Multi-hypersonic aircraft formation maneuvering control method based on hierarchical control architecture

Abstract

The invention belongs to the field of multi-aircraft formation control, and relates to a multi-hypersonic-velocity aircraft formation maneuvering control method based on a hierarchical control architecture. The invention provides a formation maneuvering control method for multiple hypersonic aircrafts based on a hierarchical control architecture and a leader-following strategy. According to the control architecture provided in the method, the follower can follow the leader to converge to the designed target position and form the target formation without acquiring the target formation or maneuvering parameters, and the communication consumption between the aircrafts can be greatly reduced. The matrix weight position constraint proposed in the method can enable followers to realize richer formation transformation under the condition of fewer neighbors. Under the condition that dynamic characteristics and engine characteristics of the hypersonic flight vehicle are fully considered, a motion state tracking controller corresponding to the dynamic characteristics and the engine characteristics is designed, and formation and maneuvering control of a multi-flight-vehicle system are achieved. A controller parameter selection method is provided, so that the method can be implemented in practical engineering.

Description

Technical Field

[0001] The present invention belongs to the field of multi - vehicle formation control, and relates to a multi - hypersonic vehicle formation maneuver control method based on a hierarchical control architecture. Background Art

[0002] Hypersonic Flight Vehicles (HFVs) have received extensive attention in the fields related to aircraft design and control due to their advantages such as supersonic speed, wide flight envelopes, and high penetration capabilities. Different from single - vehicle systems, multi - vehicle systems have better performance in aspects such as global information sharing, team information management, and anti - interference. In the motion control of a single hypersonic vehicle, a variety of advanced technologies have been widely adopted. Although these methods have advantages in dealing with non - linear uncertainties, it is not yet clear how to use these methods to drive multi - hypersonic vehicle systems to handle more complex tasks, especially the formation maneuver control problem. Therefore, the formation maneuver control problem of multi - hypersonic vehicles has gradually become a research hotspot.

[0003] Traditional multi - hypersonic vehicle formation control methods mainly include consensus control and containment control. Consensus control enables the followers in the system to follow an actual or virtual leader. However, this method requires real - time broadcasting of the time - varying target formation to each vehicle, resulting in a sharp increase in the communication network load when the number of vehicles increases. In addition, each vehicle needs to have the same level of intelligence, which is difficult to achieve in practical applications. Containment control ensures that the followers converge to a specific space determined by the leader. This specific space is usually a convex polygon or convex polyhedron formed by the leader. Compared with consensus control, containment control only requires the leader to have more advanced sensors, etc., thus reducing costs and network communication loads. However, containment control cannot ensure that the followers converge to a precise position, but usually converges to a position determined by the initial position of the leader, and the followers also cannot move outside the convex polygon determined by the leader.

[0004] The formation maneuver control method based on constraints can effectively solve the deficiencies of consensus control and containment control. For example, traditional real - number - weighted position constraints can achieve precise position control of followers when the followers do not know the target formation parameters and can also achieve formation maneuver transformation. However, this real - number - weighted position constraint requires each follower in the d - dimensional space to have at least d + 1 neighbors and only allows a part of formation transformations. Although the angle - constraint method can reduce the number of neighbors, it cannot achieve formation transformation or special formations such as vehicle collinearity.

[0005] To address the limitations of existing methods, based on a hierarchical control architecture, the present invention proposes a formation maneuver control method for multiple hypersonic vehicles with a leader-follower strategy. The proposed method can achieve formation and maneuver control of a multi-vehicle system while considering the dynamic characteristics of hypersonic vehicles and engine characteristics. In addition, during formation flight and maneuvers, the followers do not need to obtain target formation or maneuver parameters, which can greatly reduce communication consumption between vehicles. At the same time, the matrix weight position constraints proposed in the method enable the followers to achieve richer formation transformations with fewer neighbors.

