization problem into a nonlinear programming problem;
s4: processing the constraint in the nonlinear programming problem in the step S3 by using a penalty method, and further converting the original problem model into a constraint-free optimization problem;
s5: solving the unconstrained optimization problem obtained in the step S4 by utilizing nonlinear programming to obtain a reentry optimization trajectory of the hypersonic glide vehicle meeting the path constraint and the terminal constraint;
the specific operation of step S1 includes the following steps,
s101: establishing a dynamic equation of reentry of the hypersonic glide aircraft
Figure FDA0003810424440000011
In the formula (I), the compound is shown in the specification,
Figure FDA0003810424440000012
representing the state quantity, r is the earth center distance of the aircraft, V is the earth relative speed of the aircraft, psi and gamma are the heading angle and track angle of the aircraft, theta and gamma, respectively
Figure FDA0003810424440000013
Respectively, the longitude and latitude at which the aircraft is located; m and g are the mass of the aircraft and the gravitational acceleration of the current geocentric distance, respectively; u ═ α, σ] T Expressing two control quantities, wherein sigma and alpha respectively refer to a sideslip angle and an attack angle of the aircraft; d ═ρV 2 S ref C D P V ═ L and/2 2 S ref C L The/2 respectively refers to the aerodynamic drag and the lift of the aircraft in the flight process, wherein rho is the air density of the aircraft at the current altitude, and S ref Is a reference cross-sectional area of the aircraft, C L And C D Aerodynamic parameters relating to the angle of attack α and mach number of the aircraft, respectively;
s102: mathematical model for establishing conventional path constraint
Figure FDA0003810424440000021
Wherein the content of the first and second substances,
Figure FDA0003810424440000022
n and
Figure FDA0003810424440000023
respectively representing heat flow rate constraint, overload constraint and dynamic pressure constraint;
Figure FDA0003810424440000024
n max and
Figure FDA0003810424440000025
maximum values of heat flow rate, overload and dynamic pressure during the flight of the aircraft, respectively, and a heat flow rate constant K Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 )；
S103: the mathematical model of the conventional path constraint in step S102 is recorded as
Figure FDA0003810424440000026
S104: mathematical model for establishing terminal constraint
Figure FDA0003810424440000027
In the formula, r f And gamma f Respectively, at terminal time t f Then, the expected terminal time values of the earth center distance and the track angle; Δ r andΔ γ represents at the terminal time t f The earth center distance r and the track angle gamma are relative to r f And gamma f The allowable offset of (d);
s105: establishing an objective function J (u) ═ V (t) f )-V f In the formula, V (t) f ) Is the velocity value of the terminal moment, V f The expected value of the terminal time speed is obtained;
s106: combining the step S101 to the step S105, describing a hypersonic glide vehicle reentry trajectory optimization problem model as follows:
Figure FDA0003810424440000028
the specific operation of step S2 includes the following steps,
s201: according to the time scale change strategy, the time scale [0, t ] of the whole problem is divided f ]Mapping to [01]Time scale change strategy is recorded as
Figure FDA0003810424440000031
In the formula, t is equal to [0, t ∈ [ ] f ]，s∈[0，1]；
S202: after the time scale changes, the reentry trajectory optimization problem of the hypersonic gliding aircraft is converted into
Figure FDA0003810424440000032
The specific operation of step S3 includes the following steps,
s301: using fine piecewise constant functions
Figure FDA0003810424440000033
Figure FDA0003810424440000034
Approximating the control quantity in the hypersonic glide vehicle reentry trajectory optimization problem model in the step S2; wherein l represents s ∈ [0, 1 ]]Divided into l segments, k representing the k-th segment, u i (s) represents the ith control quantity, τ i，k An approximation constant representing a k-th segment; s ∈ E[S k-1 ，s k ) Represents a span segment;
s302: after the controlled variable is approximated by a piecewise constant function, a discrete form of a reentry trajectory optimization problem of the hypersonic aerocraft is obtained,
Figure FDA0003810424440000035
the specific operation of step S4 includes the following steps,
