CN115291526A - Optimal tracking guidance method based on rolling time domain - Google Patents

Optimal tracking guidance method based on rolling time domain Download PDF

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Publication number
CN115291526A
CN115291526A CN202211207671.6A CN202211207671A CN115291526A CN 115291526 A CN115291526 A CN 115291526A CN 202211207671 A CN202211207671 A CN 202211207671A CN 115291526 A CN115291526 A CN 115291526A
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optimal
control
time
vector
deviation
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CN115291526B (en
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程晓明
靳蕊溪
禹春梅
张惠平
陈曦
柳嘉润
李明华
郑卓
杨庆军
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Beijing Aerospace Automatic Control Research Institute
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Beijing Aerospace Automatic Control Research Institute
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    • 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

Abstract

An optimal tracking guidance method based on a rolling time domain belongs to the field of aircraft guidance and control and solves the problem of nonlinear optimal online trajectory tracking of an aircraft. The optimal tracking guidance method comprises the following steps: tracking a track based on a kinematic model to obtain state quantity deviation and control vector deviation; linearizing the kinematic model by using the state quantity deviation and the control vector deviation; and solving the optimal control objective function to minimize the optimal control objective function on the basis of the linearized kinematic model under the condition of meeting terminal constraints, namely obtaining a guidance instruction. According to the method, the trajectory tracking problem is constructed into a convex quadratic programming problem through small-disturbance linearization processing, the minimum trajectory tracking error is taken as a performance quality guarantee, an optimal tracking instruction can be generated in real time, and the trajectory tracking precision is improved.

Description

Optimal tracking guidance method based on rolling time domain
Technical Field
The invention relates to an optimal tracking guidance method based on a rolling time domain, and belongs to the field of aircraft guidance and control.
Background
With the complex situation requirements of large-scale disturbance, aerodynamic influence and the like which may occur in the flight process of the aircraft, the aircraft is required to autonomously realize trajectory planning and realize tracking guidance, and finally, the requirement of completing the payload delivery task quickly, with low cost, reliably and accurately is met. The prior art scheme has the following defects: 1) The control system has insufficient capacity to cope with large-scale disturbance; 2) The emission preparation period is long, and the requirement of quick emission is difficult to meet with high efficiency; 3) The control system has insufficient task adaptability and is difficult to adapt to the guidance requirements of diversified delivery trajectories.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and the problem of nonlinear optimal online trajectory tracking of the aircraft is solved.
The purpose of the invention is realized by the following technical scheme:
an optimal tracking guidance method based on a rolling time domain comprises the following steps:
tracking a track based on a kinematic model to obtain state quantity deviation and control vector deviation;
linearizing the kinematic model by using the state quantity deviation and the control vector deviation;
and solving the optimal control objective function to minimize the optimal control objective function on the basis of the linearized kinematic model under the condition of meeting terminal constraints, namely obtaining a guidance instruction.
Preferably, an interior point method is adopted to solve the optimal control objective function.
Preferably, the rolling time domain-based method includes:
measuring the system state of the current time from the initial time, solving an optimal control objective function at a certain time interval according to the system constraints of the current time and a future time interval, and solving to obtain a control sequence in the future time interval, wherein the time interval is recorded as the length of a rolling time domain;
and using the control sequence for the next guidance period, and repeating the process to calculate a new control sequence in the next guidance period.
Preferably, when the period for resolving the new control sequence is smaller than the guidance period, in a certain guidance period, after the control sequence process is resolved, the control sequence which is not executed in the guidance period is replaced by the newly resolved control sequence.
Preferably, the terminal constraints include a terminal position and a terminal speed.
Preferably, the state quantity deviation is:
Figure 205165DEST_PATH_IMAGE001
wherein, the first and the second end of the pipe are connected with each other,
Figure 173121DEST_PATH_IMAGE002
the state vector for the nominal trajectory at time t,
Figure 269253DEST_PATH_IMAGE003
for the current state vector of the aircraft at time t,
Figure 980857DEST_PATH_IMAGE004
in order to be the state quantity deviation,
Figure 783728DEST_PATH_IMAGE005
is composed of
Figure 922585DEST_PATH_IMAGE006
A space vector.
