CN105005651B - Optimization Design between the gradient cut section of spacecraft pulse intersection track - Google Patents

Abstract

The present invention be a kind of spacecraft pulse intersection track gradient cut section between Optimization Design, belong to the Track desigh in spacecraft orbit dynamic and control field and optimisation technique, particularly based on the Orbit of Rendezvous designing technique of the Spacecraft Rendezvous track global optimization solution utilizing Interval Computation mathematic(al) mode to calculate.For the matter of the whole of method, gradient optimizing result is only used for determining interal separation point and upgrading the objective function value upper bound by the present invention, has saved the of overall importance of range optimization algorithm from damage; For the problem that range optimization algorithm calculated amount is large, introduce gradient optimizing method, to upgrade the objective function value upper bound fast and to use gradient split plot design, combined symbol split plot design and range optimization strategy, effectively be separated and remove the interval not comprising optimum solution, improve operation efficiency; For the problem that the storage demand solving range optimization algorithm is high, iteration is only chosen limited interval and is processed each time, ensures not occur storage space spillover in computing.

Description

Optimization Design between the gradient cut section of spacecraft pulse intersection track

Technical field

The invention belongs to the Track desigh in spacecraft orbit dynamic and control field and optimisation technique, relating to a spacecraft utilizes the thrust of the jet thrust device generations such as the rocket engine carried by it and predetermined natural celestial body or another spacecraft to arrive the designing technique of the Orbit of Rendezvous of same position at one time with identical speed, particularly based on the Orbit of Rendezvous designing technique of the Spacecraft Rendezvous track global optimization solution utilizing Interval Computation mathematic(al) mode to calculate.

Background technology

In the task analysis of spacecraft, Track desigh occupies critical positions.In track design objective, a spacecraft applies acting force, the design making itself and predetermined nature celestial body or another spacecraft arrive the Orbit of Rendezvous of same position at one time with identical speed is the condition precedent that multiple space mission realizes.These tasks comprise: the maintenance in-orbit etc. of the detection of the spacecrafts rendezvous of space platform (as space station) in orbit and other spacecraft (as manned shuttle vehicle, space transoportation freighter), natural celestial body and landing, in-orbit spacecraft.The quantity realizing the possible track of intersection is infinite many in theory, so Orbit of Rendezvous design objective just becomes a track optimizing task, and the result that the track namely finding out certain Least-cost from above-mentioned infinite multiple track designs as Orbit of Rendezvous.So-called Least-cost can be that the flight time is the shortest, fuel consumption is minimum.The benefit that this optimization brings comprises the reduction of space mission cost, the raising etc. of space mission efficiency.Therefore, the design optimizing of Spacecraft Rendezvous track has very important position in aerospace engineering.

The realization of Spacecraft Rendezvous track generally can be divided into two kinds of approach.Use various rocket engines for traditional, ripe use chemical propellant, by instruction rocket engine predetermined instant carry out the short time, the igniting that can be considered pulse action, produce the acting force that spacecraft is flown by predetermined Orbit of Rendezvous.Another kind of use advanced, not yet full-fledged, that low thrust can be exported continuously various thrusters at present, in flight course all or in part, carry out long thrust output by instruction thruster, produce the acting force realizing intersection.

The Optimization Design of Spacecraft Rendezvous track can be divided into indirect method, direct method and mixing method three major types.Indirect method utilizes variational principle and Pang Te lia king maximal principle that Spacecraft Rendezvous Orbit Optimized problem is converted into the two-point boundary value problem meeting necessary condition for optimality and solves.Under given conditions, use indirect method can obtain the analytic solution of Spacecraft Rendezvous Orbit Optimized, but in most cases, become abnormal difficult by the susceptibility of the non-linear integral operation caused to association's state initial value of problem by making solving of problem.Direct method utilizes and the nonlinear programming problem that Spacecraft Rendezvous Orbit Optimized problem is converted into multidimensional is solved the discretize of quantity of state and control function and parametrization.Research about direct method uses based on the Sequential Quadratic Programming method of gradient or based on bionic intelligent optimization algorithm mostly, as genetic algorithm, simulated annealing, Artificial Immune Algorithm, particle cluster algorithm, ant group algorithm.The shortcoming of Sequential Quadratic Programming method is that it can only ensure to obtain the characteristic of locally optimal solution to the susceptibility of the initial guess of parameter and its.The shortcoming of intelligent optimization algorithm is that it cannot ensure its Global Optimality separated.Direct method and indirect method are combined use by mixing method, introduce association's state on the one hand to determine necessary condition for optimality, introduce parametric method on the other hand and solve optimal control problem.Research about mixing method often uses the method for solving identical with direct method, therefore also has the shortcoming similar to direct method research.

Above-mentionedly all belong to randomness optimization method based on bionic intelligent optimization algorithm.The ultimate principle of randomness optimization method is: from selected initial guess, by generating new conjecture value to the random perturbation of initial guess, and repeat this process until reach termination condition given in advance.When long enough operation time, randomness optimization method can obtain the solution of approaching globally optimal solution with high probability in theory.But in actual use, the Global Optimality of the operation result of randomness optimization method is undemonstrable.Relative to randomness optimization method, what deterministic optimization method was determined by structure puts by limited point or to unlimited that delimits interior the sequence formed, and by iterative process, this sequence converges is included in enough little compass in globally optimal solution or by globally optimal solution.

Interval Optimization Method is exactly a kind of determinacy global optimization method received much concern in recent years.Interval Optimization Method is based on the Study on Interval Analysis Theory proposed clearly and systematically in the works " IntervalAnalysis " of publication in 1966 by American scholar RamonEdgarMoore, by the segmentation to interval, progressively get rid of the interval that can not comprise globally optimal solution, and the final list obtaining interval that contain globally optimal solution, that meet pre-provisioning request.Within 2010, Erik-JanvanKampen is at AIAAGuidance, Navigation, the paper " Optimizationofspacecraftrendezvousanddockingusinginterva lanalysis " that andControlConference delivers gives comparing of an interval Optimization Method and gradient optimizing method, result shows that gradient optimizing method converges on non-globally optimal solution when processing the non-convex optimization problem closer to reality, and interval Optimization Method still can obtain globally optimal solution.But range optimization algorithm is also because storage space is excessive needed for computing, calculated amount is large, the shortcomings such as speed of convergence is slow, pind down in practicality, Chen Cheng in 2014 give also above-mentioned viewpoint at the paper of Shanghai University's application master's degree " realizing based on the research of the parallel global optimizing algorithm of intervl mathematics and system " by name.Much research is attempted by being combined to solve the problem with other optimization methods by interval Optimization Method.The paper of keeping gentle room few pure " a kind of novel interval-particle swarm optimization algorithm " by name delivered on " Northeastern University's journal (natural science edition) " 2012 end of the year discloses a kind of method be combined with interval Optimization Method by particle cluster algorithm, but the result of calculation provided in literary composition shows, objective function codomain interval is very close but do not comprise actual optimum value.The people such as TongChen in 2013 are at " JournalofGuidance, ControlandDynamics " on the paper of by name " Optimizationoftime-openconstrainedLambertrendezvoususing intervalanalysis " delivered indicate that interval Optimization Method storage demand is excessive, in computing, internal memory such as easily to overflow at the deficiency, and disclose a kind of for spacecraft pulse intersection Optimal design of trajectory, the method that interval Optimization Method and gradient optimizing method combine, the method first uses interval Optimization Method to try to achieve the still satisfied predetermined interval comprising global optimum required of some interval width, then use gradient optimizing method instead and carry out local optimum calculating, improve optimization efficiency, but its cost is the Global Optimality that cannot ensure optimum results.

In summary, although the Optimization Design of spacecraft pulse intersection track has a lot of existing method available, each have their own weakness, and the Global Optimality that generally cannot ensure optimum results.And can ensure that the weakness of the existing interval Optimization Method of trying to achieve globally optimal solution is mainly that operand when being applied to practical problems is large, storage demand this 2 point high in theory, the method for existing this two problems of solution is often to destroy the guarantee of Global Optimality for cost.

Summary of the invention

For the deficiency that above-mentioned prior art exists, the present invention proposes a kind of for spacecraft pulse intersection Optimal design of trajectory, based on the method for range optimization theory.

For solving the problems of the technologies described above, technical scheme of the present invention is as follows:

According to the spacecraft pulse intersection track optimizing model that adopts or set up, construct the Global Optimal Problem based on Study on Interval Analysis Theory and according to the following step, set up Global Optimal Problem solved:

Step 1, intervalization process is carried out to spacecraft pulse intersection track optimizing model, comprises following sub-step:

Sub-step 1.1, the impulse force effect times N that should use in given spacecraft pulse intersection process (N be more than or equal to 2 natural number), get last impulse force t action time _f, last impulse force t action time _fand t interval time between each subpulse time of thrust application except last impulse force _{i → f}component (the v of the speed increment that (i=1,2...N-1), each subpulse thrust are brought to pursuit spacecraft _ix, v _iy, v _iz) (i=1,2 ..., N) as decision variable, and form decision variable interval [u]=[[v by the possible span of each decision variable _1x], [v _1y], [v _1z] ..., [v _{(N-1) x}], [v _{(N-1) y}], [v _{(N-1) z}], [t _{1 → f}], [t _{2 → f}] ..., [t _{n-1 → f}], [t _f]].

Sub-step 1.2, by the relative distance constraint S of X, Y, the Z tri-under relative coordinate system during Spacecraft Rendezvous on direction of principal axis _iu (i=x, y, z) is converted into inequality constrain in ()=0 | [S _i] ([u]) | (ε is little arithmetic number to < ε; I=x, y, z) and equation characteristic formp 0 ∈ [S _i] ([u]) (i=x, y, z).[S _i] ([u]) (i=x, y, z) represent the relative distance function in i direction;

Sub-step 1.3, the interval extension getting fuel optimal conditions is objective function and the upper bound J of given objective function value _mininitial value;

Sub-step 1.4, decision variable interval number M, the predetermined positive number δ of each inspection of setting _uwith predetermined positive number δ _j;

Step 2, according to spacecraft pulse intersection track optimizing model, interal separation is carried out to decision-making range of variables [u], be called " symbol segmentation method ", comprise following sub-step:

Sub-step 2.1, by the component ([v of the speed increment that each subpulse thrust is brought to pursuit spacecraft _ix], [v _iy], [v _iz]) (i=1,2 ..., N) be that boundary is respectively divided into only containing on the occasion of interval with the component only containing two speed increments of negative value with 0;

Sub-step 2.2, by last impulse force [t action time _f], last [t interval time between impulse force action time and each subpulse time of thrust application except last impulse force _{i → f}] (i=1,2...N-1), with the quadrant of used spacecraft pulse intersection track optimizing model intermediate cam function for boundary is respectively divided into multiple time interval;

Sub-step 2.3, by the component of the speed increment of sub-step 2.1 and sub-step 2.2 gained, to obtain Q decision variable interval for interval and time interval combination in any, and Q described decision variable is interval forms interval group's queue L;

Step 3, interval selection strategy, according to the interval number M of the decision variable of each inspection of setting, if Q≤M, then make M=Q, select M decision variable interval composition sub-range queue L1 at the most from interval group's queue L assigned address, from interval group's queue L, delete M at the most the decision variable selected interval simultaneously;

Step 4, uses on each the decision variable interval in the sub-range queue L1 of the optimized algorithm based on gradient respectively selected by step 3 and solves spacecraft pulse intersection track optimizing problem, one of proceed as follows respectively by solving result:

Step 4 result 1: any one the decision variable interval [u in sub-range queue L1 _□] on, the optimized algorithm based on gradient has solution, carries out the operation of following sub-step 4.1 and sub-step 4.2:

Sub-step 4.1, gradient split plot design, namely centered by the decision variable value of this solution correspondence, decision variable value expanded to [I between the expansion area of the solution of the optimized algorithm included based on gradient for radius to the numerical value of sizing _Δ], with [I between expansion area _Δ] the boundary value of each interval variable split described decision variable interval [u respectively _□] each corresponding interval variable, by decision variable interval [u _□] each interval variable be divided into 3 intervals or 2 intervals, and combined as interval queue Lnew;

Sub-step 4.2, the upper bound based on the objective function value of gradient upgrades, [I between the expansion area namely decision variable value being expanded to the solution of the optimized algorithm included based on gradient centered by the decision variable value of this solution correspondence, with very little numerical value for radius _{Δ 1}], utilize Study on Interval Analysis Theory [I between expansion area _{Δ 1}] upper calculating, check whether the interval upper bound of the objective function of its constraint condition whether meeting spacecraft pulse intersection track optimizing model, its correspondence is less than the upper bound J of objective function value _min, when above-mentioned two results checked are all "Yes", with [I between expansion area _{Δ 1}] upper bound in corresponding objective function interval upgrades the upper bound J of objective function value _min, otherwise keep the upper bound J of existing objective function value _minconstant;

Step 4 result 2: any one the decision variable interval [u in sub-range queue L1 _□] on, the optimized algorithm based on gradient is not separated, with decision variable interval [u _□] on the interval midpoint of each interval variable split each interval variable respectively, by decision variable interval [u _□] each interval variable be divided into 2 intervals, and combined as interval queue Lnew;

Step 5, interval deletion strategy, namely carries out interval analysis respectively, and carries out the operation of following sub-step 5.1 ~ sub-step 5.4 on each decision variable interval of the interval queue Lnew of step 4 gained:

Sub-step 5.1, if relative distance constraint S _iu in ()=0 (i=x, y, z), each impulse speed is linear correlation, then utilize the decision variable except the component of the speed increment brought to pursuit spacecraft except jth subpulse thrust in decision variable interval [u] to pass through

[S _i] to solve the component of the speed increment that jth subpulse thrust is brought to spacecraft interval in ([u])=0 (i=x, y, z)

[[v _{jx_f}], [v _{jy_f}], [v _{jz_f}]] (j=1,2...N-1), and calculate itself and [[v in [u] _jx], [v _jy], [v _jz]] common factor

[[v _{jx_new}], [v _{jy_new}], [v _{jz_new}]], if this common factor is empty set, then this decision variable interval [u] is deleted from interval queue Lnew, otherwise the component interval upgrading the speed increment that the jth subpulse thrust in decision variable interval [u] is brought to pursuit spacecraft is [[v _{jx_new}], [v _{jy_new}], [v _{jz_new}]], and obtain the interval queue Lnew of renewal simultaneously;

Sub-step 5.2, checks whether each the decision variable interval in the interval queue Lnew after step 5.1 upgrades meets relative distance constraint condition, and is deleted from interval queue Lnew in the decision variable interval not meeting relative distance constraint condition;

Sub-step 5.3, appoints and gets 3 speed increment variablees corresponding to pulsatile once effect in decision variable, according to relative distance constraint S _i(u)=0 (i=x, y, z), 3 speed increment variablees of specifying can be expressed as the function of other decision variables, be the spacecraft pulse intersection track optimizing model that is decision variable with its dependent variable except 3 named variables by spacecraft pulse intersection track optimizing model conversation with this, check and whether each the decision variable interval in the interval queue Lnew of objective function J after processing through step 5.2 comprises 0 to the first-order partial derivative interval of new decision variable, if check result is no, then corresponding decision variable interval is deleted from interval queue Lnew;

Sub-step 5.4, to the interval upper bound J checking objective function interval and objective function value respectively of each decision variable in the interval queue Lnew after sub-step 5.3 process _minbetween relation, and carry out the operation of following grandson step 5.4.1 and grandson step 5.4.2:

Grandson step 5.4.1, if the lower bound in objective function interval is greater than the upper bound J of objective function value _min, then corresponding decision variable interval is deleted from interval queue Lnew;

Grandson step 5.4.2, if the upper bound in objective function interval is less than the upper bound J of objective function value _min, then the upper bound J of objective function value is upgraded _minfor the upper bound in objective function interval;

Step 6, interval deflation strategy, namely checks relative distance function [S _i] in ([u]) (i=x, y, z) interval queue Lnew after processing through step 5 on each decision variable interval [u] to [u] in the monotonicity of each interval variable, and carry out the operation of following sub-step 6.1:

Sub-step 6.1, if interval to any one decision variable in interval queue Lnew, relative distance function [S _i] ([u]) to the interval variable [u of the kth in decision-making range of variables [u] _k] be dull, and [u _k] lower bound place [S _i] ([u _k] .inf) or [u _k] upper bound place

[S _i] ([u _k] .sup) and symbol be just or be negative, then at [u _k] in find be greater than [u _k] lower bound and the [S of correspondence _i] and [u _k] lower bound place

[S _i] ([u _k] .inf) u of jack per line _k1if do not have, then make u _k1=[u _k] .inf; Searching is less than [u _k] upper bound and the [S of correspondence _i] and [u _k] on

Place of boundary [S _i] ([u _k] .sup) u of jack per line _k2if do not have, then make u _k2=[u _k] .sup; With interval [u _k1, u _k2] upgrade the kth interval variable [u of the corresponding decision range of variables [u] in this interval queue Lnew _k], wherein, [u _k] .inf represents [u _k] lower bound, [u _k] .sup represents [u _k] the upper bound;

Step 7, the interval end condition of each decision variable between test zone in queue Lnew, the width B in the width A in each the decision variable interval namely between test zone in queue Lnew and the objective function interval corresponding to each the decision variable interval in interval queue Lnew, wherein the width in decision variable interval is the maximal value of the width of all interval variables in decision variable interval, performs the operation of following sub-step 7.1 and sub-step 7.2:

Sub-step 7.1, when above-mentioned width A is less than predetermined positive number δ _u, or width B is less than predetermined positive number δ _jtime, corresponding decision variable interval is deleted from interval queue Lnew, and described corresponding decision variable interval is inserted in the interval queue R of design result;

Sub-step 7.2, after the operation to the interval completing steps 7.1 of each decision variable in interval queue Lnew, upgrade interval group's queue L, the deletion point that interval group's queue L deletes M at the most interval of selection is in step 3 inserted into, using the interval group's queue L after queue Lnew between insert district as new interval group's queue L by interval queue Lnew;

Step 8, the number in decision variable interval in group's queue L between test zone, and carry out one of following operation respectively according to result:

Step 8 result 1, in interval group's queue L, the number in decision variable interval is not 0, then proceed to step 3, continues design operation;

Step 8 result 2, in interval group's queue L, the number in decision variable interval is 0, then design end;

Step 9, appoint from the interval queue R of design result and get a design result interval, in the interval of each interval variable in selected design result interval, any value combines, and the speed increment that the last impulse force effect accordingly that calculates brings to pursuit spacecraft, just obtain an optimal design solution of aforementioned spacecraft pulse intersection track.

Preferably, assigned address described in the step 3 of said method is the tail of the queue of interval group's queue L, in the sub-step 7.2 corresponded, interval queue Lnew is placed in interval group's queue L tail of the queue to form new interval group's queue L.

Preferably, assigned address described in the step 3 of said method is the head of the queue of interval group's queue L, in the sub-step 7.2 corresponded, interval group's queue L is placed in interval queue Lnew tail of the queue to form new interval group's queue L.

Two kinds of preferred versions of above-mentioned steps 3 make the deletion of interval group's queue L and renewal rewards theory more convenient.

Preferably, at [u in the sub-step 6.1 of said method _k] in find be greater than [u _k] lower bound and the [S of correspondence _i] and [u _k] lower bound place [S _i] ([u _k] .inf) the maximal value u of jack per line _k3if do not have, then make u _k3=[u _k] .inf, find and be less than [u _k] upper bound and the [S of correspondence _i] and [u _k] upper bound place [S _i] ([u _k] .sup) jack per line minimum value u _k4if do not have, then make u _k4=[u _k] .sup, with interval [u _k3, u _k4] upgrade the kth interval variable [u of the corresponding decision range of variables [u] in this interval queue Lnew _k].

The preferred version of above-mentioned sub-step 6.1 will obtain better interval deflation result.

