CN113110576B - Self-adaptive fixed time convergence cooperative guidance method capable of realizing continuous switching - Google Patents
Self-adaptive fixed time convergence cooperative guidance method capable of realizing continuous switching Download PDFInfo
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Abstract
The invention discloses a continuously switchable self-adaptive fixed time convergence cooperative guidance method, which comprises the steps of firstly establishing a motion relation mathematical model of a missile relative to a target, predicting the residual hit time of each missile on the basis, further defining the consistency error variable of the residual hit time, and finally providing a continuously switchable self-adaptive fixed time convergence cooperative guidance law capable of ensuring that a plurality of missiles hit the target simultaneously. The method can enable a plurality of missiles to finally hit the target at the same time, and compared with the existing fixed-time convergence cooperative guidance method, the method designed by the invention can effectively reduce the impact of the initial guidance instruction.
Description
Technical Field
The invention belongs to the technical field of guidance, and particularly relates to a collaborative guidance method.
Background
With the continuous progress and improvement of the counterguidance defense system, the traditional one-to-one guidance attack tactics have great difficulty in effectively striking the target equipped with the defense system, and the ideal combat efficiency is difficult to achieve. The high-density simultaneous hit saturation attack tactics of multiple aircrafts become an effective method for hitting the targets due to the characteristics of strong penetration capacity and high hit rate.
The convergence time obviously influences the execution effect of the cooperative guidance algorithm, and the finite time convergence method is widely applied to the design of the cooperative guidance algorithm due to the advantages of fast convergence time, estimable convergence time upper bound and strong robustness. However, the upper bound of the convergence time of the finite time convergence method has strong dependence on the initial state of the system, and it is difficult to estimate the upper bound of the convergence time when the initial state of the system is unknown. Inspired by this problem, researchers have proposed a fixed time convergence method in which the upper bound of the convergence time does not depend on the initial state. Therefore, the research on the cooperative guidance method capable of realizing fixed time convergence is of great significance, and the initial control quantity of the existing fixed time convergence method is considered to be large in impact and is not beneficial to being directly applied to the cooperative guidance algorithm.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a continuously switchable self-adaptive fixed time convergence cooperative guidance method, which comprises the steps of firstly establishing a motion relation mathematical model of a missile relative to a target, predicting the residual hit time of each missile on the basis, further defining the consistency error variable of the residual hit time, and finally providing a continuously switchable self-adaptive fixed time convergence cooperative guidance law capable of ensuring that a plurality of missiles hit the target simultaneously. The method can enable a plurality of missiles to finally hit the target at the same time, and compared with the existing fixed-time convergence cooperative guidance method, the method designed by the invention can effectively reduce the impact of the initial guidance instruction.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: establishing a missile relative target motion relation mathematical model;
assuming that n missiles strike a static target, the communication relation between every two missiles adopts an adjacency matrix A ═ a in graph theory ij ]It shows that if the i (i is 1,2, …, n) th missile can be built with the j (j is 1,2, …, n) th missileCommunication relation rule a ij 1, otherwise, a ij ＝0；
Aiming at the striking of a plurality of missiles on a fixed target under a two-dimensional plane, the communication topology among the missiles is assumed to be an undirected connected graph, and a relative kinematic model of the ith missile and the target is described by a formula (1):
in the formula, r i Indicates the distance, V, between the ith missile and the target i Representing constant flight speed of the ith missile, q i Is the i-th missile line-of-sight angle, gamma i And phi i Respectively is a track angle and a lead angle of the ith missile; a is i The normal acceleration of the ith missile is perpendicular to the speed direction;
step 2: predicting the residual hit time of the missile;
residual hit time of ith missile
The following formula was used for prediction:
in the formula N s >2 denotes the navigation ratio;
and 3, step 3: variable xi defining residual hit time consistency error i ：
In the formula (I), the compound is shown in the specification,
the residual hit time of the jth missile is obtained;
and 4, step 4: designing continuous switching self-adaptive fixed time convergence cooperative guidance law a i ：
In the formula, k i For guidance gain, 0<μ 1 <1，μ 2 >1，s i ＝(sign(ξ i +δ)－sign(ξ i －δ))/2，δ>0 denotes the switching boundary, ∈ i Is a positive real number; definition of
Is phi i The upper bound of (a) is,
is composed of
Is determined by the estimated value of (c),
the values of (a) are determined by the adaptation law:
wherein gamma is d And σ is a positive real number.
Preferably, k is i ＝1.3，μ 1 ＝0.5，μ 2 ＝1.5，γ d ＝2.7，N s ＝3，δ＝1.2，
ε i ＝9，σ＝0.1。
The invention has the following beneficial effects:
the invention designs a continuously switchable self-adaptive fixed time convergence cooperative guidance method, and multiple missiles can finally hit a target at the same time under a designed cooperative guidance law. Compared with the existing fixed-time convergence cooperative guidance method, the method designed by the invention can effectively reduce the impact of the initial guidance instruction.
Drawings
FIG. 1 is a schematic diagram of a multi-missile communication topology of the method of the invention.
FIG. 2 is a conventional fixed time convergence collaborative guided flight trajectory plot.
FIG. 3 is a conventional fixed time convergence coordinated guidance projectile distance curve.
FIG. 4 is a conventional fixed time convergent cooperative guidance consistency error curve.
FIG. 5 is a conventional fixed time convergence coordinated guided normal acceleration curve.
FIG. 6 is a continuously switched adaptive fixed time convergence cooperative guidance flight trajectory curve of the present invention.
FIG. 7 is a continuously switched adaptive fixed time convergence cooperative guided missile distance curve of the present invention.
FIG. 8 is a continuously switched adaptive fixed time convergence cooperative guidance consistency error curve of the present invention.
FIG. 9 is a continuously switched adaptive fixed time convergence cooperative guided normal acceleration curve of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention provides a continuously switched self-adaptive fixed time convergence cooperative guidance method aiming at the problem that multiple missiles hit a static target at the same time. The cooperative guidance method has the characteristic of fixed time convergence, meanwhile, the impact of an initial guidance instruction can be effectively reduced through the continuous switching characteristic, and the gain in the cooperative guidance law realizes real-time self-adjustment through a self-adaptive law.
A continuously switchable self-adaptive fixed time convergence cooperative guidance method comprises the following steps:
step 1: establishing a missile relative target motion relation mathematical model;
assuming that n missiles strike a static target, the communication relation between every two missiles adopts an adjacency matrix A ═ a in graph theory ij ]That is, if the ith (i is 1,2, …, n) missile can establish a communication relationship with the jth (j is 1,2, …, n) missile, a is represented ij 1, otherwise, a ij 0; for convenience of reference, the physical quantities associated with the ith missile are indicated by the subscript i. If any two missiles in the communication topology can find at least one communication path, the communication topology map is called a connected map. If the links in the communication topology are all bidirectional, i.e. a ij ＝a ji The graph is called an undirected graph, and a directed graph if unidirectional links exist.
Aiming at the striking of a plurality of missiles on a fixed target under a two-dimensional plane, the communication topology among the missiles is assumed to be an undirected connected graph, and a relative kinematic model of the ith missile and the target is described by a formula (1):
in the formula, r i Indicates the distance between the ith missile and the target, V i Representing constant flight speed of the ith missile, q i Is the i-th missile line-of-sight angle, gamma i And phi i Respectively is a track angle and a lead angle of the ith missile; a is i The normal acceleration of the ith missile is vertical to the speed direction;
and 2, step: predicting the residual hit time of the missile;
residual hit time of ith missile
The following formula is used for prediction:
in the formula N s >2 denotes a navigation ratio;
and step 3: variable xi defining residual hit time consistency error i ：
In the formula (I), the compound is shown in the specification,
the remaining hit time of the jth missile;
and 4, step 4: designing continuous switching self-adaptive fixed time convergence cooperative guidance law a i ：
In the formula, k i For guidance gain, 0<μ 1 <1，μ 2 >1，s i ＝(sign(ξ i +δ)－sign(ξ i －δ))/2，δ>0 denotes the switching boundary, ∈ i Is a positive real number; definition of
Is phi i The upper bound of (a) is,
is composed of
Is determined by the estimated value of (c),
the values of (a) are determined by the adaptation law:
wherein gamma is d And σ is a positive real number.
The specific embodiment is as follows:
the Matlab simulation platform is used for verifying the designed method, and the designed method is combined with the traditional fixed time convergence cooperative guidance law in order to verify the effectiveness of the continuously switched self-adaptive fixed time convergence cooperative guidance law
Making a comparison, wherein k 1,i And k 2,i Is the guidance gain.
In the embodiment, 3 missiles at different positions are selected for simulation verification with the background of hitting a static target in the air, the topology of undirected strong connectivity among the missiles is shown in fig. 1, the target position (5000m and 5000m), the speeds of three missiles are all selected to be 200m/s, the initial horizontal axis coordinate position and the initial vertical axis coordinate position are respectively (500 ), (2000,500) and (500,2000), and the guidance law parameter is set to be k i ＝1.3,μ 1 ＝0.5,μ 2 ＝1.5,γ d ＝2.7,N s ＝3，δ＝1.2，
ε i With 9, σ 0.1, the maximum overload limit is 30 g.
Simulation results under the two methods are respectively shown in fig. 2-5 and fig. 6-9, and the plane motion trail and the missile-eye distance curve show that although response curves are different, the two methods can ensure that three missiles hit a target simultaneously, and consistency errors can be rapidly converged. Compared with an acceleration instruction curve, the acceleration initial value of the continuously switched self-adaptive fixed time convergence cooperative guidance law is obviously smaller than that of the traditional fixed time convergence cooperative guidance method, and the result verifies that the designed guidance method can effectively reduce the impact of the initial control quantity.
Claims (2)
1. A continuously switchable self-adaptive fixed time convergence cooperative guidance method is characterized by comprising the following steps:
step 1: establishing a missile relative target motion relation mathematical model;
assuming that n missiles strike a static target, the communication relation between every two missiles adopts an adjacency matrix A ═ a in graph theory ij ]That is, if the ith missile can establish a communication relationship with the jth missile, j is 1,2, …, n missiles, i is 1,2, …, a ij 1, otherwise, a ij ＝0；
Aiming at the striking of a plurality of missiles on a fixed target under a two-dimensional plane, the communication topology among the missiles is assumed to be an undirected connected graph, and a relative kinematic model of the ith missile and the target is described by a formula (1):
in the formula, r i Indicates the distance, V, between the ith missile and the target i Representing constant flight speed of the ith missile, q i Is the i-th missile line-of-sight angle, gamma i And phi i Respectively is a track angle and a lead angle of the ith missile; a is i The normal acceleration of the ith missile is vertical to the speed direction;
step 2: predicting the residual hit time of the missile;
residual hit time of ith missile
The following formula is used for prediction:
in the formula N s >2 denotes the navigation ratio;
and step 3: variable xi defining residual hit time consistency error i ：
In the formula (I), the compound is shown in the specification,
the remaining hit time of the jth missile;
and 4, step 4: designing continuous switching self-adaptive fixed time convergence cooperative guidance law a i ：
In the formula, k i For guidance gain, 0<μ 1 <1，μ 2 >1，s i ＝(sign(ξ i +δ)－sign(ξ i －δ))/2，δ>0 denotes the switching boundary, ∈ i Is a positive real number; definition of
Is phi i The upper bound of (a) is,
is composed of
Is determined by the estimated value of (c),
the values of (a) are determined by the adaptation law:
wherein gamma is d And σ is a positive real number.
2. The adaptive fixed-time convergent cooperative guidance method for continuous switching according to claim 1, wherein k is i ＝1.3，μ 1 ＝0.5，μ 2 ＝1.5，γ d ＝2.7，N s ＝3，δ＝1.2，
ε i ＝9，σ＝0.1。
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| CN112113466A (en) * | 2020-08-19 | 2020-12-22 | 南京理工大学 | Multi-missile cooperative guidance method with limited time convergence |
| CN112129292A (en) * | 2020-09-02 | 2020-12-25 | 北京航空航天大学 | Heterogeneous aircraft cooperative guidance method considering attack time and attack angle constraints |
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| CN112577373B (en) * | 2020-11-27 | 2022-05-27 | 南京理工大学 | Guidance law for multiple missiles to attack static target simultaneously based on proportion guidance law |
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| CN106843265A (en) * | 2016-12-30 | 2017-06-13 | 哈尔滨工业大学 | Three-dimensional many guided missile cooperative guidance method and systems of finite time convergence control |
| CN112113466A (en) * | 2020-08-19 | 2020-12-22 | 南京理工大学 | Multi-missile cooperative guidance method with limited time convergence |
| CN112129292A (en) * | 2020-09-02 | 2020-12-25 | 北京航空航天大学 | Heterogeneous aircraft cooperative guidance method considering attack time and attack angle constraints |
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