[0006] The technical solution of the present invention is as follows:

[0007] A formation maneuver control method for multiple hypersonic vehicles based on a hierarchical control architecture, comprising the following steps:

[0008] Step 1: Establish a dynamic model of an n-high hypersonic vehicle system;

[0009] Further, Step 1 is specifically as follows:

[0010] The dynamic model of the i-th hypersonic vehicle is expressed as:

[0011]

[0012] where the subscript i ∈ {1, 2,..., n} represents the vehicle number. In the dynamic model, h i represents the flight altitude, x i represents the flight forward position, V i represents the flight speed, α i represents the angle of attack, γ i represents the track angle, q i represents the pitch angular velocity, respectively represent their derivatives. g represents the acceleration due to gravity, m i represents the mass of the i-th vehicle, I i represents the moment of inertia of the i-th vehicle. L i represents the lift, D i represents the drag, M i represents the torque, and is expressed using the following formula:

[0013]

[0014] where δ ei represents the elevator of the vehicle and is one of the control inputs of the vehicle; represents the average aerodynamic parameter; S represents the reference area; z T represents the thrust moment coupling parameter; represents the dynamic pressure, which is the air density ρi as a function of the flight speed V i , is defined as

[0015]

[0016] where ρ0 is the reference air density, h i is the flight altitude, h0 is the initial flight altitude, and h e is the reference altitude. The C in equations (6) and (7) L is the lift coefficient, and the C D is the drag coefficient. The C M,α is the torque coefficient related to the angle of attack, and the C related to the elevator is the torque coefficient related to the elevator. They are all functions of the angle of attack α i and the elevator δ ei , and are defined as

[0017]

[0018] where c e are all constant parameters.

[0019] The T in equations (2), (3), and (7) i represents the thrust of the aircraft engine and is defined as

[0020] T i = C T,Φ Φ i + C T

[0021] In the formula, Φ i represents the fuel-air ratio; C T,Φ and C T are both thrust coefficients and are functions of the angle of attack, defined as

[0022]

[0023] where β1, β2, …, β8 are all constant parameters. The fuel-air ratio Φ i of the engine is represented by a second-order system, that is

[0024]

[0025] In the formula, Φ ci is the fuel-air ratio command, which is one of the control inputs of the aircraft; is the derivative of the fuel-air ratio Φ i , is the second derivative of the fuel-air ratio Φ i ; ξ is the damping ratio of the second-order system, and ω f is the natural frequency of the second-order system.

[0026] Step 2: Decompose the dynamic models (1)-(5) of the hypersonic vehicle into a top-level subsystem and a bottom-level subsystem;

[0027] Further, Step 2 is specifically as follows:

[0028] Step 2.1: The top-level subsystem is the decomposition of formula (1). Define the position of the vehicle as p i =(x i , h i ) T . Since the flight path angle γ i is small enough, so sinγ i =γ i . According to formula (1), the differential equation satisfied by the vehicle position can be obtained

[0029]

[0030] wherein, is the set of vehicle numbers, u vi represents the virtual input of the top-level subsystem, defined as u vi =G i ·(V i , γ i ) T , and

[0031]

[0032] Step 2.2: The bottom-level subsystem is the decomposition of formulas (2)-(5).

[0033]

[0034] wherein

[0035]

[0036] Step 3: Establish a nominal formation and relative position constraints;

[0037] Further, Step 3 is specifically as follows:

[0038] The directed graph is expressed as where represents the set of nodes, and ε represents the set of edges. The edge from the j-th vehicle to the i-th vehicle is expressed as (i, j). The neighbor set of the i-th vehicle is expressed as defined as

[0039] Take the number of leaders as m and the total number of vehicles as n. Then the leader set The follower set is The nominal layout of the UAV swarm is denoted as \(r=(r_1,\ldots,r\) n ) T , where \(r\) i represents the nominal position of the \(i\)-th UAV. In the nominal formation, the relative position \(e\) ij between the \(i\)-th UAV and the \(j\)-th UAV is defined as

[0040] e ij =r j -r i =(e ij,1 ,e ij,2 ) T

[0041] where \(e\) ij,1 and \(e\) ij,2 are the first and second dimensional coordinates of the relative position, respectively.