Preferably, the control vector deviation is:
Figure 506013DEST_PATH_IMAGE007
wherein
Figure 755729DEST_PATH_IMAGE008
For the purpose of controlling the vector in the actual motion,
Figure 741003DEST_PATH_IMAGE009
is the control vector of the nominal trajectory,
Figure 739177DEST_PATH_IMAGE010
in order to control the deviation of the vector,
Figure 620021DEST_PATH_IMAGE011
is composed of
Figure 673427DEST_PATH_IMAGE012
A space vector.
Preferably, the optimal control objective function is:
Figure 513207DEST_PATH_IMAGE013
the constraints are as follows:
Figure 993867DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 974724DEST_PATH_IMAGE015
as the current time of day, the time of day,
Figure 831821DEST_PATH_IMAGE016
the corresponding time is constrained for the terminal,
Figure 526108DEST_PATH_IMAGE017
is composed of
Figure 177669DEST_PATH_IMAGE016
The deviation of the state quantity at the time of day,
Figure 222986DEST_PATH_IMAGE010
controlling the vector deviation for time t;
Figure 742829DEST_PATH_IMAGE018
is a matrix of coefficients of 6 x 6,
Figure 291622DEST_PATH_IMAGE019
the two coefficient matrixes can be obtained by the current flight state of the aircraft;
Figure 317346DEST_PATH_IMAGE020
、
Figure 584380DEST_PATH_IMAGE021
the speed and the position at the current moment are taken as the data,
Figure 783280DEST_PATH_IMAGE022
、
Figure 186579DEST_PATH_IMAGE023
the position and the speed of the terminal at the moment,
Figure 445522DEST_PATH_IMAGE024
in order to control the vector limiter value,
Figure 715416DEST_PATH_IMAGE025
as a function of the position of the sensor,
Figure 390111DEST_PATH_IMAGE026
as a function of speed.
Preferably, the length of the rolling time domain is determined according to the flight altitude, when the flight altitude belongs to the severe environment disturbance condition, the length of the rolling time domain is shorter, and when the flight altitude belongs to the stable environment condition, the length of the rolling time domain is longer.
Preferably, the length of the rolling time domain is specifically:
Figure 913496DEST_PATH_IMAGE027
wherein the content of the first and second substances,
Figure 343340DEST_PATH_IMAGE028
in order to scroll the time-domain length,
Figure 506337DEST_PATH_IMAGE029
；
Figure 47040DEST_PATH_IMAGE030
、
Figure 690511DEST_PATH_IMAGE031
and
Figure 25677DEST_PATH_IMAGE032
calculated as follows:
first of all, calculate
Figure 754599DEST_PATH_IMAGE033
，
Figure 771096DEST_PATH_IMAGE034
Then calculate
Figure 269074DEST_PATH_IMAGE035
，
Figure 775142DEST_PATH_IMAGE036
Figure 679775DEST_PATH_IMAGE037
（
Figure 562280DEST_PATH_IMAGE038
）
Figure 914764DEST_PATH_IMAGE039
Wherein, the first and the second end of the pipe are connected with each other,
Figure 857312DEST_PATH_IMAGE040
is composed of
Figure 295247DEST_PATH_IMAGE041
The amount of change in the amount of change,
Figure 653547DEST_PATH_IMAGE042
is composed of
Figure 126117DEST_PATH_IMAGE041
The initial value of (a) is set,
Figure 973987DEST_PATH_IMAGE043
is composed of
Figure 899218DEST_PATH_IMAGE041
The final value of (a) is,
Figure 123526DEST_PATH_IMAGE044
is composed of
Figure 637552DEST_PATH_IMAGE041
The maximum rate of change of the adjustment of (c),
Figure 921903DEST_PATH_IMAGE045
is composed of
Figure 334430DEST_PATH_IMAGE041
The time required for the adjustment is set to,
Figure 96850DEST_PATH_IMAGE046
in order to adjust the process factor of 1,
Figure 216115DEST_PATH_IMAGE047
for adjusting the process coefficient 2,t to
Figure 671368DEST_PATH_IMAGE041
The timing of the adjusted starting time is timed,
Figure 571190DEST_PATH_IMAGE048
the initial value of the adjustment is 5, the final value is 4,
Figure 137301DEST_PATH_IMAGE044
is 0.2;
Figure 173390DEST_PATH_IMAGE031
the initial value of the adjustment is 4, the final value is 5,
Figure 485029DEST_PATH_IMAGE044
is 0.15;
Figure 872148DEST_PATH_IMAGE032
the initial value of the adjustment is 5, the final value is 6.5,
Figure 976371DEST_PATH_IMAGE044
the content of the organic acid is 0.1,
Figure 132545DEST_PATH_IMAGE049
is the flying height.