s401: by using
Figure FDA0003810424440000041
Figure FDA0003810424440000042
The penalty method of (1) deals with the constraints in the nonlinear programming problem in step S3, where k is 1, 2, …, l;
s402: according to the processing method in step S401, question P is processed 2 To the target function form of
Figure FDA0003810424440000043
S403: after the constraints in the nonlinear programming problem in the step S3 are processed, the reentry trajectory optimization problem of the original hypersonic velocity aircraft can be converted into an unconstrained optimization problem
Problem P 3
Figure FDA0003810424440000044
The specific operation of step S5 includes the following steps,
s501: generating a Tent chaotic sequence, and mapping the chaotic sequence to a solution space to obtain an initial population of the PSO particle swarm algorithm;
s502: using the initial population obtained in the step S501 and a particle swarm algorithm to preliminarily solve the unconstrained optimization problem of the reentry trajectory optimization of the hypersonic flight vehicle obtained in the step S4 to obtain a better initial guess solution of an objective function;
s503: using the initial guess solution obtained in the step S502, resolving the unconstrained optimization problem obtained in the step S4 by adopting an interior point method to obtain an optimal solution;
the specific operation of step S501 includes the following steps,
s5011: assuming that the population scale is N and the solution space dimension is M, generating a chaos sequence p (p) by using Tent chaos mapping i ，i＝1，2，3，…，N}，p i ＝[p i1 ，p i2 ，p i3 ，…，p iM ]Wherein p is i Can be represented by Tent chaos mapping formula
Figure FDA0003810424440000051
To obtain the compound, wherein M is 1, 2, 3 … M;
s5012: mapping the chaotic sequence p to a solution space to obtain a population
Figure FDA0003810424440000052
The corresponding individual in the population is
Figure FDA0003810424440000053
In the formula (I), the compound is shown in the specification,
Figure FDA0003810424440000054
is calculated by the formula
Figure FDA0003810424440000055
In the formula (I), the compound is shown in the specification,
Figure FDA0003810424440000056
is a population X 1 The value in the m-dimension of the ith individual, l m Is the value lower bound of the mth dimension of a certain body, u m Is the value upper bound, p, of the mth dimension of a certain body im Is the value of the ith sequence in the chaotic sequence p in the mth dimension;
the specific operation of step S502 includes,
s5021: group of people
Figure FDA0003810424440000057
As an initial population of the particle swarm algorithm, a problem P is set 3 Substituting the positions of the particles of the initial population into the fitness function to calculate the fitness values of all the particles in the initial population;
s5022: sorting the fitness values of all the particles from good to bad to obtain the position of the particle corresponding to the optimal fitness of the contemporary population and recording the position as g best Historical optimum position is noted as p best ；
S5023: updating the speed and the position of each particle in the population in a v mode i+1 ＝ω×v i +c 1 ×rand 1 ×(p best -x i )+c 2 ×rand 2 ×(g best -x i )，x i+1 ＝x i +v i Wherein v is velocity; x is a position; rand 1 And rand 2 Is two [0, 1 ]]A random number of (c); omega is a weight factor which changes linearly; c. C 1 And c 2 As a learning factor, c 1 ＝c 2 ＝2；
S5024: substituting the updated particle speed and position into a fitness function to calculate a fitness value, and repeating the step S5022;
s5025: judging whether the particle position corresponding to the optimal fitness of the contemporary population obtained in the step S5024 meets the optimization ending condition, if so, turning to the step S5026, and if not, turning to the step S5023;
s5026: and after the optimization is finished, outputting an optimal position and an optimal objective function value, wherein the particle position corresponding to the output population optimal fitness is an initial guess solution in the track optimization problem.
CN202110490602.XA 2021-05-06 2021-05-06 Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization Active CN113325706B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110490602.XA CN113325706B (en) 2021-05-06 2021-05-06 Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110490602.XA CN113325706B (en) 2021-05-06 2021-05-06 Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization

Publications (2)

Publication Number Publication Date
CN113325706A CN113325706A (en) 2021-08-31
CN113325706B true CN113325706B (en) 2022-09-23

Family

ID=77414193

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110490602.XA Active CN113325706B (en) 2021-05-06 2021-05-06 Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization

Country Status (1)

Country Link
CN (1) CN113325706B (en)

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114118365B (en) * 2021-11-08 2022-09-06 北京理工大学 Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network
CN114355770A (en) * 2021-11-30 2022-04-15 浙江大学 Hypersonic aircraft reentry segment controller for optimizing invasive weed population distribution
CN115167126B (en) * 2022-06-24 2024-04-30 西北工业大学 Method for designing and optimizing longitudinal track of ascending section of two-stage orbital hypersonic aircraft
CN115373263A (en) * 2022-07-20 2022-11-22 中国航天空气动力技术研究院 Intelligent optimal control method for aerodynamic force of aircraft with locally-convex surface

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103995540A (en) * 2014-05-22 2014-08-20 哈尔滨工业大学 Method for rapidly generating finite time track of hypersonic aircraft
CN104656450A (en) * 2015-01-20 2015-05-27 北京航空航天大学 Method for designing hypersonic aircraft to re-enter into trajectory in smooth gliding mode
WO2016091728A1 (en) * 2014-12-10 2016-06-16 The Provost, Fellows, Foundation Scholars, And The Other Members Of Board, Of The College Of The Holy And Undivided Trinity Of Queen Elizabeth, Near Dublin Computer modelling of atmospheric re-entry of objects such as satellites
CN106227972A (en) * 2016-08-04 2016-12-14 北京航空航天大学 A kind of optimization method of the steady glide trajectories of hypersonic aircraft
CN107590297A (en) * 2016-07-08 2018-01-16 北京空间技术研制试验中心 The online planing method of aircraft reentry trajectory based on particle swarm optimization algorithm
CN110304278A (en) * 2019-06-20 2019-10-08 南京航空航天大学 A kind of high-precision optimization method of great-jump-forward reentry trajectory
CN111045447A (en) * 2019-11-21 2020-04-21 浙江大学 High-precision hypersonic aircraft trajectory optimization multi-scale optimal control system
CN111061294A (en) * 2019-11-21 2020-04-24 浙江大学 Trajectory optimization self-adaptive optimal control system for nonstationary hypersonic aircraft
CN111123700A (en) * 2019-11-21 2020-05-08 浙江大学 Constraint full-course satisfied optimal control system for obstacle-detouring flight of hypersonic aircraft
CN111324035A (en) * 2019-11-21 2020-06-23 浙江大学 Adaptive optimal controller for trajectory optimization of hypersonic aircraft
CN111881518A (en) * 2020-07-30 2020-11-03 中国人民解放军火箭军工程大学 Intelligent reentry maneuver guidance method and system for hypersonic aircraft