[0042] The relative position constraint of the \(i\)-th UAV is written as

[0043]

[0044] where \(H\) ij and \(H\) ik are 2×2 weight matrices, calculated as

[0045]

[0046] where \(c_1\), \(c_2\), \(c_3\), \(c_4\) are calculated as

[0047]

[0048] where \(\|\cdot\|_2\) represents the 2-norm of the vector.

[0049] The nominal formation consists of a directed graph and the nominal layout \(r\), denoted as The set relationship contained in the nominal formation is represented by the weight matrix \(R\) f . The weight matrix \(R\) f is a block matrix, composed of \(n - m\) rows and \(n\) columns of 2×2 matrices, and the submatrix \([R\) f ij at the \(i\)-th row and \(j\)-th column position is

[0050]

[0051] The matrix \(R\) f can be decomposed into \(R\) f =[R\) fl R\) ff , where \(R\) fl is an \(n - m\) row by \(m\) column block submatrix, \(R\) ff ​It is a sub - matrix with \(n - m\) rows and \(n - m\) columns in blocks.

[0052] Step 4: Determine the target formation;

[0053] Furthermore, Step 4 is specifically as follows:

[0054] The target formation \(p\) * (t) is designed as

[0055]

[0056] In the formula, \(p\) * (t) is a column vector composed of the target positions of the aircraft, which can be decomposed into the leader target position and the follower target position That is denotes the Kronecker product; \(I\) n is an \(n -\)dimensional identity matrix; \(1\) n is an \(n -\)dimensional vector with all elements equal to 1; \(\beta(t)\) is a scaling parameter; \(\delta(t)\) is a translation parameter; \(A(t)\) is a two - dimensional rotation matrix; denotes the time - varying target shape parameter, satisfying

[0057] \(R\) fl ·\(\eta\) l (t)+R ff ·\(\eta\) f (t)=0

[0058] It should be noted that the geometric relationship between aircrafts is invariant to the transformation in the target formation, that is

[0059]

[0060] Step 5: Determine the control objective;

[0061] Furthermore, Step 5 is specifically as follows:

[0062] According to Step 4, the target formation is written as

[0063]

[0064] Thus, the control objectives of the leader and the followers are

[0065]

[0066] In the formula, \(p\) l (t) is the position of the leader at time \(t\), \(p\) f (t) is the position of the follower at time \(t\), \(I\) m is an \(m -\)dimensional identity matrix, \(1\) m is an \(m -\)dimensional vector with all elements equal to 1.

[0067] Step 6: Design the motion state planning module;

[0068] Specifically, Step 6 is as follows:

[0069] The motion state planning module calculates the target motion state required for the leader and the followers to maintain the target formation, where the target motion state refers to the flight speed V i and the track angle γ i , that is, the virtual input u of the subsystem in formula (8) vi expectation value.

[0070] The motion state planner of the leader is designed as:

[0071]

[0072] where k1, k2, k3 > 0 are the designed control gains; v ∈ (0, 1) is a constant parameter; sat(·) represents the saturation function, satisfying

[0073]

[0074] represents the error between the leader's position and the target position; is the derivative of the leader's target position, which can be pre-calculated according to the designed target position trajectory.

[0075] The motion state planner of the follower is designed as:

[0076]

[0077] where c1 > 0 is the designed control gain; represents the actual position change of the follower's neighbor, that is, the speed; H ij is the sub-matrix of R in formula (9) f .

[0078] After calculating the expectation value u of the virtual input pi , the expectation value V of the flight speed can be calculated di and the expectation value γ of the track angle di , that is

[0079]

[0080] Step 7: Design the motion control module;

[0081] Specifically, Step 7 is as follows:

[0082] The motion control module calculates the value that can make the flight speed V i and the track angle γ iFollow the expected flight speed V calculated in step 6 di and the expected track angle γ di to obtain the aircraft control signal, i.e., the fuel-air ratio command Φ ci and the elevator δ ei . It consists of two parts: speed control and track angle control.