Preferably, in the step 9 of said method, the upper bound of getting a corresponding objective function interval from design result interval queue R is the upper bound J of objective function value _mindesign result interval, in selected design result interval, in the interval of each decision variable, any value combines, and the speed increment that the last impulse force effect accordingly that calculates brings to pursuit spacecraft, just obtain an optimal design solution of aforementioned spacecraft pulse intersection track.

The preferred version of above-mentioned steps 9 by the target function value that ensures corresponding to design result not higher than J _min.

Compared with prior art, beneficial effect of the present invention is the Global Optimality that ensure that gained design result.In the present invention, can not ensure that because depending on Initial value choice the optimization method based on gradient obtaining globally optimal solution is used in step 4.But based on the operation result of the optimization method of gradient only for determining interal separation point and upgrading the upper bound of objective function value, the present invention is a kind of interval Optimization Method completely, and therefore inherits the Global Optimality of interval Optimization Method.

Compared with prior art, beneficial effect of the present invention is also that to the maximal value of the demand in Computer Storage space be pre-determined, and this will cause the abnormal situation of interrupting of design process to occur to thus avoid memory space inadequate (spilling) that range optimization algorithm may occur.This beneficial effect provides primarily of the step 3 in technique scheme.According to step 3, each limited individual (maximum M) interval of only selecting from pending interval group processes, and M value can be arranged according to the storage space of used computing machine, and therefore can ensure not occur storage space spillover in design process.

Compared with prior art, beneficial effect of the present invention is also the raising of design efficiency, namely obtains the minimizing of design result required time.This beneficial effect provides primarily of the step 2 in technique scheme and step 4-step 6.According to step 2, the whole region of search is divided into multiple interval, avoid because interval comprises 0 and the too extensive interval extension caused, be conducive to carrying out in early days and the quick minimizing of consequent pending interval quantity of interval deletion action, and thereby reduce design process required time.According to step 4, based on the use of the operation result of the optimization method of gradient, be conducive to utilizing the information of locally optimal solution or globally optimal solution to upgrade the upper bound of objective function value fast.According to step 4, the optimization method computing acquired results based on gradient is utilized to carry out interal separation, be conducive to obtaining fast the decision variable interval having and comprise local optimum and there is less interval width, be also conducive to other and do not comprise giving up fast of optimum solution interval.These two advantages provided by step 4 are obviously conducive to the minimizing of design process required time.According to the operation of step 5, be conducive to reducing the number in pending interval and upgrading the upper bound of objective function value, and be therefore conducive to the minimizing of design process required time.According to step 6, local monotonicity in constraint condition is used to the width reducing pending interval further, be conducive to the reduction of interval extension in interval analysis computing, and be therefore conducive to carrying out in early days of interval deletion action, thereby produce the effect reducing design process required time.

Accompanying drawing explanation

Fig. 1 be spacecraft pulse intersection track provided by the invention gradient cut section between the schematic flow sheet of Optimization Design;

Fig. 2 is the schematic diagram that the step 3-step 7 of method provided by the invention performs interval group's queue change in the process of twice continuously;

Fig. 3 is the renewal process schematic diagram based on the upper bound of gradient objective function value in method provided by the invention;

Fig. 4 be gained according to one embodiment of present invention two spacecrafts between the schematic diagram of relative movement orbit;

Fig. 5 is the schematic diagram of the interval queue of Optimum Design Results of gained according to one embodiment of present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the present invention is described in further detail.

For the dipulse spacecrafts rendezvous optimization problem of on-fixed time, relative coordinate system X-axis in orbit plane along passive space vehicle heading, Z axis points to the earth's core from passive space vehicle barycenter, Y-axis meets right hand orthogonal coordinate system, perpendicular to orbit plane, and following CW equation approximate description is adopted to set up spacecraft pulse intersection track optimizing model:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{x}-2\mathrm{\&omega;}\stackrel{\&CenterDot;}{z}=0\\ \stackrel{\&CenterDot;\&CenterDot;}{y}+{\mathrm{\&omega;}}^{2}y=0\\ \stackrel{\&CenterDot;\&CenterDot;}{z}+2\mathrm{\&omega;}\stackrel{\&CenterDot;}{x}-3{\mathrm{\&omega;}}^{2}z=0\end{array}\right.---\left(1\right)$

In formula, ω is passive space vehicle orbit angular velocity, and x, y, z is respectively pursuit spacecraft relative position in the X, Y, Z direction, be respectively pursuit spacecraft relative velocity in the X, Y, Z direction, be respectively pursuit spacecraft relative acceleration in the X, Y, Z direction.

Through type (1), can obtain t pursuit spacecraft relative to the relative position of passive space vehicle and speed as follows:

$\{\begin{array}{c}x\left(t\right)=\left(\frac{4{\stackrel{\&CenterDot;}{x}}_0}{\mathrm{\&omega;}}-6z_0\right)\sin \left(\mathrm{\&omega;}t\right)-\frac{2{\stackrel{\&CenterDot;}{z}}_0}{\mathrm{\&omega;}}\cos \left(\mathrm{\&omega;}t\right)+\left(6{\mathrm{\&omega;z}}_0-3{\stackrel{\&CenterDot;}{x}}_0\right)t+\left(x_0+\frac{2{\stackrel{\&CenterDot;}{z}}_0}{\mathrm{\&omega;}}\right)\\ y\left(t\right)=y_0\cos \left(\mathrm{\&omega;}t\right)+\frac{{\stackrel{\&CenterDot;}{y}}_0}{\mathrm{\&omega;}}\sin \left(\mathrm{\&omega;}t\right)\\ z\left(t\right)=\left(\frac{2{\stackrel{\&CenterDot;}{x}}_0}{\mathrm{\&omega;}}-3z_0\right)\cos \left(\mathrm{\&omega;}t\right)+\frac{{\stackrel{\&CenterDot;}{z}}_0}{\mathrm{\&omega;}}\sin \left(\mathrm{\&omega;}t\right)+\left(4z_0-\frac{2{\stackrel{\&CenterDot;}{x}}_0}{\mathrm{\&omega;}}\right)\\ \stackrel{\&CenterDot;}{x}\left(t\right)=\left(4{\stackrel{\&CenterDot;}{x}}_0-6{\mathrm{\&omega;z}}_0\right)\cos \left(\mathrm{\&omega;}t\right)+2{\stackrel{\&CenterDot;}{z}}_0\sin \left(\mathrm{\&omega;}t\right)+\left(6{\mathrm{\&omega;z}}_0-3{\stackrel{\&CenterDot;}{x}}_0\right)\\ \stackrel{\&CenterDot;}{y}\left(t\right)=-{\mathrm{\&omega;y}}_0\sin \left(\mathrm{\&omega;}t\right)+{\stackrel{\&CenterDot;}{y}}_0\cos \left(\mathrm{\&omega;}t\right)\\ \stackrel{\&CenterDot;}{z}\left(t\right)=\left(3{\mathrm{\&omega;z}}_0-2{\stackrel{\&CenterDot;}{x}}_0\right)\sin \left(\mathrm{\&omega;}t\right)+{\stackrel{\&CenterDot;}{z}}_0\cos \left(\mathrm{\&omega;}t\right)\end{array}---\left(2\right)$

In formula, (x ₀, y ₀, z ₀) and be respectively initial position and the initial velocity in pursuit spacecraft 0 moment.

If the moment of pursuit spacecraft and passive space vehicle intersection is t _f.From 0 moment, at t ₁in the moment, pursuit spacecraft applies first time pulse, and impulse force effect is v to the speed increment that pursuit spacecraft brings ₁(v _1x, v _1y, v _1z).Through t _{1 → f}=t _f-t ₁time, at t _fin the moment, pursuit spacecraft applies second time pulse, and impulse force effect is v to the speed increment that pursuit spacecraft brings ₂(v _2x, v _2y, v _2z), two Spacecraft Rendezvous.

Through type (2) can obtain intersection moment t _frelative distance S and relative velocity V, and make S=0 and V=0.

S(t ₁,t _f,v ₁)＝0

（3）

V(t ₁,t _f,v ₁,v ₂)＝0

Then (3) formula is with t ₁, t _f, v ₁, v ₂for the constraint condition of the spacecraft pulse intersection track optimizing model of decision variable, be respectively relative distance constraint and relative velocity constraint.

If only consider the requirement to fuel consumption, then the objective function of spacecraft pulse intersection track optimizing model is:

$J=\underset{i=1}{\overset{2}{\&Sigma;}}\left|{\mathrm{\&nu;}}_i\right|=\underset{i=1}{\overset{2}{\&Sigma;}}\sqrt{{\left(v_{ix}\right)}^2+{\left(v_{iy}\right)}^2+{\left(v_{iz}\right)}^2}---\left(4\right)$

J gets minimum value, then dipulse intersection fuel consumption is minimum.

Adopt Optimization Design between the gradient cut section of spacecraft pulse intersection track to solve above Optimized model, between the gradient cut section of spacecraft pulse intersection track, the schematic flow sheet of Optimization Design, as shown in Figure 1, specifically comprises the steps:

Step 1, intervalization process is carried out to spacecraft pulse intersection track optimizing model, comprises following sub-step:

Sub-step 1.1, assuming that two spacecrafts move in the orbit plane of passive space vehicle, then has decision variable interval

[u]＝[[v _1x],[v _1z],[t _1→f],[t _f]]。

Sub-step 1.2, the relative velocity constraint V=0 speed increment (v that can be brought to pursuit spacecraft by the effect of second time impulse force at Spacecraft Rendezvous place _2x, v _2y, v _2z) ensured.And for relative distance constraint S=0, because two spacecrafts move in the orbit plane of passive space vehicle, so S=0 can be decomposed into S _x=0, S _z=0.By S _x=0, S _z=0 is converted into inequality constrain form | [S _x] ([u]) | < ε, | [S _z] ([u]) | < ε (ε is little arithmetic number) and equation characteristic formp 0 ∈ [S _x] ([u]), 0 ∈ [S _z] ([u]).[S _x] ([u]) represent the relative distance function in x direction, [S _z] ([u]) represent the relative distance function in z direction.

Sub-step 1.3, the interval extension getting fuel optimal conditions is objective function $J=\underset{i=1}{\overset{N}{\&Sigma;}}\left|{\mathrm{\&nu;}}_i\right|=\underset{i=1}{\overset{N}{\&Sigma;}}\sqrt{{\left(v_{ix}\right)}^2+{\left(v_{iy}\right)}^2+{\left(v_{iz}\right)}^2},$ And the upper bound J of given objective function value _mininitial value; N=2.

Sub-step 1.4, decision variable interval number M, the predetermined positive number δ of each inspection of setting _uwith predetermined positive number δ _j;

Step 2, uses symbol segmentation method, comprises following sub-step:

Sub-step 2.1, by the component [v of the speed increment that first time impulse force effect brings to pursuit spacecraft _1x] and [v _1z] be that boundary is respectively divided into only containing on the occasion of interval with the component only containing two speed increments of negative value with 0;

Sub-step 2.2, will second time impulse force [t action time _f], [t interval time between second time impulse force action time and impulse force action time first time _{1 → f}], with the quadrant of used spacecraft pulse intersection track optimizing model intermediate cam function for boundary is respectively divided into multiple time interval;

Sub-step 2.3, by the component of the speed increment of sub-step 2.1 and sub-step 2.2 gained, to obtain Q decision variable interval for interval and time interval combination in any, and Q described decision variable is interval forms interval group's queue L;

Step 3, according to the interval number M of the decision variable of each inspection of setting, if Q≤M, then make M=Q, M decision variable interval composition sub-range queue L1 is at the most selected from interval group's queue L tail of the queue (or optional position), from interval group's queue L, delete M at the most the decision variable selected interval, step 3 ~ step 7 performs the signal of interval group's queue change in the process of twice continuously, as shown in Figure 2 simultaneously;

Step 4, uses on each the decision variable interval in the sub-range queue L1 of the optimized algorithm based on gradient respectively selected by step 3 and solves spacecraft pulse intersection track optimizing problem, one of proceed as follows respectively by solving result:

Step 4 result 1: any one the decision variable interval [u in sub-range queue L1 _□] on, the optimized algorithm based on gradient has solution, carries out the operation of following sub-step 4.1 and sub-step 4.2:

Sub-step 4.1, centered by the decision variable value of this solution correspondence, decision variable value expanded to [I between the expansion area of the solution of the optimized algorithm included based on gradient for radius to the numerical value of sizing _Δ], with [I between expansion area _Δ] the boundary value of each interval variable split described decision variable interval [u respectively _□] each corresponding interval variable, by decision variable interval [u _□] each interval variable be divided into 3 intervals or 2 intervals, and combined as interval queue Lnew;

Sub-step 4.2, based on the renewal in the objective function value upper bound of gradient, [I between the expansion area namely decision variable value being expanded to the solution of the optimized algorithm included based on gradient centered by the decision variable value of this solution correspondence, with very little numerical value for radius _{Δ 1}], utilize Study on Interval Analysis Theory [I between expansion area _{Δ 1}] on calculate, check whether the interval upper bound of the objective function of its constraint condition whether meeting spacecraft pulse intersection track optimizing model, its correspondence is less than the upper bound J of objective function value _min, when above-mentioned two results checked are all "Yes", with [I between expansion area _{Δ 1}] upper bound in corresponding objective function interval upgrades the upper bound J of objective function value _min, otherwise keep the upper bound J of existing objective function value _minconstant, process schematic as shown in Figure 3;

Step 4 result 2: the decision variable interval [u in sub-range queue L1 _□] on, the optimized algorithm based on gradient is not separated, with decision variable interval [u _□] on each interval variable mid point split each interval variable respectively, by decision variable interval [u _□] each interval variable be divided into 2 intervals, and combined as interval queue Lnew;

Step 5, interval deletion strategy, namely carries out interval analysis respectively, and carries out the operation of following sub-step 5.1 ~ sub-step 5.4 on each decision variable interval of the interval queue Lnew of step 4 gained:

Sub-step 5.1, if relative distance constraint S _iu in ()=0 (i=x, y, z), each impulse speed is linear correlation, then utilize interval variable [t in decision variable interval [u] _{1 → f}] and [t _f], by [S _i] ([u])=0 (i=x, z) solve component the interval [[v of the speed increment that first time impulse force effect brings to pursuit spacecraft _{1x_f}], [v _{1z_f}]], and calculate itself and [[v in [u] _1x], [v _1z]] common factor

[[v _{1x_new}], [v _{1z_new}]], if this common factor is empty set, then this decision variable interval [u] is deleted from interval queue Lnew, otherwise the component interval upgrading the speed increment that the first time impulse force effect in decision variable interval [u] brings to pursuit spacecraft is [[v _{1x_new}], [v _{1z_new}]], and obtain the interval queue Lnew of renewal simultaneously;

Sub-step 5.2, checks whether each the decision variable interval in the interval queue Lnew after step 5.1 upgrades meets relative distance constraint condition, and is deleted from interval queue Lnew in the decision variable interval not meeting relative distance constraint condition;

Sub-step 5.3, appoints and gets 3 speed increment variablees corresponding to pulsatile once effect in decision variable, according to relative distance constraint S _i(u)=0 (i=x, y, z), 3 speed increment variablees of specifying can be expressed as the function of other decision variables, be the spacecraft pulse intersection track optimizing model that is decision variable with its dependent variable except 3 named variables by spacecraft pulse intersection track optimizing model conversation with this, check and whether each the decision variable interval in the interval queue Lnew of objective function J after processing through sub-step 5.2 comprises 0 to the first-order partial derivative interval of new decision variable, if check result is no, then corresponding decision variable interval is deleted from interval queue Lnew,

Sub-step 5.4, to the interval upper bound J checking objective function interval and objective function value respectively of each decision variable in the interval queue Lnew after sub-step 5.3 process _minbetween relation, and carry out the operation of following grandson step 5.4.1 and grandson step 5.4.2:

Grandson step 5.4.1, if the lower bound in objective function interval is greater than the upper bound J of objective function value _min, then corresponding decision variable interval is deleted from interval queue Lnew;

Grandson step 5.4.2, if the upper bound in objective function interval is less than the upper bound J of objective function value _min, then the upper bound J of objective function value is upgraded _minfor the upper bound in objective function interval;

Step 6, interval deflation strategy, namely checks relative distance function [S _i] on each decision variable interval [u] in ([u]) (i=x, z) interval queue Lnew after processing through step 5 to [u] in each interval variable monotonicity, and carry out the operation of following sub-step 6.1:

Sub-step 6.1, if interval to any one decision variable in interval queue Lnew, relative distance function [S _i] ([u]) to the interval variable [u of the kth in decision-making range of variables [u] _k] be dull, and [u _k] lower bound place [S _i] ([u _k] .inf) or [u _k] upper bound place

[S _i] ([u _k] .sup) and symbol be just or be negative, then at [u _k] in find be greater than [u _k] lower bound and the [S of correspondence _i] and [u _k] lower bound place

[S _i] ([u _k] .inf) the maximal value u of jack per line _k1if do not have, then make u _k1=[u _k] .inf; Searching is less than [u _k] upper bound and the [S of correspondence _i] with

[u _k] upper bound place [S _i] ([u _k] .sup) the minimum value u of jack per line _k2if do not have, then make u _k2=[u _k] .sup; With interval [u _k1, u _k2] upgrade the kth interval variable [u of the corresponding decision range of variables [u] in this interval queue Lnew _k], wherein, [u _k] .inf represents [u _k] lower bound, [u _k] .sup represents [u _k] the upper bound;

Step 7, the interval end condition of each decision variable between test zone in queue Lnew, the width B in the width A in each the decision variable interval namely between test zone in queue Lnew and the objective function interval corresponding to each the decision variable interval in interval queue Lnew, wherein the width in decision variable interval is the maximal value of the width of all interval variables in decision variable interval, performs the operation of following sub-step 7.1 and sub-step 7.2:

Sub-step 7.1, when above-mentioned width A is less than predetermined positive number δ _u, or width B is less than predetermined positive number δ _jtime, corresponding decision variable interval is deleted from interval queue Lnew, and described corresponding decision variable interval is inserted in the interval queue R of design result;

Sub-step 7.2, after the operation to the interval completing steps 7.1 of each decision variable in interval queue Lnew, upgrade interval group's queue L, namely interval queue Lnew is inserted into interval group's queue L tail of the queue;

Step 8, the number in decision variable interval in group's queue L between test zone, and carry out one of following operation respectively according to result:

Step 8 result 1, in interval group's queue L, the number in decision variable interval is not 0, then proceed to step 3, continues design operation;

Step 8 result 2, in interval group's queue L, the number in decision variable interval is 0, then design end.

Step 9, chooses Optimum Design Results, gets the upper bound J that the interval upper bound of the interval corresponding objective function of a design result is objective function value from the interval queue R of design result _mindesign result interval, in selected design result interval, in the interval of each decision variable, any value combines, and the speed increment that the last impulse force effect accordingly that calculates brings to spacecraft, just obtain an optimal design solution of aforementioned spacecraft pulse intersection track.

The design effect of method provided by the invention is shown further below in conjunction with a concrete example.

If passive space vehicle is on the circular orbit that 400km is high, relative distance precision ε is 0.015m, δ _uand δ _jbe 0.01, if initial decision range of variables [u]=[[-30,30], [-30,30], [0,8000], [0,8000]], objective function estimated value initial value is 100ms ^-1, pursuit spacecraft initial position is (-10000,0,8000) m, and initial velocity is (10,0 ,-15) ms ^-1.

Simulation calculating show that the upper bound of objective function value and the solution interval of correspondence are as shown in table 1 under current accuracy

The upper bound J of table 1 objective function value _mincorresponding solution is interval

In this group decision variable interval, any value, its target function value all in [J] interval, the wherein upper bound J of objective function value _minthe higher limit being [J] is 8.750384691131890ms ^-1.

As shown in Figure 4, As time goes on relative distance, be progressively reduced to 0, and error is within the scope of the 0.015m specified.From path, demonstrate the correctness that the present invention solves intuitively.

As shown in Figure 5, within the scope of designated precision, the feasible solution interval that may comprise optimization solution satisfied condition has 5520, each [t _f] corresponding to [J] all contain the upper bound of objective function value.

Adopt this problem of genetic algorithm for solving, decision variable is t _{1 → f}and t _f, hunting zone is [0,8000] s, if initial population is 100, in maximum genetic algebra 100 generation, solve 10 times, result is as table 2.

Table 2 genetic algorithm result table

As shown in Table 2, genetic algorithm, due to algorithmic characteristic, depends on Initial value choice, is easily absorbed in local optimum, is unable to undergo computing repeatedly.In table 2,10 genetic algorithm objective function optimal values are the objective function optimization value 8.750384691363504 of the 6th computing, the upper dividing value 8.750384691131890ms of the objective function value of the global optimization approach proposed with the present invention ^-1very nearly the same, prove the correctness that the present invention solves, also provide support for advantage of overall importance of the present invention.

Claims (5)

1. an Optimization Design between the gradient cut section of spacecraft pulse intersection track, is characterized in that, said method comprising the steps of:

Step 1, intervalization process is carried out to spacecraft pulse intersection track optimizing problem, comprises following sub-step:

Sub-step 1.1, the impulse force effect times N that should use in given spacecraft pulse intersection process, gets last impulse force t action time _f, last impulse force t action time _fand t interval time between each subpulse time of thrust application except last impulse force _{i → f}, the component (v of speed increment that brings to pursuit spacecraft of each subpulse thrust _ix, v _iy, v _iz) as decision variable, and it is interval to form decision variable by the possible span of each decision variable

[u]=[[v _1x], [v _1y], [v _1z] ..., [v _{(N-1) x}], [v _{(N-1) y}], [v _{(N-1) z}], [t _{1 → f}], [t _{2 → f}] ..., [t _{n-1 → f}], [t _f]]; N be more than or equal to 2 natural number; Interval time t _{i → f}middle i=1,2...N-1, the component (v of speed increment _ix, v _iy, v _iz) middle i=1,2 ..., N;

Sub-step 1.2, by the relative distance constraint S of X, Y, the Z tri-under relative coordinate system during Spacecraft Rendezvous on direction of principal axis _iu ()=0 is converted into inequality constrain | [S _i] ([u]) | < ε and equation characteristic formp 0 ∈ [S _i] ([u]); ε is little arithmetic number, i=x, y, z;

Sub-step 1.3, the interval extension getting fuel optimal conditions is objective function and the upper bound J of given objective function value _mininitial value;

Sub-step 1.4, decision variable interval number M, the predetermined positive number δ of each inspection of setting _uwith predetermined positive number δ _j;

Step 2, according to spacecraft pulse intersection track optimizing model, interal separation is carried out to decision-making range of variables [u], comprise following sub-step:

Sub-step 2.1, component the interval ([v of the speed increment that each subpulse thrust is brought to pursuit spacecraft _ix], [v _iy], [v _iz]) be that boundary is respectively divided into only containing on the occasion of interval with the component only containing two speed increments of negative value with 0; Wherein i=1,2 ..., N;

Sub-step 2.2, by last impulse force interval action time [t _f], last interval [t interval time between impulse force action time and each subpulse time of thrust application except last impulse force _{i → f}], i=1,2...N-1, with the quadrant of used spacecraft pulse intersection track optimizing model intermediate cam function for boundary is respectively divided into multiple time interval;

Sub-step 2.3, by sub-step 2.1 gained only containing on the occasion of to obtain Q decision variable interval with the multiple time interval combination in any in only and sub-step 2.2 interval containing the component of two speed increments of negative value, Q described decision variable is interval forms interval group's queue L;

Step 3, according to the interval number M of the decision variable of each inspection of setting, if Q≤M, then make M=Q, select M decision variable interval composition sub-range queue L1 at the most from interval group's queue L assigned address, from interval group's queue L, delete M at the most the decision variable selected interval simultaneously;

Step 4, uses on each the decision variable interval in the sub-range queue L1 of the optimized algorithm based on gradient respectively selected by step 3 and solves spacecraft pulse intersection track optimizing problem, one of proceed as follows respectively by solving result:

Step 4 result 1: any one decision variable in sub-range queue L1 is interval on, the optimized algorithm based on gradient has solution, carries out the operation of following sub-step 4.1 and sub-step 4.2:

Sub-step 4.1, gradient split plot design, namely centered by the decision variable value of this solution correspondence, decision variable value expanded to [I between the expansion area of the solution of the optimized algorithm included based on gradient for radius to the numerical value of sizing _Δ], with [I between expansion area _Δ] the boundary value of each interval variable to split described decision variable respectively interval each corresponding interval variable, decision variable is interval each interval variable be divided into 3 intervals or 2 intervals, and combined as interval queue Lnew;

Sub-step 4.2, [I between expansion area decision variable value being expanded to the solution of the optimized algorithm included based on gradient centered by the decision variable value of this solution correspondence, with very little numerical value for radius _{Δ 1}], utilize Study on Interval Analysis Theory [I between expansion area _{Δ 1}] upper calculating, check whether the interval upper bound of the objective function of its constraint condition whether meeting spacecraft pulse intersection track optimizing model, its correspondence is less than the upper bound J of objective function value _min, when above-mentioned two results checked are all "Yes", with [I between expansion area _{Δ 1}] the interval upper bound of corresponding objective function upgrades the upper bound J of objective function value _min, otherwise keep the upper bound J of existing objective function value _minconstant;

Step 4 result 2: any one decision variable in sub-range queue L1 is interval on, the optimized algorithm based on gradient is not separated, interval with decision variable on the interval midpoint of each interval variable split each interval variable respectively, decision variable is interval each interval variable be divided into 2 intervals, and combined as interval queue Lnew;

Step 5, interval analysis is carried out respectively in each decision variable interval [u] of the interval queue Lnew of step 4 gained, and carries out the operation of following sub-step 5.1 ~ sub-step 5.4:

Sub-step 5.1, if relative distance constraint S _iu in ()=0, each impulse speed is linear correlation, i=x, y, z, then the decision variable except the component utilizing the speed increment brought to pursuit spacecraft except jth subpulse thrust in decision variable interval [u] is by relative distance function [S _i] ([u])=0 solves component the interval [[v of the speed increment that jth subpulse thrust is brought to spacecraft _{jx_f}], [v _{jy_f}], [v _{jz_f}]], i=x, y, z, j=1,2...N-1, and component the interval [[v calculating itself and decision variable interval [u] medium velocity increment _jx], [v _jy], [v _jz]] common factor [[v _{jx_new}], [v _{jy_new}], [v _{jz_new}]], if this common factor is empty set, then this decision variable interval [u] is deleted from interval queue Lnew, otherwise the component interval upgrading the speed increment that the jth subpulse thrust in decision variable interval [u] is brought to pursuit spacecraft is [[v _{jx_new}], [v _{jy_new}], [v _{jz_new}]], and obtain the interval queue Lnew of renewal simultaneously;

Sub-step 5.2, checks whether each the decision variable interval [u] in the interval queue Lnew after step 5.1 upgrades meets relative distance constraint condition, and is deleted from interval queue Lnew in the decision variable interval not meeting relative distance constraint condition;

Sub-step 5.3, appoints the component getting 3 speed increments corresponding to pulsatile once effect in decision variable, according to relative distance constraint S _i(u)=0, i=x, y, z, the component of 3 speed increments is specified to be expressed as the function of other decision variables, be the spacecraft pulse intersection track optimizing model that is decision variable with other decision variables except the component except 3 speed increments of specifying by spacecraft pulse intersection track optimizing model conversation with this, check and whether each the decision variable interval [u] in the interval queue Lnew of objective function J after processing through step 5.2 comprises 0 to the first-order partial derivative interval of new decision variable, if check result is no, then corresponding decision variable interval is deleted from interval queue Lnew,

Sub-step 5.4, checks the upper bound J of objective function interval and objective function value respectively to each the decision variable interval [u] in the interval queue Lnew after sub-step 5.3 process _minbetween relation, and carry out the operation of following grandson step 5.4.1 and grandson step 5.4.2:

Grandson step 5.4.1, if the lower bound in objective function interval is greater than the upper bound J of objective function value _min, then corresponding decision variable interval is deleted from interval queue Lnew;

Grandson step 5.4.2, if the upper bound in objective function interval is less than the upper bound J of objective function value _min, then the upper bound J of objective function value is upgraded _minfor the upper bound in objective function interval;

Step 6, interval deflation strategy, namely checks relative distance function [S _i] in ([u]) interval queue Lnew after processing through step 5 on each decision variable interval [u] to decision-making range of variables [u] in the monotonicity of each interval variable, i=x, y, z, and the operation carrying out following sub-step 6.1:

Sub-step 6.1, if to any one the decision variable interval [u] in interval queue Lnew, relative distance function [S _i] ([u]) to the interval variable [u of the kth in decision-making range of variables [u] _k] be dull, and a kth interval variable [u _k] lower bound place relative distance function [S _i] ([u _k] .inf) or a kth interval variable [u _k] upper bound place relative distance function [S _i] ([u _k] .sup) and symbol be just or be negative, then at a kth interval variable [u _k] in find be greater than a kth interval variable [u _k] lower bound and the relative distance function [S of correspondence _i] and a kth interval variable [u _k] lower bound place relative distance function [S _i] ([u _k] .inf) the interval variable u of jack per line _k1if do not have, then make interval variable u _k1=[u _k] .inf, find and be less than a kth interval variable [u _k] upper bound and the relative distance function [S of correspondence _i] and a kth interval variable [u _k] upper bound place relative distance function [S _i] ([u _k] .sup) the interval variable u of jack per line _k2if do not have, then make interval variable u _k2=[u _k] .sup, with decision variable interval [u _k1, u _k2] upgrade the kth interval variable [u of the corresponding decision range of variables [u] in this interval queue Lnew _k], wherein, interval variable [u _k] .inf represents a kth interval variable [u _k] lower bound, interval variable [u _k] .sup represents a kth interval variable [u _k] the upper bound;

Step 7, each decision variable interval [u] end condition between test zone in queue Lnew, the width B in the width A in each the decision variable interval [u] namely between test zone in queue Lnew and the objective function interval corresponding to each the decision variable interval [u] in interval queue Lnew, wherein the width of decision variable interval [u] is the maximal value of the width of all interval variables in decision variable interval [u], performs the operation of following sub-step 7.1 and sub-step 7.2:

Sub-step 7.1, when above-mentioned width A is less than predetermined positive number δ _u, or width B is less than predetermined positive number δ _jtime, corresponding decision variable interval is deleted from interval queue Lnew, and described corresponding decision variable interval is inserted in the interval queue R of design result;

Sub-step 7.2, after the operation to each decision variable interval [u] completing steps 7.1 in interval queue Lnew, upgrade interval group's queue L, the deletion point that interval group's queue L deletes M at the most decision variable interval of selection is in step 3 inserted into, using the interval group's queue L after queue Lnew between insert district as new interval group's queue L by interval queue Lnew;

Step 8, the number in decision variable interval in group's queue L between test zone, and carry out one of following operation respectively according to result:

Step 8 result 1, in interval group's queue L, the number in decision variable interval is not 0, then proceed to step 3, continues design operation;

Step 8 result 2, in interval group's queue L, the number in decision variable interval is 0, then design end;

Step 9, appoint from the interval queue R of design result and get a design result interval, in the interval of each interval variable in selected design result interval, any value combines, and the speed increment that the last impulse force effect accordingly that calculates brings to pursuit spacecraft, just obtain an optimal design solution of aforementioned spacecraft pulse intersection track.

2. Optimization Design between the gradient cut section of a kind of spacecraft pulse intersection track according to claim 1, it is characterized in that, assigned address described in step 3 is the tail of the queue of interval group's queue L, accordingly, in sub-step 7.2, interval queue Lnew is placed in interval group's queue L tail of the queue to form new interval group's queue L.

3. Optimization Design between the gradient cut section of a kind of spacecraft pulse intersection track according to claim 1, it is characterized in that, assigned address described in step 3 is the head of the queue of interval group's queue L, accordingly, in sub-step 7.2, interval group's queue L is placed in interval queue Lnew tail of the queue to form new interval group's queue L.

4., according to Optimization Design between the gradient cut section of the spacecraft pulse intersection track in claims 1 to 3 described in any one claim, it is characterized in that, in step 6.1, at a kth interval variable [u _k] in find be greater than a kth interval variable [u _k] lower bound and the relative distance function [S of correspondence _i] and a kth interval variable [u _k] lower bound place relative distance function [S _i] ([u _k] .inf) the maximal value u of jack per line _k3if do not have, then make u _k3=[u _k] .inf, find and be less than a kth interval variable [u _k] upper bound and the relative distance function [S of correspondence _i] and a kth interval variable [u _k] upper bound place relative distance function [S _i] ([u _k] .sup) jack per line minimum value u _k4if do not have, then make u _k4=[u _k] .sup, with decision variable interval [u _k3, u _k4] upgrade the kth interval variable [u of the corresponding decision range of variables [u] in this interval queue Lnew _k].

5., according to Optimization Design between the gradient cut section of the spacecraft pulse intersection track in claims 1 to 3 described in any one claim, it is characterized in that, step 9 is as follows:

The upper bound of getting a corresponding objective function interval from design result interval queue R is the upper bound J of objective function value _mindesign result interval, in the interval of each interval variable in selected design result interval, any value combines, and the speed increment that the last impulse force effect accordingly that calculates brings to spacecraft, just obtain an optimal design solution of spacecraft pulse intersection track.