CN112346339B - Differential countermeasure guidance law design method considering target acceleration direction observation - Google Patents

Differential countermeasure guidance law design method considering target acceleration direction observation Download PDF

Info

Publication number
CN112346339B
CN112346339B CN202011139459.1A CN202011139459A CN112346339B CN 112346339 B CN112346339 B CN 112346339B CN 202011139459 A CN202011139459 A CN 202011139459A CN 112346339 B CN112346339 B CN 112346339B
Authority
CN
China
Prior art keywords
target
target acceleration
missile
maneuver
disturbance
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011139459.1A
Other languages
Chinese (zh)
Other versions
CN112346339A (en
Inventor
胥彪
许佳骆
李翔
李爽
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN202011139459.1A priority Critical patent/CN112346339B/en
Publication of CN112346339A publication Critical patent/CN112346339A/en
Application granted granted Critical
Publication of CN112346339B publication Critical patent/CN112346339B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—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 using a perturbation signal
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42—AMMUNITION; BLASTING
    • F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
    • F42B15/00—Self-propelled projectiles or missiles, e.g. rockets; Guided missiles
    • F42B15/01—Arrangements thereon for guidance or control

Abstract

The invention discloses a differential game guidance law design method considering target acceleration direction observation, which comprises the following steps: 1) obtaining a kinetic equation of the missile and the target on the basis of the last guidance premise; 2) assuming that the target maneuver comprises a disturbance maneuver and an escape maneuver, the missile maneuver comprises a disturbance maneuver and a pursuit maneuver, and obtaining a differential countermeasure problem considering the disturbance maneuver by combining a related payment function; 3) solving the differential countermeasure problem by using a state dependence Riccati equation method to obtain a differential countermeasure guidance law considering disturbance maneuver; 4) assuming that the target only carries out disturbance maneuver and the missile only carries out pursuit maneuver, simplifying the guidance law in 3) and obtaining a differential countermeasure guidance law containing real-time target acceleration; 5) under the condition of delay information, a target acceleration direction observation method is used for compensation to obtain a target acceleration predicted value; 6) replacing the real-time target acceleration value in the step 4) with the target acceleration predicted value to obtain a differential game guidance law considering target acceleration direction observation.