[0083] Step 7.1: Speed control; The aircraft speed is controlled by the fuel-air ratio command Φ ci . According to the subsystem obtained in step 2.2, design the controller as

[0084]

[0085] where k v1 , k v2 , k v3 > 0 are controller gains; e vi = V i - V di represents the flight speed tracking error; represents the derivative of the expected flight speed.

[0086] Step 7.2: Track angle control; The track angle is controlled by the elevator δ ei . According to the subsystem obtained in step 2.2, calculate the following controller. Calculate the expected angle of attack α di of the aircraft as

[0087]

[0088] where k γ1 , k γ2 , k γ3 > 0 are controller gains; e γi = γ i - γ di represents the track angle tracking error; represents the derivative of the expected track angle.

[0089] Calculate the expected pitch angular velocity q di of the aircraft as

[0090]

[0091] where k α1 , k α2 , k α3 > 0 are controller gains; e αi = α i - α di represents the angle of attack tracking error; represents the derivative of the expected angle of attack.

[0092] Calculating the elevator command δ of the aircraft ei where

[0093]

[0094] k q1 , k q2 , k q3 > 0 are controller gains; e qi = q i - q di represents the pitch angular velocity tracking error; represents the derivative of the desired pitch angular velocity.

[0095] Based on the obtained fuel - air ratio command Φ ci and the elevator δ ei formation maneuver control is performed on multiple hypersonic aircraft.

[0096] Advantages of the present invention: For a cluster of multiple hypersonic aircraft, considering the dynamic characteristics of hypersonic aircraft, the present invention proposes a formation maneuver control scheme based on a hierarchical control architecture. The present invention uses matrix weight constraints to achieve the positioning, formation, and maneuver effects of multiple aircraft. Compared with traditional real - number weight constraints, the aircraft in the method of the present invention require fewer neighbors, thereby reducing the communication requirements within the cluster. The present invention can not only achieve formation rotation, scaling, and translation in existing methods, but also achieve more types of formation transformations. In the present invention, the follower controller only needs to obtain the relative position relationship with its neighbors, which can be directly measured by the follower, thereby reducing the information transmission with its neighbors and at the same time reducing the complexity of the cluster system, making this method easy to implement in engineering.

[0097] The present invention is different from the existing control methods for multi - hypersonic aircraft systems. The containment control can only make the hypersonic aircraft converge to a specific area determined by the leader, while the method of the present invention can make each hypersonic aircraft reach the desired precise position. At the same time, due to the invariance of the geometric relationship between hypersonic aircraft in the method of the present invention, the follower does not need to obtain time - varying target formation information to achieve precise formation control, thus greatly reducing the communication performance requirements. Compared with the traditional method of separately controlling the altitude and position of hypersonic aircraft, the method of the present invention can simultaneously achieve aircraft altitude and position control, thereby reducing the performance requirements for aircraft sensors and being more easily implemented in engineering. The present invention provides certain experience for the research of formation maneuver control technology for multi - hypersonic aircraft clusters and also has high practical engineering application value. Brief Description of the Drawings

[0098] Figure 1Structural diagram of the formation maneuver control method for multiple hypersonic vehicles based on a hierarchical control architecture;

[0099] Figure 2 The directed graph used for the nominal formation in the example;

[0100] Figure 3 Schematic diagram of the formation change of multiple hypersonic vehicles. Among them, (a) is the formation of multiple hypersonic vehicles at t = 0s, (b) is the formation of multiple hypersonic vehicles at t = 50s, (c) is the formation of multiple hypersonic vehicles at t = 100s, (d) is the formation of multiple hypersonic vehicles at t = 150s, (e) is the formation of multiple hypersonic vehicles at t = 200s, (f) is the formation of multiple hypersonic vehicles at t = 250s, (g) is the formation of multiple hypersonic vehicles at t = 300s, and (h) is the formation of multiple hypersonic vehicles at t = 350s;

[0101] Figure 4 The formation control error of each hypersonic vehicle, where (a) is the change in the forward position error and (b) is the change in the altitude error. Detailed implementation method

[0102] The following further illustrates the detailed implementation method of the present invention in combination with the attached drawings and technical solutions.