Compared with the prior art, the invention has the following beneficial effects:
(1) The trajectory tracking problem is constructed into a convex quadratic programming problem through small-disturbance linearization processing, the minimum trajectory tracking error is taken as the performance quality guarantee, the optimal tracking instruction can be generated in real time, and the trajectory tracking precision is improved;
(2) Based on the rolling time domain idea, the first instruction sequence is executed in real time, the length of a tracked track can be shortened when a guidance instruction is resolved, the instruction resolving time is prolonged, the resolving time can be less than 10ms, and the guidance period requirement of a task is met;
(3) The method has advancement and universality in guidance tasks with similar guidance requirements, and has practical significance for solving the problem of real-time tracking of diversified trajectories at present;
(4) The method combines the rapid convergence characteristic of the convex optimization theory, solves the basic problem of nonlinear optimal online trajectory tracking of the aircraft by establishing the nonlinear optimal guidance theory in the atmosphere based on the convex optimization theory, and realizes the optimal guidance of trajectory tracking based on convex optimization;
(5) The method can realize the optimal control problem of trajectory tracking guidance, and can also modify and update the guidance instruction in real time according to various current disturbances and errors, so that the guidance system has stronger robustness.
Drawings
Fig. 1 is a diagram of an optimal tracking guidance control strategy based on a rolling horizon.
Fig. 2 is a diagram of the effect of vertical position tracking.
Fig. 3 is a graph of the velocity tracking effect.
FIG. 4 is a graph of vertical position tracking error.
Fig. 5 is a velocity tracking error map.
Fig. 6 is a plot of pitch tracking results.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The optimal tracking guidance method based on the rolling time domain comprises the following steps:
(1) Kinematic model
The optimal tracking guidance adopts a kinematic model as follows:
Figure 867283DEST_PATH_IMAGE050
(1)
wherein the content of the first and second substances,
Figure 476119DEST_PATH_IMAGE051
is a vector of the position of the object,
Figure 649611DEST_PATH_IMAGE052
、
Figure 660293DEST_PATH_IMAGE053
and
Figure 628249DEST_PATH_IMAGE054
the positions of the three directions are adopted,
Figure 911331DEST_PATH_IMAGE055
in the form of a velocity vector, the velocity vector,
Figure 357356DEST_PATH_IMAGE056
、
Figure 488123DEST_PATH_IMAGE057
and
Figure 626981DEST_PATH_IMAGE058
is composed of
Figure 210409DEST_PATH_IMAGE059
、
Figure 397808DEST_PATH_IMAGE053
And
Figure 383081DEST_PATH_IMAGE054
the speed of the motor in the three directions,
Figure 692840DEST_PATH_IMAGE060
in order to be the mass of the aircraft,
Figure 763564DEST_PATH_IMAGE061
、
Figure 816971DEST_PATH_IMAGE062
and
Figure 345166DEST_PATH_IMAGE063
the gravity acceleration in three directions is adopted,
Figure 825826DEST_PATH_IMAGE064
representing the thrust of the engine of the aircraft,
Figure 118267DEST_PATH_IMAGE065
a scalar quantity that is the engine thrust represents the magnitude of the thrust.
Figure 975365DEST_PATH_IMAGE066
Is the specific impulse of an aircraft engine,
Figure 607334DEST_PATH_IMAGE067
at sea levelThe magnitude of the gravitational acceleration.
Figure 258896DEST_PATH_IMAGE068
Is the component of aircraft aerodynamic force in three dimensions.
Figure 304212DEST_PATH_IMAGE070
In order to be the pitch angle,
Figure 699421DEST_PATH_IMAGE071
in order to determine the yaw angle,
Figure 248214DEST_PATH_IMAGE072
is the time of flight.
(2) Equation of state
When the trajectory tracking is carried out based on the kinematic model, the state quantity deviation can be obtained as
Figure 523207DEST_PATH_IMAGE073
（2）
Wherein, the first and the second end of the pipe are connected with each other,
Figure 790240DEST_PATH_IMAGE074
is composed of
Figure 723561DEST_PATH_IMAGE075
The state vector of the nominal trajectory at the moment,
Figure 392440DEST_PATH_IMAGE076
is composed of
Figure 651383DEST_PATH_IMAGE072
At the moment in time the current state vector of the aircraft,
Figure 77816DEST_PATH_IMAGE077
in order to be the state quantity deviation,
Figure 80407DEST_PATH_IMAGE005
is composed of
Figure 603792DEST_PATH_IMAGE006
A spatial vector.
Control vector deviation of
Figure 768057DEST_PATH_IMAGE078
（3）
Wherein
Figure 9683DEST_PATH_IMAGE079
Is composed of
Figure 241731DEST_PATH_IMAGE075
The control vector in the actual motion at the moment,
Figure 619622DEST_PATH_IMAGE080
is composed of
Figure 220368DEST_PATH_IMAGE072
The control vector of the nominal trajectory at the moment,
Figure 683710DEST_PATH_IMAGE081
in order to control the deviation of the vector,
Figure 965787DEST_PATH_IMAGE011
is composed of
Figure 463765DEST_PATH_IMAGE012
A space vector.
To nominal trajectory according to kinematic model
Figure 969832DEST_PATH_IMAGE082
The small-disturbance linearization treatment can be carried out to obtain:
Figure 186050DEST_PATH_IMAGE083
（4）
wherein, the first and the second end of the pipe are connected with each other,
Figure 68555DEST_PATH_IMAGE084
is a matrix of coefficients of 6 x 6,
Figure 607990DEST_PATH_IMAGE085
is a 6 x 2 coefficient matrix, wherein the coefficients can be obtained by the current flight state of the aircraft.
3) Terminal optimization hypothesis
Considering terminal constraint and minimizing the correction quantity of the control quantity in the tracking guidance process, the optimal control problem objective function can be set to be in the following form:
Figure 284959DEST_PATH_IMAGE086
（5）
wherein, the first and the second end of the pipe are connected with each other,
Figure 722894DEST_PATH_IMAGE087
is the current time of day and is,
Figure 409090DEST_PATH_IMAGE088
the corresponding time instant is constrained for the terminal,
Figure 616080DEST_PATH_IMAGE089
in order to control the transposition of the vector deviations,
Figure 667213DEST_PATH_IMAGE090
is the transpose of the terminal state vector bias.
Based on the linearized kinematic model equation (4), the objective function equation (5) is minimized when the terminal constraint is satisfied, and the following form can be obtained:
Figure 592444DEST_PATH_IMAGE013
the constraints are as follows:
Figure 816751DEST_PATH_IMAGE091
（6）
wherein the content of the first and second substances,
Figure 143828DEST_PATH_IMAGE092
、
Figure 428178DEST_PATH_IMAGE093
the speed and the position at the current moment,
Figure 263542DEST_PATH_IMAGE094
、
Figure 291540DEST_PATH_IMAGE095
the position and the speed of the terminal at the moment,
Figure 473123DEST_PATH_IMAGE096
to control vector clipping. The optimal tracking guidance control problem described by the formula (6) can be quickly solved through an interior point method, and a guidance instruction is obtained.
(4) Rolling time domain control
And (3) optimizing the guidance instruction according to the parameter deviation of the current model, the pneumatic deviation and the atmospheric parameter deviation on the basis of the formula (6), and performing real-time rapid solving by adopting a rolling time domain-based method.
1) Solving optimal solutions in fixed time domain
At the initial i moment, measuring the system state at the current moment
Figure 928375DEST_PATH_IMAGE097
At a fixed time interval, based on various system constraints (e.g., speed, position, etc.) at the current time and in future time intervals
Figure 765881DEST_PATH_IMAGE098
The optimal control problem described by the internal solvable formula (6) is obtained by solving
Figure 331992DEST_PATH_IMAGE098
Control sequence in time intervals
Figure 368081DEST_PATH_IMAGE099
Wherein the time interval is fixed
Figure 994234DEST_PATH_IMAGE100
Called rolling time domain length, can be written as
Figure 115774DEST_PATH_IMAGE101
Wherein the time domain length is scrolled
Figure 672526DEST_PATH_IMAGE101
The selection is carried out according to the following principle:
while in flight
Figure 828701DEST_PATH_IMAGE101
The length can be according to the flying height
Figure 625756DEST_PATH_IMAGE102
Self-adaptive regulation is carried out, and the flight stage with severe disturbance of the flight environment (such as a big wind zone in the atmosphere and the like)
Figure 234592DEST_PATH_IMAGE101
The length is shortened, and the flight segment (such as a vacuum segment and the like) with stable flight environment is formed
Figure 142505DEST_PATH_IMAGE101
The length is increased, and the specific form is as follows:
Figure 90869DEST_PATH_IMAGE103
wherein, the first and the second end of the pipe are connected with each other,
Figure 58825DEST_PATH_IMAGE104
，
Figure 154957DEST_PATH_IMAGE105
、
Figure 866561DEST_PATH_IMAGE106
and
Figure 997328DEST_PATH_IMAGE107
it can be calculated as follows:
Figure 821671DEST_PATH_IMAGE108
Figure 139520DEST_PATH_IMAGE109
（
Figure 654815DEST_PATH_IMAGE110
）
Figure 640089DEST_PATH_IMAGE111
Figure 949847DEST_PATH_IMAGE112
wherein the content of the first and second substances,
Figure 754992DEST_PATH_IMAGE113
is composed of
Figure 746082DEST_PATH_IMAGE114
The amount of change in the amount of change,
Figure 585862DEST_PATH_IMAGE115
is composed of
Figure 66522DEST_PATH_IMAGE114
The initial value of (a) is,
Figure 624542DEST_PATH_IMAGE116
is composed of
Figure 216061DEST_PATH_IMAGE114
The final value of (a) is,
Figure 175926DEST_PATH_IMAGE117
is composed of
Figure 14438DEST_PATH_IMAGE114
The maximum rate of change of the adjustment of (c),
Figure 794175DEST_PATH_IMAGE118
is composed of
Figure 189385DEST_PATH_IMAGE114
The time required for the adjustment is set to,
Figure 3757DEST_PATH_IMAGE119
in order to adjust the process factor of 1,
Figure 826219DEST_PATH_IMAGE120
to adjust the process coefficient 2,t to
Figure 93253DEST_PATH_IMAGE114
The adjusted starting time is timed.
Figure 229836DEST_PATH_IMAGE121
The initial value of the adjustment is 5, the final value is 4,
Figure 898715DEST_PATH_IMAGE117
is 0.2;
Figure 892079DEST_PATH_IMAGE106
the initial value of the adjustment is 4, the final value is 5,
Figure 646408DEST_PATH_IMAGE117
is 0.15;
Figure 648999DEST_PATH_IMAGE107
the initial value of the adjustment is 5, the final value is 6.5,
Figure 172384DEST_PATH_IMAGE117
is 0.1.
2) At the time of the next guidance cycle
Figure 25065DEST_PATH_IMAGE122
Executing the first control instruction of the obtained control sequence
Figure 266690DEST_PATH_IMAGE123
；
3) Measuring to obtain new current time
Figure 807393DEST_PATH_IMAGE124
System state of time of day
Figure 185285DEST_PATH_IMAGE125
；
4) Rolling to solve the optimal solution at the subsequent time
According to measured
Figure 786030DEST_PATH_IMAGE124
System state of time of day
Figure 187056DEST_PATH_IMAGE125
In a
Figure 531450DEST_PATH_IMAGE124
Repeating the step (1) at any time, and in a time interval
Figure 763848DEST_PATH_IMAGE126
Solving the optimal control problem to obtain
Figure 535495DEST_PATH_IMAGE124
Control sequence of time of day
Figure 486133DEST_PATH_IMAGE127
. And rolling and advancing according to the strategy in the rest time interval until the whole control process is finally finished. An optimal tracking guidance control strategy diagram based on the rolling horizon is shown in fig. 1.