Description

Differential countermeasure guidance law design method considering target acceleration direction observation
Technical Field
The invention relates to a differential countermeasure guidance law design method considering target acceleration direction observation, and relates to the technical field of aircraft guidance.
Background
The guided missile terminal guidance means that in the terminal flight stage of the guided missile, a flight control instruction is provided for the guided missile through a guidance law so as to help the guided missile hit a target. The missile guidance law design has direct influence on the operational efficiency of the missile, and the key research of the current major military and the country is obtained.
Current missile guidance laws can be largely classified into two categories: classical guidance law and modern guidance law. The classical guidance law mainly comprises a tracking method, a parallel approach method, a proportional guidance method, a three-point method and a lead angle method. The tracking method always keeps the speed direction of the missile pointing to a target, and although simple and easy to implement, the result is that the trajectory bends, and the missile overload required to be used is large. The parallel approach method keeps the sight of the missile moving in parallel in space during flight, has flat trajectory, requires less overload than a target, and requires accurate measurement of speed and lead angle information. The three-point method needs the base station to participate in the combat process, always keeps the missile on a connecting line between the base station and the target, has strong anti-interference performance, but has bent trajectory and larger overload needed to be used when the missile approaches the target. The preposed angle method is an improvement of a three-point method, the connecting line of the missile and the base station is kept ahead of the connecting line of the target and the base station in the intercepting process, and the included angle is reduced according to a certain rule until the target is intercepted, so that the anti-interference performance is poor. The classical guidance method is gradually eliminated, while the proportional guidance method is still widely used due to the technical easiness in realization, good robustness and flat trajectory. The pure proportion guidance method has a good intercepting effect on a fixed target or a non-maneuvering target with the acceleration of 0, but has a poor intercepting effect when the maneuvering target is intercepted. A series of modifications are derived on the basis of a pure proportional guidance method, and the proportional guidance law can obtain a good intercepting effect under the condition of obtaining accurate target acceleration information.
The modern guidance law is designed based on a modern control theory to deal with a missile guidance law of a high maneuvering target, and an optimal guidance law, a sliding mode guidance law and a differential countermeasure guidance law are common. The sliding mode variable structure control is used for controlling a nonlinear and uncertain system and has certain robustness. And the optimal guidance law is based on an optimal control theory, the miss distance or the line-of-sight angular rate is used as a control object, and final interception is realized by reducing the miss distance or the line-of-sight angular rate. When the modern guidance law and the classical guidance law face a high maneuvering target, effective interception can be realized only when maneuvering information of the target is obtained, but the real-time maneuvering information of the target is often difficult to obtain in real time, so that the guidance law is limited to play when the high maneuvering target is intercepted. The differential countermeasure guidance law has low dependence degree on the maneuvering information of the target, and can still obtain good interception effect even if the information of the target is inaccurate, thereby gaining common attention and research of countries in the world.
The differential strategy theory was originally proposed by Issacs in combination with the dynamic programming of Bellman when studying missile interception. From the time of proposing, just extensively be applied to the guided missile guidance law design. A differential countermeasure is simply defined in the literature (lienshan peak. differential countermeasure and its application [ M ]. national defense industry press, 2000), i.e. it refers to a type of countermeasure that requires the use of a differential equation to describe the countermeasure activity. The method aims to solve a differential countermeasure solution which is also called a saddle point solution and is an optimal solution for decision-making parties, and if any party does not adopt the saddle point solution, the other party can benefit in the game process. The missile pursuit problem belongs to the natural differential countermeasure problem, and the design of a guidance law by using a differential countermeasure method is widely researched.
Two common missile interception models are an interception model for zero miss distance and an interception model for zero line-of-sight angular velocity. The interception model based on the zero miss distance takes the predicted miss distance of the missile and the target as a design object, but the state space dimensionality is higher, the state transition matrix is required to be used for dimensionality reduction, the residual time is required, and certain influence is generated on the guidance precision. The design model of the zero line-of-sight angular rate is derived from a parallel approach method, and researches show that if the line-of-sight angular rate is converged at a value of 0, the missile and a target are in a collision triangular state, the missile and the target can finally realize collision, and the model state space dimension is small so as to facilitate design.
The state-Dependent Riccati Equation (SDRE) method is widely applied in the field of nonlinear system Control, and Tayfun is discussed in detail for the SDRE method in the literature (Imen T. State-Dependent Riccati Equation (SDRE) Control: A Survey [ J ]. IFAC Proceedings Volumes,2008,41(2): 3761-. It is pointed out that the control design using the SDRE method is mainly divided into calculation of a state-dependent parameter (SDC) and solution of an algebraic ricanti equation. In the aspect of Differential countermeasure Guidance law design, the SDRE method is mainly used for solving the Differential countermeasure problem, and Rajarshi in the document (Bardhan r. an SDRE Based Differential Game application for Maneuvering Target Interception [ C ]. AIAA Guidance, Navigation, and Control coherence.2013) indicates that the traditional Differential countermeasure problem needs to solve the hamilton-jacobian-bellman-issatch partial Differential equation, but the partial Differential equation is difficult to solve, while the SDRE method can be used for solving the solution of the suboptimal Differential countermeasure problem, and the SDRE method is used for designing the Differential countermeasure law SDRE-DG which does not need residual time estimation.
The acceleration direction observation method is to compensate the target acceleration by using low-delay target acceleration direction information, and Oshman Y in the literature (Oshman Y, Rad D A. differential-gain-based estimation and estimation orientation [ J ]. IEEE Transactions on Aerospace & Electronic Systems,2006,42(1): 316-) -proposes a differential countermeasure guidance law improved by using acceleration direction observation. The missile seeker can be used for identifying the acceleration direction of the target conveniently, namely the real-time sign of the target acceleration. Under the condition that the target acceleration observation is delayed, the range of the target acceleration reachable domain can be generally obtained by utilizing a dynamic response equation, and the range of the target acceleration reachable domain can be further reduced after the target acceleration direction is identified, so that the real-time target acceleration can be more accurately estimated. Under the condition of delaying the target acceleration information, the guidance law which needs to be calculated by using the target acceleration can be improved by using the method for observing the acceleration direction.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for designing the differential countermeasure guidance law considering the target acceleration direction observation is provided, and the missile and the target disturbance maneuver are considered in the design process of the differential countermeasure problem aiming at the missile pursuit problem. The solved guidance law comprises the compensation of the maneuvering of the target, and the interception effect of the guidance law on the maneuvering target is improved. And the SDRE method is used for solving the differential countermeasure problem, and the solving problem of the saddle point solution is simplified. The method for observing the target acceleration direction and the method for calculating the guidance law by using the compensated predicted target acceleration can be used for solving the calculation problem of the guidance law under the condition of delaying the target acceleration information. And finally, designing a differential game guidance law for intercepting the maneuvering target under the condition of delaying information, and improving the guidance effect.
The invention adopts the following technical scheme for solving the technical problems:
the differential countermeasure guidance law design method considering target acceleration direction observation comprises the following steps:
step 1, on the premise of guided missile terminal guidance, under the conditions that the target speed is unchanged, the influence of gravity and air resistance is ignored, and the guided missile and the target accord with first-order dynamic response, establishing a dynamic model of the guided missile and the target and a relative motion model of the guided missile and the target, and obtaining a design model of the line-of-sight angular speed according to the relative motion model of the guided missile and the target;
step 2, designing a pursuit differential countermeasure problem by adopting a method of zero line-of-sight angular velocity, dividing missile maneuvering into pursuit maneuvering and disturbance maneuvering, dividing target maneuvering into escape maneuvering and disturbance maneuvering, designing payment functions related to the line-of-sight angular velocity, the missile pursuit maneuvering and the target escape maneuvering, and combining a design model of the line-of-sight angular velocity to obtain the pursuit differential countermeasure problem considering the disturbance maneuvering;
step 3, solving the pursuit differential countermeasure problem considering the disturbance maneuver by using a state dependence Riccati equation method to obtain a differential countermeasure guidance law considering the disturbance maneuver;
step 4, when all target maneuvers are disturbance maneuvers and all missile maneuvers are pursuit maneuvers, converting the differential countermeasure guidance law considering the disturbance maneuvers into a differential countermeasure guidance law containing real-time target acceleration;
step 5, under the condition of delay information, solving by using a known target maximum maneuvering capacity value and a delayed target acceleration value and combining a first-order dynamic response kinetic equation to obtain a real-time target acceleration reachable domain center, and correcting the real-time target acceleration reachable domain center by using a target acceleration direction observation method to obtain the corrected target acceleration reachable domain center of the target acceleration direction observation method;
and 6, taking the target acceleration reachable center corrected by the target acceleration direction observation method as a target acceleration predicted value, and replacing the real-time target acceleration value required by the differential countermeasure guidance law containing the real-time target acceleration in the step 4 by using the target acceleration predicted value to obtain the differential countermeasure guidance law considering the target acceleration direction observation.
As a preferable aspect of the present invention, step 2 is a countermeasure problem of evasive differentiation in consideration of disturbance maneuver, specifically as follows:
Figure BDA0002737778420000041
wherein the content of the first and second substances,
Figure BDA0002737778420000042
R、
Figure BDA0002737778420000043
relative distance and relative speed, theta,
Figure BDA0002737778420000044
Respectively the angle of sight and the angular rate of sight, alpham、αtRespectively the flight path angle u of the missile to the targetpManeuvering for missile pursuit, veFor target escape manoeuvres, ud、vdRespectively missile and target disturbance maneuver, J is a payment function, t0For guidance initiation time, q (x) is a weight matrix with respect to line-of-sight angular rate, R1And R2Weight matrices for missile pursuit maneuvers and target escape maneuvers, respectively.
As a preferable aspect of the present invention, the differential countermeasure guidance law considering disturbance maneuver in step 3 specifically includes:
Figure BDA0002737778420000045
wherein u is*Differential countermeasure guidance law for disturbance maneuver consideration, R1A, b, c are state dependent parameters for a weight matrix related to missile pursuit maneuversQ is a weight matrix relating to the angular rate of sight, γ is the coefficient of maneuverability available to the target relative to the missile, ud、vdAre respectively missile and target disturbance maneuver, p is variable,
Figure BDA0002737778420000051
Figure BDA0002737778420000052
is the line-of-sight angular rate.
As a preferable aspect of the present invention, the differential game guidance law including the real-time target acceleration in step 4 specifically includes:
Figure BDA0002737778420000053
wherein u is**For a differential game guidance law including real-time target acceleration, a, b, c are state dependent parameters, q is a weight matrix related to the angular velocity of line of sight, gamma is a coefficient of maneuvering capability available for the target relative to the missile, p is a variable,
Figure BDA0002737778420000054
Figure BDA0002737778420000055
is the line-of-sight angular rate.
As a preferred embodiment of the present invention, the target acceleration reachable domain center after the target acceleration direction observation method is modified in step 5 specifically includes:
Figure BDA0002737778420000056
wherein sgn (. cndot.) is a sign function, at(t)min、at(t)maxLower and upper bounds, a, respectively, of the real-time target acceleration reachable domaint(t)oA center of a reachable region of the target acceleration corrected by the target acceleration direction observation methodt(tΔ t) target acceleration obtained by the missile at time t, Δ t delay time, τtIn order to target the first order dynamic response time,
Figure BDA0002737778420000057
is the target maximum acceleration command.
As a preferable aspect of the present invention, the differential countermeasure guidance law regarding observation in the target acceleration direction in step 6 is specifically:
Figure BDA0002737778420000058
wherein u isSDRE-ODGIn order to consider the differential countermeasure guidance law observed in the target acceleration direction, a, b and c are state dependent parameters, gamma is an available maneuvering capability coefficient of the target relative to the missile,
Figure BDA0002737778420000059
Figure BDA00027377784200000510
for line-of-sight angular rate, p is a variable, at(t)oThe target acceleration corrected by the target acceleration direction observation method can reach the center of the domain, q is a weight matrix related to the visual line angular rate, ud、vdRespectively missile and target disturbance maneuver, p is variable, alpham、αtThe angles of flight paths of the missile and the target, theta, respectively,
Figure BDA0002737778420000061
Respectively, the line-of-sight angle and the line-of-sight angular rate,
Figure BDA0002737778420000062
is the relative velocity.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the invention provides a differential countermeasure guidance law design method considering target acceleration direction observation, which comprises the steps of firstly providing a differential countermeasure model considering disturbance maneuver aiming at the actual pursuit problem, supposing that the target carries out pure disturbance maneuver, and solving by using an SDRE (software development kit) method to obtain the differential countermeasure guidance law containing target acceleration. Compared with the guidance law before improvement, the method not only keeps the advantage of no need of residual time estimation, but also can better realize interception on maneuvering targets. And then, under the condition of delaying the target acceleration information, compensating the delayed target acceleration by using a target acceleration direction observation method, and calculating a guidance law by using the predicted target acceleration to obtain a differential countermeasure guidance law considering the target acceleration direction observation under the condition of delaying the information, wherein the guidance law can realize effective interception of the maneuvering target under the condition of delaying the information, and has practical engineering significance.
Drawings
FIG. 1 is a diagram of the relative motion of a missile and target during the final guidance phase of the invention.
Fig. 2, fig. 3, and fig. 4 are graphs comparing simulation results of the line-of-sight angular velocity, the movement locus, and the missile acceleration command value, respectively, under the condition that the target performs constant maneuvering.
Fig. 5, 6 and 7 are graphs comparing simulation results of the line-of-sight angular velocity, the movement locus and the missile acceleration command value under the condition that the target performs snake-shaped maneuvering, respectively.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention provides a differential countermeasure guidance law considering target acceleration direction observation under a delay information condition, which comprises the following specific steps:
the method comprises the following steps: aiming at the problem of plane terminal guidance, the invention assumes that the target speed is unchanged, ignores the influence of air resistance and gravity, and the missile and the target conform to first-order dynamic response, thereby obtaining the kinetic equation of the missile and the target. And then obtaining a relative motion equation of the missile and the target by combining the figure 1, and performing guidance law design by adopting a method of zero line-of-sight angular velocity.
Step two: the maneuver of the missile is divided into a pursuit maneuver and a disturbance maneuver, and the maneuver of the target is divided into an escape maneuver and a disturbance maneuver. And then, designing a payment function related to the line-of-sight angular velocity, the missile pursuit maneuver and the target escape maneuver, and combining the design model related to the line-of-sight angular velocity to obtain a pursuit differential countermeasure problem considering the disturbance maneuver.
Step three: the above differential countermeasure problem is solved by using a state-dependent rica equation method. The solving process mainly comprises the following steps: solving state dependent parameters and solving algebraic Riccati equations. Wherein the state-dependent parameters are derived from a design model relating to line-of-sight angular rate, and each decision stage is calculated using the real-time information obtained. Substituting the state dependent parameters obtained by real-time calculation into a state dependent Riccati equation to obtain an algebraic Riccati equation, and solving the Riccati equation to obtain a differential countermeasure guidance law considering disturbance maneuver.
Step four: assuming that all the maneuvers of the target are disturbance maneuvers and all the maneuvers of the missile are pursuit maneuvers, the differential game guidance law is converted into a differential game guidance law containing target acceleration information, and the related guidance law needs to use real-time acceleration information of the target.
Step five: under the condition of delay information, the observation of the target acceleration is considered to have a certain delay. And solving by utilizing the known target maximum maneuvering capacity value and the delayed target acceleration value in combination with a first-order dynamic response kinetic equation to obtain a real-time target acceleration reachable region. And then observing by using the target acceleration direction, further reducing the range of the acceleration reachable domain of the target, and taking the compensated center of the reachable domain of the target acceleration as a target acceleration value.
Step six: and replacing the real-time target acceleration value required in the differential game guidance law with the target acceleration value obtained by considering the target acceleration direction observation, and finally designing the differential game guidance law considering the target acceleration direction observation under the condition of delay information.
The steps are simplified as follows:
(1) and obtaining a kinetic equation of the missile and the target on the basis of the premise of terminal guidance, and designing a guidance law on the basis of a method for zero line-of-sight angular rate.
(2) And assuming that the target maneuver comprises a disturbance maneuver and an escape maneuver, and the missile maneuver comprises a disturbance maneuver and a pursuit maneuver, and combining the related payment functions to obtain a differential countermeasure problem considering the disturbance maneuver.
(3) And solving the differential countermeasure problem by using a method of a state dependence Riccati equation to obtain a differential countermeasure guidance law considering disturbance maneuver.
(4) And (3) assuming that the target only carries out disturbance maneuver and the missile only carries out pursuit maneuver, further simplifying the guidance law in the step (3), and obtaining a differential countermeasure guidance law containing real-time target acceleration.
(5) Under the condition of delay information, a more accurate target acceleration predicted value is obtained by compensation by using a target acceleration direction observation method.
(6) And (4) replacing the real-time target acceleration value in the step (4) with the target acceleration predicted value to obtain a differential countermeasure guidance law considering the target acceleration direction observation.
With reference to fig. 1, the present invention proposes a differential countermeasure guidance problem model of the terminal guidance condition:
the method comprises the following steps: on the premise of terminal guidance, assuming that the target speed is unchanged, omitting the influence of gravity and air resistance, and establishing a dynamic model, wherein the missile and the target have first-order dynamic response delay:
Figure BDA0002737778420000081
Figure BDA0002737778420000082
wherein x ism、zmAnd xt、ztThe coordinates of the missile and the target on the x axis and the z axis respectively, VmAnd VtVelocity of missile and target, respectively, alphamAnd alphatIs the angle of flight path of the missile to the target, amAnd atAcceleration of the missile to the target, τmAnd τtThe first-order dynamic response time of the missile and the target is shown, u and v are maneuvering instructions of the missile and the target, and a relative motion model is obtained by combining the following steps of 1:
Figure BDA0002737778420000083
Figure BDA0002737778420000084
wherein R is substituted with
Figure BDA0002737778420000085
Relative distance and relative velocity, θ and
Figure BDA0002737778420000086
respectively, the line-of-sight angle and the line-of-sight angular rate. The formula for the line of sight angular rate is derived:
Figure BDA0002737778420000087
step two: assuming that the maneuvers of the target and missile comprise gaming maneuvers and disturbance maneuvers:
u＝up+ud
v＝ve+vd
wherein u ispFor following the missile, veTargeted escape manoeuvres, udAnd vdRespectively, the perturbation maneuver of the missile and the target. Selecting a payment function:
Figure BDA0002737778420000088
wherein t is0For guidance initiation time, q (x) is a weight matrix with respect to line-of-sight angular rate, R1And R2Are respectively asA weight matrix for missile pursuit maneuvers and target escape maneuvers. And gamma is the maneuvering capability coefficient of the target relative to the missile, and the larger the value of gamma is, the larger the penalty of the target for carrying out escape maneuvering is, which indicates that the maneuvering capability of the target relative to the missile is weaker. Based on the method of zero line-of-sight angular velocity, the differential countermeasure problem considering the target disturbance maneuver is obtained:
Figure BDA0002737778420000091
to the above game guidance problem, to
Figure BDA0002737778420000092
X, the missile needs to adopt a pursuit maneuver to reduce the apparent angular rate value, and the target increases the apparent angular rate value as much as possible through an escape maneuver. And the perturbation maneuver of the missile and the target does not limit the payment function because of the randomness.
The saddle point solution is required to solve the above differential countermeasure problem
Figure BDA0002737778420000093
The saddle point solution satisfies:
Figure BDA0002737778420000094
if any party of the two pursuing evasion parties does not adopt the saddle point solution to carry out maneuver, the other party can benefit in the game process.
Step three: the above differential countermeasure problem is solved by using a state dependent ricattes equation.
In solving the SDRE problem, if the condition of f (0) ═ 0 is satisfied, then f (x) can be converted into a (x) x, and the formula can be used
Figure BDA0002737778420000095
The following non-linear formula is obtained by adopting a proper mode:
Figure BDA0002737778420000096
wherein a (x), b (x), c (x) are SDC required to be calculated in real time. The SDC is obtained based on a method of zero line-of-sight angular rate:
Figure BDA0002737778420000097
Figure BDA0002737778420000098
Figure BDA0002737778420000099
each decision stage makes use of the obtained measurement value R,
Figure BDA00027377784200000910
αm，αt，θ，τm，τtthe real-time SDC value is obtained for further solution of SDRE.
Solving by using a Hamilton method, and establishing the following Hamilton equation:
Figure BDA00027377784200000911
where λ is a covariate and is assumed to be λ ═ p (x) x + ξ. When the target equation is to obtain the minimum value, it needs to satisfy:
Figure BDA0002737778420000101
a saddle point solution is obtained:
Figure BDA0002737778420000102
Figure BDA0002737778420000103
derivative of λ it to get the following SDRE equation:
Figure BDA0002737778420000104
Figure BDA0002737778420000105
the state-dependent parameter values a (x), b (x), c (x) and the weight matrix q (x), R1、R2Substituting into the SDRE equation, converting the SDRE equation into an algebraic Riccati equation, and directly solving by using a unitary quadratic equation solving method to obtain the following result:
Figure BDA0002737778420000106
Figure BDA0002737778420000107
assuming that all maneuvers performed by the target are disturbance maneuvers, obtaining a differential countermeasure guidance law considering the target disturbance:
Figure BDA0002737778420000108
step four: for design convenience, R may be used1(x)，R2(x) And q (x) takes a value of 1, while assuming that the missile only performs a pursuit maneuver, i.e.:
u＝up
meanwhile, the target only carries out perturbation maneuver, namely:
v＝vd＝at
obtaining a differential countermeasure guidance law:
Figure BDA0002737778420000109
and substituting the SDC obtained by solving at each moment into the SDC, so that the guidance law control quantity at each moment can be obtained through calculation.
Step five: and under the condition that the target acceleration observation is delayed, predicting to obtain a target acceleration value by using an acceleration direction observation method.
Assuming that the target acceleration information obtained by the missile is delayed by delta t under the condition of delay information, the target acceleration information obtained at the time t is actually a (t-delta t). In the case of a mobile and variable target, the guidance accuracy is seriously reduced by using the delay information to calculate the guidance amount. The maximum maneuvering instruction of the target is used as input and is combined with a first-order dynamic response equation to obtain the upper and lower bounds of the acceleration reachable domain of the target at the time t, the center of the target acceleration reachable domain is used for replacing the original required acceleration information, and the obtained upper and lower bounds of the acceleration are as follows:
Figure BDA0002737778420000111
Figure BDA0002737778420000112
and the center of the acceleration reachable domain of the target at the time t is as follows:
Figure BDA0002737778420000113
the target acceleration can be used to reach the center of the domain instead of a (t) in the guidance law.
And then, correcting by using a method for observing the direction of the target acceleration, and further reducing the reachable range of the acceleration of the target by using the target acceleration information without delay.
Target acceleration direction is in the workingCan be conveniently obtained in practical application, sgn (·) is a sign function, if sgn (a)t(t)min)＝sgn(at(t)max) The obtained acceleration reachable domain center is:
Figure BDA0002737778420000114
if sgn (a)t(t)min)≠sgn(at(t)max) If the sign of the acceleration value of the target is known, the range of the acceleration reachable domain of the target can be further narrowed, the upper bound or the lower bound of the reachable domain becomes 0, and the center of the obtained acceleration reachable domain is as follows:
Figure BDA0002737778420000115
the obtained reachable domain center of the acceleration observed by the target acceleration direction is as follows:
Figure BDA0002737778420000116
the improved acceleration can be used for reaching the domain center at(t)oReplacing a real-time target acceleration value in the guidance law, selecting a weight matrix q (x) with the value of 1, and finally calculating to obtain an improved differential countermeasure guidance law SDRE-ODG considering target acceleration direction observation:
Figure BDA0002737778420000121
comparison of simulations
The following compares the SDRE-ODG guidance law with the SDRE-DG guidance law, and because the SDRE-DG guidance law does not consider target disturbance maneuver in the design process, the guidance law is obtained as follows:
Figure BDA0002737778420000122
wherein b (x) and p (x) are the same as the SDRE-ODG guidance law.
The initial parameters of the target during constant maneuvering and snake maneuvering are respectively given in the table 1 and the table 2, and the miss distance comparison of the target during constant maneuvering and snake maneuvering is given in the table 3.
TABLE 1 initial parameters for a constant maneuver of an object
x(0)/m z(0)/m α(0)/° V(0)/m·s-1 τ/s
Missile (missile) 0 0 0 2500 0.1
Target 50000 20000 180 1500 0.1
And gamma is 7.5, r1＝1、r 21, q (x) 1, target maximum mobility
Figure BDA0002737778420000124
The target acceleration observation delay time is delta t 0.2s, and the maneuvering instruction value of the target is 50m/s2。
TABLE 2 initial parameters for snake maneuvering of an object
x(0)/m z(0)/m α(0)/° V(0)/m·s-1 τ/s
Missile (missile) 0 0 0 2500 0.1
Target 20000 10000 180 1500 0.1
The target was subjected to a snake maneuver with a peak value of 100, γ ═ 7.5, r1＝1、r 21, q (x) 1, target maximum mobility
Figure BDA0002737778420000123
The target acceleration observation delay time Δ t is 0.2 s.
TABLE 3 off-target comparison
Target constant maneuver Target snake maneuvering
SDRE-DG 1.36m 1.47m
SDRE-ODG 0.23m 0.65m
FIGS. 2-4 reflect the target being taken at 50m/s2When the acceleration of the missile is subjected to constant maneuvering, the two guidance laws are compared with each other in the aspect of angular velocity and track and the missile acceleration instruction.
FIGS. 5-7 reflect target acquisitionTake 100m/s2When the acceleration peak value of the two guidance laws is subjected to snake-shaped maneuvering, the two guidance laws are compared with the sight line acceleration rate, the track and the missile acceleration instruction.
The above results show that the SDRE-ODG guidance law can more effectively utilize the maneuvering capabilities of missiles than the SDRE-DG guidance law, as can be seen from fig. 4 and 7. As can be seen in particular from fig. 7, the SDRE-ODG guidance law can react more effectively to a maneuvering target. As can be seen from FIGS. 3 and 6, the SDRE-ODG guidance law trajectory is more straight compared with the SDRE-DG guidance law. As can be seen from fig. 2 and 5, compared with the SDRE-DG guidance law, the SDRE-ODG guidance law can more effectively achieve convergence of the line-of-sight angular rate because the influence of disturbance maneuver of the target is considered in designing the guidance law. And it can be seen from the miss distance result that the SDRE-ODG guidance law can effectively intercept the maneuvering target under the condition of delay information. Under the condition of delay information, the SDRE-ODG guidance law can utilize target acceleration direction observation to improve the guidance effect, realize more accurate interception on maneuvering targets and better intercept variable maneuvering targets.
In conclusion, the differential countermeasure guidance law considering the target acceleration direction observation under the condition of the delay phenomenon can effectively intercept the target, improves the guidance effect and has practical significance.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (1)

1. A differential countermeasure guidance law design method considering target acceleration direction observation is characterized by comprising the following steps:
step 1, on the premise of guided missile terminal guidance, under the conditions that the target speed is unchanged, the influence of gravity and air resistance is ignored, and the guided missile and the target accord with first-order dynamic response, establishing a dynamic model of the guided missile and the target and a relative motion model of the guided missile and the target, and obtaining a design model of the line-of-sight angular speed according to the relative motion model of the guided missile and the target;
step 2, designing a pursuit differential countermeasure problem by adopting a method of zero line-of-sight angular velocity, dividing missile maneuvering into pursuit maneuvering and disturbance maneuvering, dividing target maneuvering into escape maneuvering and disturbance maneuvering, designing payment functions related to the line-of-sight angular velocity, the missile pursuit maneuvering and the target escape maneuvering, and combining a design model of the line-of-sight angular velocity to obtain the pursuit differential countermeasure problem considering the disturbance maneuvering;
the following is specific to the problem of the differential pursuit countermeasure considering disturbance maneuver:
Figure FDA0003396367090000011
wherein the content of the first and second substances,
Figure FDA0003396367090000012
R、
Figure FDA0003396367090000013
relative distance and relative speed, theta,
Figure FDA0003396367090000014
Respectively the angle of sight and the angular rate of sight, alpham、αtRespectively the flight path angle u of the missile to the targetpManeuvering for missile pursuit, veFor target escape manoeuvres, ud、vdRespectively missile and target disturbance maneuver, J is a payment function, t0For guidance initiation time, q (x) is a weight matrix with respect to line-of-sight angular rate, R1And R2Weight matrixes related to missile pursuit maneuvers and target escape maneuvers respectively;
step 3, solving the pursuit differential countermeasure problem considering the disturbance maneuver by using a state dependence Riccati equation method to obtain a differential countermeasure guidance law considering the disturbance maneuver;
the differential countermeasure guidance law considering disturbance maneuver specifically includes:
Figure FDA0003396367090000015
wherein u is*Differential countermeasure guidance law for disturbance maneuver consideration, R1A, b and c are state dependent parameters, q is a weight matrix related to the angular velocity of sight line, gamma is the maneuvering capability coefficient of the target relative to the missile, and u isd、vdAre respectively missile and target disturbance maneuver, p is variable,
Figure FDA0003396367090000021
Figure FDA0003396367090000022
is the line-of-sight angular rate;
step 4, when all target maneuvers are disturbance maneuvers and all missile maneuvers are pursuit maneuvers, converting the differential countermeasure guidance law considering the disturbance maneuvers into a differential countermeasure guidance law containing real-time target acceleration;
the differential game guidance law including the real-time target acceleration specifically includes:
Figure FDA0003396367090000023
wherein u is**For a differential game guidance law including real-time target acceleration, a, b, c are state dependent parameters, q is a weight matrix related to the angular velocity of line of sight, gamma is a coefficient of maneuvering capability available for the target relative to the missile, p is a variable,
Figure FDA0003396367090000024
Figure FDA0003396367090000025
is the line-of-sight angular rate;
step 5, under the condition of delay information, solving by using a known target maximum maneuvering capacity value and a delayed target acceleration value and combining a first-order dynamic response kinetic equation to obtain a real-time target acceleration reachable domain center, and correcting the real-time target acceleration reachable domain center by using a target acceleration direction observation method to obtain the corrected target acceleration reachable domain center of the target acceleration direction observation method;
the target acceleration corrected by the target acceleration direction observation method can reach the center of the domain, and specifically comprises the following steps:
Figure FDA0003396367090000026
wherein sgn (. cndot.) is a sign function, at(t)min、at(t)maxLower and upper bounds, a, respectively, of the real-time target acceleration reachable domaint(t)oA center of a reachable region of the target acceleration corrected by the target acceleration direction observation methodt(t- Δ t) is the target acceleration obtained by the missile at time t, Δ t is the delay time, τtIn order to target the first order dynamic response time,
Figure FDA0003396367090000027
a target maximum acceleration command;
step 6, taking the target acceleration reachable center corrected by the target acceleration direction observation method as a target acceleration predicted value, and replacing the real-time target acceleration value required by the differential countermeasure guidance law containing the real-time target acceleration in the step 4 with the target acceleration predicted value to obtain the differential countermeasure guidance law considering the target acceleration direction observation;
the differential countermeasure guidance law considering the target acceleration direction observation specifically includes:
Figure FDA0003396367090000031
wherein u isSDRE-ODGIn order to consider the differential countermeasure guidance law observed in the target acceleration direction, a, b and c are state dependent parameters, gamma is an available maneuvering capability coefficient of the target relative to the missile,
Figure FDA0003396367090000032
Figure FDA0003396367090000033
for line-of-sight angular rate, p is a variable, at(t)oThe target acceleration corrected by the target acceleration direction observation method can reach the center of the domain, q is a weight matrix related to the visual line angular rate, ud、vdRespectively missile and target disturbance maneuver, p is variable, alpham、αtThe angles of flight paths of the missile and the target, theta, respectively,
Figure FDA0003396367090000034
Respectively, the line-of-sight angle and the line-of-sight angular rate,
Figure FDA0003396367090000035
is the relative velocity.
CN202011139459.1A 2020-10-22 2020-10-22 Differential countermeasure guidance law design method considering target acceleration direction observation Active CN112346339B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011139459.1A CN112346339B (en) 2020-10-22 2020-10-22 Differential countermeasure guidance law design method considering target acceleration direction observation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011139459.1A CN112346339B (en) 2020-10-22 2020-10-22 Differential countermeasure guidance law design method considering target acceleration direction observation

Publications (2)

Publication Number Publication Date
CN112346339A CN112346339A (en) 2021-02-09
CN112346339B true CN112346339B (en) 2022-04-22

Family

ID=74359747

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011139459.1A Active CN112346339B (en) 2020-10-22 2020-10-22 Differential countermeasure guidance law design method considering target acceleration direction observation

Country Status (1)

Country Link
CN (1) CN112346339B (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0222570A2 (en) * 1985-10-31 1987-05-20 British Aerospace Public Limited Company Missile guidance systems
JPH0854929A (en) * 1994-08-09 1996-02-27 Mitsubishi Heavy Ind Ltd Flying object controller
CN101033973A (en) * 2007-04-10 2007-09-12 南京航空航天大学 Attitude determination method of mini-aircraft inertial integrated navigation system
US7487933B1 (en) * 2005-07-05 2009-02-10 Chen Robert H Homing missile guidance and estimation algorithms against advanced maneuvering targets
US7513455B1 (en) * 2005-02-18 2009-04-07 Lockhead Martin Corporation Ballistic missile interceptor guidance by acceleration relative to line-of-sight
KR20110115466A (en) * 2010-04-15 2011-10-21 국방과학연구소 Design method of a flight control system for vertical line following guidance
CN102902274A (en) * 2012-08-08 2013-01-30 空军工程大学航空航天工程学院 Self-adaptive weighting differential game guidance method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8649930B2 (en) * 2009-09-17 2014-02-11 Agjunction Llc GNSS integrated multi-sensor control system and method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0222570A2 (en) * 1985-10-31 1987-05-20 British Aerospace Public Limited Company Missile guidance systems
JPH0854929A (en) * 1994-08-09 1996-02-27 Mitsubishi Heavy Ind Ltd Flying object controller
US7513455B1 (en) * 2005-02-18 2009-04-07 Lockhead Martin Corporation Ballistic missile interceptor guidance by acceleration relative to line-of-sight
US7487933B1 (en) * 2005-07-05 2009-02-10 Chen Robert H Homing missile guidance and estimation algorithms against advanced maneuvering targets
CN101033973A (en) * 2007-04-10 2007-09-12 南京航空航天大学 Attitude determination method of mini-aircraft inertial integrated navigation system
KR20110115466A (en) * 2010-04-15 2011-10-21 국방과학연구소 Design method of a flight control system for vertical line following guidance
CN102902274A (en) * 2012-08-08 2013-01-30 空军工程大学航空航天工程学院 Self-adaptive weighting differential game guidance method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Differential-game-based guidance law using target orientation observations;Y. Oshman等;《IEEE Transactions on Aerospace and Electronic Systems》;20060131;第42卷(第1期);第316-326页 *
基于目标姿态信息的导弹微分对策制导律研究;马礼举等;《弹箭与制导学报》;20090615(第03期);第49-52页 *

Also Published As

Publication number Publication date
CN112346339A (en) 2021-02-09

Similar Documents

Publication Publication Date Title
CN110187640B (en) Multi-missile cooperative combat guidance law design method for maneuvering target and allowable communication time lag
CN113325866A (en) Differential game cooperative guidance method based on event triggering
CN108073742A (en) Interception guided missile terminal flight method for estimating state based on improved particle filter algorithm
Huang et al. Intelligent guidance and control methods for missile swarm
CN116679743A (en) Nonlinear optimal flight time control guidance method for intercepting maneuvering target
Young-Won et al. A unified formulation of optimal guidance-to-collision law for accelerating and decelerating targets
CN112346339B (en) Differential countermeasure guidance law design method considering target acceleration direction observation
Zhang et al. On-line optimization design of sliding mode guidance law with multiple constraints
Enjiao et al. An adaptive parameter cooperative guidance law for multiple flight vehicles
CN112346474B (en) Design method of differential game guidance law with limited time convergence
CN113359819B (en) Optimal guidance law with collision angle constraint and acceleration limitation
Zhang et al. Closed-form time-to-go estimation for proportional navigation guidance considering drag
You et al. Distributed synergetic guidance law for multiple missiles with angle-of-attack constraint
Shi et al. Predictive guidance strategies for active aircraft defense
Wei et al. Missile guidance law with impact angle constraint and acceleration saturation
Lee et al. Impact time and angle control guidance with rendezvous concept
Tan et al. Cooperative Strategy for Aircraft Defense Line-of-Sight Guidance in Three-Dimensional Space
Qiang et al. The research of terminal optimal guidance law of MANEUVERING vehicle with multiple constrains
Wang et al. Cooperative guidance for speed-varying vehicle against moving target
Yang et al. Research on a combined proportional guidance method with the terminal point pointing to the predicted encounter point
CN116974208B (en) Rotor unmanned aerial vehicle target hitting control method and system based on strapdown seeker
CN116753788B (en) Agile turning composite control method based on linear active disturbance rejection
Zhang et al. Nonlinear distributed model predictive control for multiple missiles against maneuvering target with a trajectory predictor
Chen et al. A Cooperative Guidance Law for Multiple Missiles based on Reinforcement Learning
Ji et al. Research on the Air Combat Countermeasure Generation of Fighter Mid-range Turn

Legal Events

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