Patent Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103995540A (en) * 2014-05-22 2014-08-20 哈尔滨工业大学 Method for rapidly generating finite time track of hypersonic aircraft
WO2016091728A1 (en) * 2014-12-10 2016-06-16 The Provost, Fellows, Foundation Scholars, And The Other Members Of Board, Of The College Of The Holy And Undivided Trinity Of Queen Elizabeth, Near Dublin Computer modelling of atmospheric re-entry of objects such as satellites
CN104656450A (en) * 2015-01-20 2015-05-27 北京航空航天大学 Method for designing hypersonic aircraft to re-enter into trajectory in smooth gliding mode
CN107590297A (en) * 2016-07-08 2018-01-16 北京空间技术研制试验中心 The online planing method of aircraft reentry trajectory based on particle swarm optimization algorithm
CN106227972A (en) * 2016-08-04 2016-12-14 北京航空航天大学 A kind of optimization method of the steady glide trajectories of hypersonic aircraft
CN110304278A (en) * 2019-06-20 2019-10-08 南京航空航天大学 A kind of high-precision optimization method of great-jump-forward reentry trajectory
CN111045447A (en) * 2019-11-21 2020-04-21 浙江大学 High-precision hypersonic aircraft trajectory optimization multi-scale optimal control system
CN111061294A (en) * 2019-11-21 2020-04-24 浙江大学 Trajectory optimization self-adaptive optimal control system for nonstationary hypersonic aircraft
CN111123700A (en) * 2019-11-21 2020-05-08 浙江大学 Constraint full-course satisfied optimal control system for obstacle-detouring flight of hypersonic aircraft
CN111324035A (en) * 2019-11-21 2020-06-23 浙江大学 Adaptive optimal controller for trajectory optimization of hypersonic aircraft
CN111881518A (en) * 2020-07-30 2020-11-03 中国人民解放军火箭军工程大学 Intelligent reentry maneuver guidance method and system for hypersonic aircraft

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
考虑气动参数扰动的再入轨迹快速优化方法;杨奔等;《力学学报》;20201130;第52卷(第6期);第1610-1620页 *
高超声速再入飞行器基于凸优化的模型预测轨迹跟踪控制;谭峰等;《第三十二届中国控制会议论文集（C卷）》;20130731;第4167-4171页 *

Also Published As

Publication number Publication date
CN113325706A (en) 2021-08-31

Similar Documents

Publication Publication Date Title
CN113325706B (en) Hypersonic aircraft reentry trajectory optimization method based on improved control parameterization
CN111351488B (en) Intelligent trajectory reconstruction reentry guidance method for aircraft
CN110806759B (en) Aircraft route tracking method based on deep reinforcement learning
CN110989626B (en) Unmanned aerial vehicle path planning method based on control parameterization
CN107563044B (en) Four-rotor unmanned aerial vehicle path tracking control method based on online safety learning
CN106371312B (en) Lift formula based on fuzzy controller reenters prediction-correction method of guidance
CN111538255B (en) Anti-bee colony unmanned aerial vehicle aircraft control method and system
CN111881518A (en) Intelligent reentry maneuver guidance method and system for hypersonic aircraft
CN110059863B (en) Aircraft four-dimensional track optimization method based on required arrival time
CN112148024A (en) Unmanned aerial vehicle real-time online flight path planning method based on self-adaptive pseudo-spectral method
CN114355777B (en) Dynamic gliding method and system based on distributed pressure sensor and sectional attitude control
CN107367941B (en) Method for observing attack angle of hypersonic aircraft
CN112947534A (en) Adaptive pseudo-spectral method trajectory optimization method for depression section of hypersonic aircraft
CN111813146A (en) Reentry prediction-correction guidance method based on BP neural network prediction voyage
CN116187199A (en) Unsteady aerodynamic modeling method integrating intelligent technology
CN113741509B (en) Hypersonic gliding aircraft hold-down section energy management method
Salichon et al. A neuro-evolutionary approach to micro aerial vehicle control
Smith et al. Application of the concept of dynamic trim control to automatic landing of carrier aircraft
Abdulla et al. Roll control system design using auto tuning LQR technique
CN112698569A (en) Reentry cross-domain aircraft trajectory integrated design method
CN114417730B (en) Aircraft glide section flight range online prediction method based on integrated neural network
CN114442673B (en) Intelligent aircraft trajectory planning method based on chaotic model and DNN
CN115963855A (en) Unpowered reentry aircraft landing area prediction method based on deep learning
CN108398883B (en) RLV approach landing trajectory rapid deduction and determination method
CN113761662B (en) Generation method of trajectory prediction pipeline of gliding target

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant