CN109085754B - Spacecraft pursuit game method based on neural network - Google Patents

Spacecraft pursuit game method based on neural network Download PDF

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CN109085754B
CN109085754B CN201810827228.6A CN201810827228A CN109085754B CN 109085754 B CN109085754 B CN 109085754B CN 201810827228 A CN201810827228 A CN 201810827228A CN 109085754 B CN109085754 B CN 109085754B
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CN109085754A (en
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袁源
张鹏
孙冲
于洋
万文娅
李晨
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Northwestern Polytechnical University
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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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/0202—Control of position or course in two dimensions specially adapted to aircraft
    • 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
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/242—Orbits and trajectories
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/64—Systems for coupling or separating cosmonautic vehicles or parts thereof, e.g. docking arrangements
    • B64G1/646—Docking or rendezvous systems

Abstract

The invention discloses a neural network-based spacecraft pursuit game method, which comprises the steps of firstly establishing a pursuit game discrete system model of a spacecraft; then, an adaptive dynamic programming iterative control strategy of zero and game synchronous convergence is designed, and an optimal control strategy is approximated by utilizing a neural network. The invention adopts a control strategy of zero and game synchronous convergence based on self-adaptive dynamic programming, and can ensure that the system performance reaches the optimum.

Description

Spacecraft pursuit game method based on neural network
Technical Field
The invention belongs to the field of spacecraft pursuit control, particularly relates to a zero-sum game optimal control algorithm for self-adaptive dynamic planning, and particularly relates to a spacecraft pursuit game method based on a neural network.
Background
In recent years, the problem of relative motion of spacecraft has received much attention from domestic and foreign scholars and scientific research institutions. Among them, the problem of pursuit gaming of spacecraft is a content of intense research in recent years. At present, the pursuit game algorithm of most spacecraft is mainly based on a linear space dynamic model of the spacecraft, and a linear feedback controller is designed by utilizing a linear quadratic differential game theory. However, in an actual system, the dynamic model of the spacecraft has a strong nonlinear characteristic, and if a general linear controller is adopted, the control performance of the system is greatly reduced. Therefore, it is important to design an adaptive nonlinear controller for the nonlinear model of the spacecraft.
Aiming at the problem of escape game of the spacecraft, various game control algorithms are proposed at present. In the field of spacecraft, a common control method is linear L∞A control method, a linear optimal control method, and the like. However, the actual spacecraft model is non-linear, and the controller designed by the method inevitably reduces the controllability of the systemCan be used. Therefore, it is urgently needed to design a nonlinear controller for a nonlinear system of a spacecraft. Currently, an adaptive dynamic programming algorithm is mainly adopted for an optimal controller of a nonlinear system. For the discrete zero sum game problem, at present, no self-adaptive dynamic programming algorithm exists to enable the control strategy to meet the condition of simultaneous convergence.
Disclosure of Invention
The invention aims to provide a neural network-based spacecraft pursuit game method to overcome the defects of the prior art, and the invention adopts a zero-sum game synchronous convergence control strategy based on adaptive dynamic programming to ensure that the system performance reaches the optimum.
In order to achieve the purpose, the invention adopts the following technical scheme:
a spacecraft pursuit game method based on a neural network comprises the following steps:
step 1: establishing a pursuit game discrete system model of the spacecraft;
step 2: and designing a self-adaptive dynamic programming iterative control strategy of zero and game synchronous convergence, and approximating an optimal control strategy by using a neural network.
Further, step 1 specifically comprises:
in the Euler-Hill coordinate system, the nonlinear relative motion equation of the aircraft is:
Figure BDA0001742769170000021
Figure BDA0001742769170000022
Figure BDA0001742769170000023
Figure BDA0001742769170000024
Figure BDA0001742769170000025
wherein x, y and z are position information of the aircraft in an Euler-Hill coordinate system; u. ofx，uyAnd uzIs a control input; mu is a universal gravitation constant; r iscAnd rdThe orbit radiuses of the main aircraft and the auxiliary aircraft are respectively; v is the true proximal angle of the primary spacecraft orbit,
Figure BDA0001742769170000026
the first derivative of x is represented as,
Figure BDA0001742769170000027
represents the second derivative of x;
order to
Figure BDA0001742769170000028
Writing the nonlinear relative motion equation into a state space is in the form:
Figure BDA0001742769170000029
wherein the content of the first and second substances,
Figure BDA0001742769170000031
in the formula, eta is a state set, u is an input set, B is an input coefficient matrix, and I is a unit matrix;
therefore, the nonlinear dynamics model of the main aircraft and the auxiliary aircraft is as follows:
Figure BDA0001742769170000032
Figure BDA0001742769170000033
wherein, ηpAnd upRespectively the state vector and the control input of the main aircraftηeAnd ueRespectively is the state vector and the control input of the auxiliary aircraft, and the nonlinear escape pursuit game model is obtained by subtracting the formula (3) from the formula (2):
Figure BDA0001742769170000034
wherein the content of the first and second substances,
Figure BDA0001742769170000035
Figure BDA0001742769170000036
is ηpAnd ηeDifference of (A), BpInput matrix of the primary spacecraft, BeAn input matrix for a secondary spacecraft;
since the function f (-) is at any point ηeThere is an arbitrary order derivative, therefore, f (η)p) At point ηeThe Taylor expansion is:
Figure BDA0001742769170000037
further obtaining:
Figure BDA0001742769170000038
wherein the content of the first and second substances,
Figure BDA0001742769170000039
is composed of
Figure BDA00017427691700000310
The high order infinitesimal quantity of (a),
Figure BDA00017427691700000311
is a sign of a gradient, which
Figure BDA00017427691700000312
Is defined as:
Figure BDA0001742769170000041
substituting formula (6) into formula (4) to obtain:
Figure BDA0001742769170000042
then, using an euler discretization method, discretizing equation (7) into:
Figure BDA0001742769170000043
wherein the content of the first and second substances,
Figure BDA0001742769170000044
Figure BDA0001742769170000045
is composed of
Figure BDA0001742769170000046
Value at time k, up,kIs the input value, u, of the primary spacecraft at the k-th timee,kIs the input value of the secondary spacecraft at the kth time instant.
Further, step 2 specifically includes:
step 2.1: initializing an error threshold
Figure BDA0001742769170000047
Admission control strategy
Figure BDA0001742769170000048
And a weight matrix
Figure BDA0001742769170000049
Let s ← 0; wherein the content of the first and second substances,
Figure BDA00017427691700000410
is a positive number;
Figure BDA00017427691700000411
and
Figure BDA00017427691700000412
is an initial control strategy;
Figure BDA00017427691700000413
is the initial value of the weight matrix; s is the number of iterations;
step 2.2: calculating Hamiltonian residual error:
Figure BDA00017427691700000414
wherein Q and R are positive definite matrixes; gamma is a preset positive number;
Figure BDA00017427691700000415
and
Figure BDA00017427691700000416
the control strategy value of the step s;
Figure BDA00017427691700000417
is the value of the weight matrix of the step s; e.g. of the typek,s+1Which is a residual error, is determined,
Figure BDA00017427691700000418
the expression is as follows:
Figure BDA00017427691700000419
in the formula (I), the compound is shown in the specification,
Figure BDA00017427691700000420
for neural network basis functions, the weight matrix is updated as follows
Figure BDA00017427691700000421
Figure BDA00017427691700000422
Wherein θ is a real number between 0 and 1;
step 2.3: let s ← s +1, calculate a value function and control strategy:
Figure BDA00017427691700000423
Figure BDA0001742769170000051
Figure BDA0001742769170000052
step 2.4: calculate and judge
Figure BDA0001742769170000053
If not, turning to step 2.2, if so, stopping iteration and outputting a control strategy
Figure BDA0001742769170000054
Compared with the prior art, the invention has the following beneficial technical effects:
the discrete self-adaptive dynamic planning pursuit escape game controller designed by the invention is convenient for engineering realization; in addition, the synchronous convergence self-adaptive dynamic programming iterative algorithm designed by the invention can effectively ensure that the control strategy is synchronously converged to an optimal value, and the algorithm can effectively process strong nonlinear characteristics existing in the system, obtain an approximate optimal control strategy and ensure that the system performance is optimal.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of simulation results of the present invention.
Detailed Description
The invention is described in further detail below:
the invention provides an optimal control strategy of zero-sum game synchronous convergence based on self-adaptive dynamic programming aiming at strong nonlinear characteristics in a spacecraft model. Firstly, establishing a pursuit game discrete system model of the spacecraft; secondly, designing a self-adaptive dynamic programming iteration control strategy of zero and game synchronous convergence; and finally, approximating an optimal control strategy by using a neural network.
As shown in fig. 1, the specific steps are as follows:
1. pursuit and escape game discrete model establishment
In the Euler-Hill coordinate system, the nonlinear relative motion equation of the aircraft is:
Figure BDA0001742769170000061
Figure BDA0001742769170000062
Figure BDA0001742769170000063
Figure BDA0001742769170000064
Figure BDA0001742769170000065
wherein x, y and z are position information of the aircraft in an Euler-Hill coordinate system; u. ofx，uyAnd uzIs a control input; mu is a universal gravitation constant; r iscAnd rdThe orbit radiuses of the main aircraft and the auxiliary aircraft are respectively; v is the true proximal angle of the main spacecraft orbit, superscript
Figure BDA0001742769170000066
The first derivative of x is represented as,
Figure BDA0001742769170000067
representing the second derivative of x.
Order to
Figure BDA0001742769170000068
The nonlinear first-hand equation of motion is written as a state space in the form:
Figure BDA0001742769170000069
wherein the content of the first and second substances,
Figure BDA00017427691700000610
where η is the state set, u is the input set, B is the input coefficient matrix, and I is the identity matrix.
Therefore, the nonlinear dynamics model of the main aircraft and the auxiliary aircraft is as follows:
Figure BDA00017427691700000611
Figure BDA0001742769170000071
wherein, ηpAnd upRespectively state vector and control input of the host aircraft ηeAnd ueRespectively, the state vector and control inputs for the secondary aircraft. Subtracting the formula (3) from the formula (2), the nonlinear escape pursuit game model is:
Figure BDA0001742769170000072
wherein the content of the first and second substances,
Figure BDA0001742769170000073
Figure BDA0001742769170000074
is ηpAnd ηeDifference of (A), BpInput matrix of the primary spacecraft, BeIs a pairAn input matrix for the spacecraft.
Since the function f (-) is at any point ηeThere is an arbitrary order derivative, therefore, f (η)p) At point ηeThe Taylor expansion is:
Figure BDA0001742769170000075
further, it is possible to obtain:
Figure BDA0001742769170000076
wherein the content of the first and second substances,
Figure BDA0001742769170000077
is composed of
Figure BDA0001742769170000078
The high order infinitesimal quantity of (a),
Figure BDA0001742769170000079
is a sign of a gradient, which
Figure BDA00017427691700000710
Is defined as:
Figure BDA00017427691700000711
when formula (6) is substituted into formula (4), it is possible to obtain:
Figure BDA00017427691700000712
then, the Euler discretization method is adopted, and the system (7) is discretized into the following components according to the sampling period T:
Figure BDA00017427691700000713
wherein the content of the first and second substances,
Figure BDA00017427691700000714
Figure BDA00017427691700000715
is composed of
Figure BDA00017427691700000716
Value at time k, up,kIs the input value, u, of the primary spacecraft at the k-th timee,kIs the input value of the secondary spacecraft at the kth time instant.
2. Adaptive dynamic planning pursuit escape game algorithm design
The synchronous self-adaptive dynamic planning pursuit game iterative algorithm based on the neural network is given as follows:
1) initializing an error threshold
Figure BDA0001742769170000081
Admission control strategy
Figure BDA0001742769170000082
And a weight matrix
Figure BDA0001742769170000083
Wherein the content of the first and second substances,
Figure BDA0001742769170000084
is a very small positive number;
Figure BDA0001742769170000085
and
Figure BDA0001742769170000086
is an initial control strategy;
Figure BDA0001742769170000087
is the initial value of the weight matrix; and s is the number of iterations. In the present example, it is shown that,
Figure BDA0001742769170000088
Figure BDA0001742769170000089
let s ← 0.
2) Computing Hamiltonian residual
Figure BDA00017427691700000810
Wherein Q and R are positive definite matrixes; gamma is a positive number which is preset in advance,
Figure BDA00017427691700000811
and
Figure BDA00017427691700000812
the control strategy value of the step s;
Figure BDA00017427691700000813
is the value of the weight matrix of the step s; e.g. of the typek,s+1Is the residual error. In this example, Q ═ diag ([ 111111)])，R＝diag([1 1 1])，γ＝20。
Figure BDA00017427691700000814
The expression is as follows:
Figure BDA00017427691700000815
in the formula (I), the compound is shown in the specification,
Figure BDA00017427691700000816
is a neural network basis function. In this example, σ (-) is defined as
σ(x)＝[tanh(x1) tanh(x2) tanh(x3) tanh(x4) tanh(x5) tanh(x6)]T
The weight matrix is updated as follows
Figure BDA00017427691700000817
Figure BDA00017427691700000818
Where θ is a real number between 0 and 1.
3) Let s ← s +1, calculate a value function and control strategy:
Figure BDA00017427691700000819
Figure BDA00017427691700000820
Figure BDA00017427691700000821
4) calculate and judge
Figure BDA00017427691700000822
If not, go to step 2). Otherwise, iteration stops and a control strategy is output
Figure BDA0001742769170000091
The simulation is carried out by adopting the method of the invention, as shown in figure 2,
Figure BDA0001742769170000092
is composed of
Figure BDA0001742769170000093
Of (1). As can be seen from the figure, the state error eventually converges to 0, indicating that the primary spacecraft has tracked the secondary spacecraft and can remain stable. Therefore, the spacecraft pursuit game method based on the neural network is effective.