Wherein
Figure 368639DEST_PATH_IMAGE128
Calculating time for a control sequence;
Figure 908073DEST_PATH_IMAGE114
is the rolling time domain length;
Figure 850621DEST_PATH_IMAGE122
is a guidance period;
Figure 288556DEST_PATH_IMAGE129
updating the time for the control instruction;
Figure 974752DEST_PATH_IMAGE130
is a control instruction.
The embodiment is as follows:
to verify the method, simulation conditions (trajectory tracking model parameters) can be set as in table 1:
TABLE 1
Figure 181743DEST_PATH_IMAGE131
The deviation of the aircraft model parameters, the deviation of the aerodynamic parameters and the deviation of the atmospheric parameters are shown in table 2, and the wind field parameters are shown in table 3.
TABLE 2
Figure 295192DEST_PATH_IMAGE132
TABLE 3
Figure 158106DEST_PATH_IMAGE133
And simultaneously setting random disturbance as follows: disturbance of resistance coefficient: 10%, lift coefficient perturbation: 10%, atmospheric density disturbance: 10%, wind direction: 45 degrees. The vertical position and velocity tracking effect obtained by the method provided by the invention is shown in figures 2 and 3. Vertical position and velocity tracking errors are shown in figures 4 and 5. The variation curve of the tracking pitch angle and the nominal pitch angle during tracking is shown in fig. 6.
According to the simulation result, the time required by the track tracking can be only millisecond level by the scheme, and meanwhile, the requirement of a control system guidance period can be met.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (10)

1. An optimal tracking guidance method based on a rolling time domain is characterized by comprising the following steps:
tracking a track based on a kinematic model to obtain state quantity deviation and control vector deviation;
linearizing the kinematic model by using the state quantity deviation and the control vector deviation;
and solving the optimal control objective function to minimize the optimal control objective function on the basis of the linearized kinematic model under the condition of meeting terminal constraints, namely obtaining a guidance instruction.
2. The optimal tracking guidance method according to claim 1, wherein the optimal control objective function is solved by an interior point method.
3. The optimal tracking guidance method according to claim 2, wherein the rolling time domain-based means that:
measuring the system state of the current moment from the initial moment, solving an optimal control objective function at a certain time interval according to the system constraints of the current moment and the future time interval, and solving to obtain a control sequence in the future time interval, wherein the time interval is recorded as the length of a rolling time domain;
and using the control sequence for the next guidance period, and repeating the process to calculate a new control sequence in the next guidance period.
4. The optimal tracking guidance method according to claim 3, characterized in that when the period for resolving the new control sequence is smaller than the guidance period, in a certain guidance period, after the control sequence process is resolved, the control sequence which is not executed in the guidance period is replaced by the newly resolved control sequence.
5. The optimal tracking guidance method of claim 1 wherein the terminal constraints include terminal position and terminal velocity.
6. The optimal tracking guidance method according to claim 1, wherein the state quantity deviation is:
Figure 114570DEST_PATH_IMAGE001
wherein, the first and the second end of the pipe are connected with each other,
Figure 954350DEST_PATH_IMAGE002
the state vector for the nominal trajectory at time t,
Figure 372693DEST_PATH_IMAGE003
for the current state vector of the aircraft at time t,
Figure 930714DEST_PATH_IMAGE004
in order to be a state quantity deviation,
Figure 522232DEST_PATH_IMAGE005
is composed of
Figure 216519DEST_PATH_IMAGE006
A spatial vector.
7. The optimal tracking guidance method according to claim 1, wherein the control vector deviation is:
Figure 133659DEST_PATH_IMAGE008
wherein
Figure 601812DEST_PATH_IMAGE009
For the purpose of controlling the vector in the actual motion,
Figure 997021DEST_PATH_IMAGE010
is the control vector of the nominal trajectory,
Figure 811393DEST_PATH_IMAGE012
in order to control the deviation of the vector,
Figure 633856DEST_PATH_IMAGE013
is composed of
Figure 838572DEST_PATH_IMAGE014
A space vector.
8. The optimal tracking guidance method according to claim 1, wherein the optimal control objective function is:
Figure 37472DEST_PATH_IMAGE015
the constraints are as follows:
Figure 706351DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 699715DEST_PATH_IMAGE017
as the current time of day, the time of day,
Figure 454044DEST_PATH_IMAGE018
the corresponding time is constrained for the terminal,
Figure 378007DEST_PATH_IMAGE019
is composed of
Figure 901392DEST_PATH_IMAGE018
The deviation of the state quantity at the time is,
Figure 331236DEST_PATH_IMAGE012
controlling the vector deviation for time t;
Figure 572862DEST_PATH_IMAGE021
is a matrix of coefficients of 6 x 6,
Figure 847985DEST_PATH_IMAGE022
the two coefficient matrixes can be obtained by the current flight state of the aircraft;
Figure 429139DEST_PATH_IMAGE023
、
Figure 764306DEST_PATH_IMAGE025
the speed and the position at the current moment,
Figure 493227DEST_PATH_IMAGE027
、
Figure 572042DEST_PATH_IMAGE028
the position and the speed of the terminal at the moment,
Figure 70019DEST_PATH_IMAGE029
in order to control the vector magnitude limiter,
Figure 544730DEST_PATH_IMAGE031
as a function of the position of the sensor,
Figure 495369DEST_PATH_IMAGE033
as a function of speed.
9. The optimal tracking guidance method according to any one of claims 1 to 8, wherein the length of the rolling time domain is determined according to the flight altitude, and when the flight altitude belongs to a severe environment disturbance condition, the length of the rolling time domain is shorter, and when the flight altitude belongs to a smooth environment condition, the length of the rolling time domain is longer.
10. The optimal tracking guidance method according to claim 9, wherein the rolling horizon length is specifically:
Figure 377874DEST_PATH_IMAGE034
wherein the content of the first and second substances,
Figure 668041DEST_PATH_IMAGE036
in order to scroll the time-domain length,
Figure 610589DEST_PATH_IMAGE037
；
Figure 235474DEST_PATH_IMAGE038
、
Figure 656091DEST_PATH_IMAGE039
and
Figure 128661DEST_PATH_IMAGE040
calculated as follows:
first of all, calculate
Figure 242111DEST_PATH_IMAGE041
，
Figure 105024DEST_PATH_IMAGE042
Then calculate
Figure 329332DEST_PATH_IMAGE043
，
Figure 390829DEST_PATH_IMAGE044
Figure 675180DEST_PATH_IMAGE045
（
Figure 776122DEST_PATH_IMAGE047
）
Figure 804121DEST_PATH_IMAGE048
Wherein the content of the first and second substances,
Figure 985704DEST_PATH_IMAGE049
is composed of
Figure 175377DEST_PATH_IMAGE051
The amount of change in the amount of change,
Figure DEST_PATH_IMAGE052
is composed of
Figure 12883DEST_PATH_IMAGE051
The initial value of (a) is,
Figure DEST_PATH_IMAGE054
is composed of
Figure 578993DEST_PATH_IMAGE051
The final value of (a) is,
Figure DEST_PATH_IMAGE055
is composed of
Figure 880662DEST_PATH_IMAGE051
The maximum rate of change of the adjustment of (c),
Figure DEST_PATH_IMAGE056
is composed of
Figure 428187DEST_PATH_IMAGE051
The time required for the adjustment is set to,
Figure DEST_PATH_IMAGE057
in order to adjust the process factor of 1,
Figure DEST_PATH_IMAGE058
to adjust the process coefficient 2,t to
Figure 752989DEST_PATH_IMAGE051
The timing of the adjusted starting time is timed,
Figure DEST_PATH_IMAGE059
the initial value of the adjustment is 5, the final value is 4,
Figure 122790DEST_PATH_IMAGE055
is 0.2;
Figure 13386DEST_PATH_IMAGE039
the initial value of the adjustment is 4, the final value is 5,
Figure 810440DEST_PATH_IMAGE055
is 0.15;
Figure 104762DEST_PATH_IMAGE040
the initial value of the adjustment is 5, the final value is 6.5,
Figure 278255DEST_PATH_IMAGE055
the content of the acid-base reaction product is 0.1,
Figure DEST_PATH_IMAGE060
is the flying height.
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