Claims (2)

1. A spacecraft pursuit and escape game method based on a neural network is characterized by comprising the following steps:
step 1: establishing a pursuit game discrete system model of the spacecraft; the method specifically comprises the following steps:
in the Euler-Hill coordinate system, the nonlinear relative motion equation of the aircraft is:
Figure FDA0002537731560000011
Figure FDA0002537731560000012
Figure FDA0002537731560000013
Figure FDA0002537731560000014
Figure FDA0002537731560000015
wherein x, y and z are position information of the aircraft in an Euler-Hill coordinate system; u. ofx，uyAnd uzIs a control input; mu is a universal gravitation constant; r iscAnd rdThe orbit radiuses of the main aircraft and the auxiliary aircraft are respectively; v is the true proximal angle of the primary spacecraft orbit,
Figure FDA0002537731560000016
the first derivative of x is represented as,
Figure FDA0002537731560000017
represents the second derivative of x;
order to
Figure FDA0002537731560000018
Writing the nonlinear relative motion equation into a state space is in the form:
Figure FDA0002537731560000019
wherein the content of the first and second substances,
Figure FDA00025377315600000110
in the formula, eta is a state set, u is an input set, B is an input coefficient matrix, and I is a unit matrix;
therefore, the nonlinear dynamics model of the main aircraft and the auxiliary aircraft is as follows:
Figure FDA0002537731560000021
Figure FDA0002537731560000022
wherein, ηpAnd upRespectively state vector and control input of the host aircraft ηeAnd ueRespectively is the state vector and the control input of the auxiliary aircraft, and the nonlinear escape pursuit game model is obtained by subtracting the formula (3) from the formula (2):
Figure FDA0002537731560000023
wherein the content of the first and second substances,
Figure FDA0002537731560000024
Figure FDA0002537731560000025
is ηpAnd ηeDifference of (A), BpInput matrix of the primary spacecraft, BeAn input matrix for a secondary spacecraft;
since the function f (-) is at any point ηeThere is an arbitrary order derivative, therefore, f (η)p) At point ηeThe Taylor expansion is:
Figure FDA0002537731560000026
further obtaining:
Figure FDA0002537731560000027
wherein the content of the first and second substances,
Figure FDA0002537731560000028
is composed of
Figure FDA0002537731560000029
The high order infinitesimal quantity of (a),
Figure FDA00025377315600000210
is a sign of a gradient, which
Figure FDA00025377315600000211
Is defined as:
Figure FDA00025377315600000212
substituting formula (6) into formula (4) to obtain:
Figure FDA00025377315600000213
then, using an euler discretization method, discretizing equation (7) into:
Figure FDA00025377315600000214
wherein the content of the first and second substances,
Figure FDA0002537731560000031
Figure FDA0002537731560000032
is composed of
Figure FDA0002537731560000033
Value at time k, up,kIs the input value, u, of the primary spacecraft at the k-th timee,kThe input value of the auxiliary spacecraft at the kth moment;
step 2: and designing a self-adaptive dynamic programming iterative control strategy of zero and game synchronous convergence, and approximating an optimal control strategy by using a neural network.
2. The spacecraft escape pursuit gaming method based on the neural network as claimed in claim 1, wherein the step 2 specifically comprises:
step 2.1: initializing an error threshold
Figure FDA00025377315600000321
Admission control strategy
Figure FDA0002537731560000034
And a weight matrix
Figure FDA0002537731560000035
Let s ← 0; wherein the content of the first and second substances,
Figure FDA00025377315600000322
is a positive number;
Figure FDA0002537731560000036
and
Figure FDA0002537731560000037
is an initial control strategy;
Figure FDA0002537731560000038
is the initial value of the weight matrix; s is the number of iterations;
step 2.2: calculating Hamiltonian residual error:
Figure FDA0002537731560000039
wherein Q and R are positive definite matrixes; gamma is a preset positive number;
Figure FDA00025377315600000310
and
Figure FDA00025377315600000311
the control strategy value of the step s;
Figure FDA00025377315600000312
is the value of the weight matrix of the step s; e.g. of the typek,s+1Which is a residual error, is determined,
Figure FDA00025377315600000313
the expression is as follows:
Figure FDA00025377315600000314
in the formula (I), the compound is shown in the specification,
Figure FDA00025377315600000315
for neural network basis functions, the weight matrix is updated as follows
Figure FDA00025377315600000316
Figure FDA00025377315600000317
Wherein θ is a real number between 0 and 1;
step 2.3: let s ← s +1, calculate a value function and control strategy:
Figure FDA00025377315600000318
Figure FDA00025377315600000319
Figure FDA00025377315600000320
step 2.4: calculate and judge
Figure FDA0002537731560000041
If not, turning to step 2.2, if so, stopping iteration and outputting a control strategy
Figure FDA0002537731560000042
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