[0103] A formation maneuver control method for multiple hypersonic vehicles based on a hierarchical control architecture, comprising the following steps:

[0104] (1) Establish the dynamic model of n hypersonic vehicle systems; the dynamic model of the i-th hypersonic vehicle is expressed as:

[0105]

[0106] Among them, the subscript i ∈ {1, 2,..., n} represents the vehicle serial number. In the dynamic model, h i represents the flight altitude, x i represents the flight forward position, V i represents the flight speed, α i represents the angle of attack, γ i represents the track angle, q i represents the pitch angular velocity, respectively represent their derivatives. g represents the acceleration due to gravity, m i represents the mass of the i-th vehicle, I i represents the moment of inertia of the i-th vehicle. In this example, take

[0107] g = 32.1522, m i = 202.2, I i= 5×10 5

[0108] L i represents lift, D i represents drag, M i represents torque and can be expressed by the following formula:

[0109]

[0110] where δ ei represents the elevator of the aircraft and is one of the control inputs of the aircraft; represents the mean aerodynamic parameter; S represents the reference area; z T represents the thrust moment coupling parameter; represents the dynamic pressure, which is a function of the air density ρ i and the flight speed V i and is defined as

[0111]

[0112] where ρ0 is the reference air density, h i is the flight altitude, h0 is the initial flight altitude, h e is the reference altitude. In this example, take

[0113]

[0114] The C in formulas (6) and (7) L is the lift coefficient, C D is the drag coefficient, C M,α is the torque coefficient related to the angle of attack, is the torque coefficient related to the elevator, and both are functions of the angle of attack α i and the elevator δ ei and are defined as

[0115]

[0116] where, c e are all steady parameters. In this example, take

[0117]

[0118] The T in formulas (2), (3) and (7) i represents the thrust of the aircraft engine and is defined as

[0119] T i = C T,Φ Φ i + C T

[0120] In the formula, Φ i represents the fuel-air ratio; C T,Φ and C T are both thrust coefficients and are functions of the angle of attack, defined as

[0121]

[0122] where β1, β2, …, β8 are all constant parameters. In this example, take

[0123] β1 = -3.7693×10 5 , β2 = -3.7225×10 4 , β3 = 2.6814×10 4 ,

[0124] β4 = -1.7277×10 4 , β5 = 3.5542×10 4 , β6 = -2.4216×10 3 ,

[0125] β7 = 6.3785×10 3 , β8 = -1.009×10 2

[0126] The fuel-air ratio Φ of the engine i is represented by a second-order system, that is

[0127]

[0128] In the formula, Φ ci is the fuel-air ratio command and is one of the control inputs of the aircraft; is the derivative of the fuel-air ratio Φ i , is the second derivative of the fuel-air ratio Φ i ; ξ is the damping ratio of the second-order system, ω f is the natural frequency of the second-order system. In this example, take

[0129] ξ = 0.707, ω f = 20

[0130] (2) Decompose the dynamic model (1)-(5) of the hypersonic vehicle into a top-level subsystem and a bottom-level subsystem;

[0131] (2.1) The top-level subsystem is the decomposition of formula (1), and the position of the vehicle is defined as p i =(x i , h i ) T . Since the flight path angle γ i is small enough, so sinγ i= γ i According to formula (1), the differential equation satisfied by the aircraft position can be obtained

[0132]

[0133] where is the set of aircraft numbers, and u vi represents the virtual input of the top-level subsystem, defined as u vi = G i ·(V i , γ i ) T , and

[0134]

[0135] (2.2) The bottom-level subsystem is the decomposition of formulas (2)-(5).

[0136]

[0137] where

[0138]

[0139] (3) Establish the nominal formation and relative position constraints; the directed graph is represented as where represents the set of nodes, and ε represents the set of edges. The directed graph used in this example is shown in the appendix Figure 2 . The edge from the j-th aircraft to the i-th aircraft is represented as (i, j). The neighbor set of the i-th aircraft is represented as defined as

[0140] In this example, the number of leaders is taken as m = 3, the total number of aircraft is n = 6, the leader set and the follower set is The nominal layout of the aircraft cluster is denoted as r = (r1,..., r n ) T , where r i represents the nominal position of the i-th aircraft. In this example, the nominal layout is

[0141] r1 = (2, 0) T , r2 = (0, 0) T , r3 = (-2, 0) T , r4 = (2, 2) T , r5 = (0, 2) T , r6 = (-2, 2) T

[0142] In the nominal formation, the relative position \(e\) between the \(i\)-th vehicle and the \(j\)-th vehicle ij is defined as

[0143] \(e\) ij = \(r\) j - \(r\) i = (\(e\) ij,1 , \(e\) ij,2 ) T

[0144] where \(e\) ij,1 and \(e\) ij,2 are the first and second dimensional coordinates of the relative position, respectively.

[0145] The relative position constraint of the \(i\)-th vehicle can be written as

[0146]

[0147] where \(H\) ij and \(H\) ik are 2×2 weight matrices and can be calculated as

[0148]

[0149] where \(c1\), \(c2\), \(c3\), \(c4\) are calculated as

[0150]

[0151] where \(\|\cdot\|_2\) represents the 2-norm of the vector.

[0152] The nominal formation consists of a directed graph and a nominal layout \(r\), denoted as The set relationship included in the nominal formation can be represented by the weight matrix \(R\) f The weight matrix \(R\) f is a block matrix composed of \(n - m\) rows and \(n\) columns of 2×2 matrices, and the sub-matrix \([R\) f ij at the \(i\)-th row and \(j\)-th column position is

[0153]

[0154] The matrix \(R\) f can be decomposed into \(R\) f = \([R\) fl \(R\) ff , where \(R\) fl is a sub-matrix with \(n - m\) rows and \(m\) columns in blocks, and \(R\) ff is a sub-matrix with \(n - m\) rows and \(n - m\) columns in blocks. In this example, the calculated weight matrix \(R\) f is

[0155] ​

[0156] (4) Determine the target formation; the target formation p * (t) is designed as

[0157]

[0158] where p * (t) is a column vector composed of the target positions of the aircraft, which can be decomposed into the target position of the leader and the target position of the follower That is denotes the Kronecker product; I n is an n-dimensional identity matrix; 1 n is an n-dimensional vector with all elements equal to 1; β(t) is a scaling parameter; δ(t) is a translation parameter; A(t) is a 2D rotation matrix; represents the time-varying target shape parameter, satisfying

[0159] R fl ·η l (t) + R ff ·η f (t) = 0

[0160] It should be noted that the geometric relationship between aircraft is invariant to the transformation in the target formation, that is

[0161]

[0162] In this example, the various maneuver parameters of the designed target formation are given in detail in the simulation verification section.

[0163] (5) Determine the control objective; according to the previous step, the target formation can be written as

[0164]

[0165] Thus, the control objectives of the leader and the follower are

[0166]

[0167] where p l (t) is the position of the leader at time t, p f (t) is the position of the follower at time t, I m is an m-dimensional identity matrix, 1 m is an m-dimensional vector with all elements equal to 1.

[0168] (6) Design the motion state planning module; the motion state planning module calculates the target motion state required for the leader and the follower to maintain the target formation, where the target motion state refers to the flight speed V of the aircraft i and the flight path angle γ i , that is, the virtual input u of the subsystem in formula (8) vi expectation value.

[0169] The motion state planner of the leader is designed as:

[0170]

[0171] where k1, k2, k3 > 0 are the designed control gains; v ∈ (0, 1) is a constant parameter; sat(·) represents the saturation function, satisfying

[0172]

[0173] represents the error between the leader's position and the target position; is the derivative of the leader's target position, which can be pre-calculated according to the designed target position trajectory. In this example, take

[0174] k1 = 0.1, k2 = 5, k3 = 0.05, v = 0.1

[0175] The motion state planner of the follower is designed as:

[0176]

[0177] where c1 > 0 is the designed control gain; represents the actual position change of the follower's neighbor, that is, the speed; H ij is the sub-matrix of R in formula (9) f . In this example, take c1 = 0.15.

[0178] Calculate the expectation value u of the virtual input pi After that, the expectation value V of the flight speed can be calculated di and the expectation value γ of the flight path angle di , that is

[0179]

[0180] (7) Design the motion control module; the motion control module calculates the aircraft control signal that can make the flight speed V i and the flight path angle γ i follow the expectation value V of the flight speed calculated in step 6 di and the expectation value γ of the flight path angle di , that is, the fuel-air ratio command Φ ciWith the elevator δ ei . It consists of two parts, speed control and flight path angle control.

[0181] (7.1) Speed control; The speed of the aircraft is controlled by the fuel-air ratio command Φ ci . According to the subsystem obtained in step (2.2), the controller is designed as

[0182]

[0183] where k v1 , k v2 , k v3 > 0 are controller gains; e vi = V i - V di represents the flight speed tracking error; represents the derivative of the desired flight speed. In this example, take

[0184] k v1 = 0.1, k v2 = 0.1, k v3 = 0.75

[0185] (7.2) Flight path angle control; The flight path angle is controlled by the elevator δ ei . According to the subsystem obtained in step (2.2), the following controller can be calculated. Calculate the expected value of the angle of attack α di of the aircraft as

[0186]

[0187] where k γ1 , k γ2 , k γ3 > 0 are controller gains; e γi = γ i - γ di represents the flight path angle tracking error; represents the derivative of the desired flight path angle. In this example, take

[0188] k γ1 = 0.01, k γ2 = 500, k γ3 = 0.15

[0189] Calculate the expected value of the pitch angular velocity q di of the aircraft as

[0190]

[0191] where k α1 , k α2 , k α3 > 0 are controller gains; eαi = α i -α di represents the angle of attack tracking error; represents the derivative of the desired angle of attack. In this example, take

[0192] k α1 = 0.03, k α2 = 200, k α3 = 0.2

[0193] Calculate the elevator command δ of the aircraft ei as

[0194]

[0195] where k q1 , k q2 , k q3 > 0 are controller gains; e qi = q i -q di represents the pitch rate tracking error; represents the derivative of the desired pitch rate. In this example, take

[0196] k q1 = 0.075, k q2 = 200, k q3 = 0.4

[0197] Perform formation maneuver control on the hypersonic vehicle through the obtained fuel-air ratio command Φ ci and the elevator δ ei

[0198] (8) Simulation verification;

[0199] In this example, design the translation parameter β(t) = (x * (t), h * (t)) T , where x * (t) and h * (t) are the expected values of the forward position and altitude respectively, and are taken as

[0200] x * (t) = 7850·t, h * (t) = 85000

[0201] Set other maneuver parameters as:

[0202] 1. When t ∈ [0, 50]: (Initial formation)

[0203] η l = (1, 0, 0, 0, -1, 0) T , η​f =(1, 1, 0, 1, -1, 1) T ,

[0204] δ = 100

[0205] 2. When t ∈ (50, 100]:

[0206] η l =(1, 0, 0, 0, -1, 0) T , η f =(1, 1, 0, 1, -1, 1) T ,

[0207] δ = 100

[0208] 3. When t ∈ (100, 150]:

[0209] η l =(1, 0, 0, 0, -1, 0) T , η f =(1, 1, 0, 1, -1, 1) T ,

[0210] δ = 200

[0211] 4. When t ∈ (150, 200]:

[0212] η l =(1, 0, 0, 0, -3, 0) T , η f =(1, 1, 0, 1, -2, 2) T ,

[0213] δ = 100

[0214] 5. When t ∈ (200, 250]:

[0215] η l =(2, 0, -2, 0, 0, 0) T , η f =(2, 4, -2, 4, -1, 1) T ,

[0216] δ = 100

[0217] 6. When t ∈ (250, 300]:

[0218] η l =(0, 0, -2, 0, 2, 0) T , η f=(0, 2, -2, 2, -1, -1) T ,

[0219] δ = 100

[0220] 7. When t ∈ (300, 350]:

[0221] η l =(0, 1, -1, 0, 1, 0) T , η f =(-1, 2, -2, 1, -1, -1) T ,

[0222] δ = 200

[0223] The initial position of the aircraft is set as: (unit: ft)

[0224] (x 10 , h 10 ) = (-100, 85000), (x 20 , h 20 ) = (0, 85200),

[0225] (x 30 , h 30 ) = (0, 84800), (x 40 , h 40 ) = (-200, 85200),

[0226] (x 50 , h 50 ) = (-200, 84800), (x 60 , h 60 ) = (100, 85000)

[0227] Under the conditions of the above experimental configuration, simulation can obtain Figure 3 and Figure 4 simulation results.

[0228] Appendix Figure 3 describes the position distribution of the aircraft at different time points, where the abscissa Δx represents the forward position difference between each aircraft and the first aircraft, and the ordinate Δh represents the height difference between each aircraft and the first aircraft, so as to better show the formation shape of the current multi - HFV system. Among them, Figure 3 in (a) is the initial position of the aircraft, and the solid line and the dotted line are auxiliary lines drawn to more clearly reflect the current formation. After a period of time, the aircraft converges to the initial formation, that is, Figure 3 in (b). Then, it rotates 90 degrees clockwise to formFigure 3 In (c) of Figure 3 it is scaled as a whole (doubled) to form Figure 3 (d) of Figure 3 (e) to Figure 3 (h) of Figure 3 show the formation changes. Among them, the leaders in (e) to (g) of Figure 3 are collinear, but their relative positions are different, resulting in different position distributions of the followers. This also shows that in the case of collinear leaders, the formation maneuver control strategy proposed by the present invention can enable a multi-HFV system to form various non-collinear formation shapes for the followers. While in

[0229] Appendix Figure 4 describes the changes in the control errors between each aircraft and their target positions. The solid line is the control error of the leader, and the dashed line is the control error of the follower. It can be seen from the figure that the control error quickly converges from the initial non-zero value to zero and remains unchanged, indicating that all aircraft in the system can move along the desired trajectory and perform corresponding formation changes after a certain time.

[0230] The above results show that after applying this method, the multi-hypersonic vehicle system can achieve formation maneuver control, and the maneuver types include not only translation, rotation, and scaling, but also formation transformation. In particular, in the cases of collinear and non-collinear leaders, it can enable the followers to form diverse non-collinear formation shapes, and the followers do not require maneuver parameters during the maneuver. In summary, the method proposed by the present invention has achieved good application effects.

Claims

1. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture, characterized in that, It includes the following steps: Step 1: Establish the dynamic models of n hypersonic vehicle systems; Step 2: Decompose the dynamic model of the hypersonic vehicle into a top-level subsystem and a bottom-level subsystem; Step 3: Establish the nominal formation and relative position constraints; Step 4: Determine the target formation; Step 5: Determine the control objectives; Step 6: Design the motion state planning module; Step 7: Design the motion control module and conduct the formation maneuver control of multiple hypersonic vehicles.

2. The multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, wherein The specific content of Step 1 is as follows: The dynamic model of the i-th hypersonic vehicle is expressed as: Among them, the subscript \(i\in\{1,2,\ldots,n\}\) represents the aircraft serial number; \(h\) in the dynamic model i represents the flight altitude, \(x\) i represents the flight forward position, \(V\) i represents the flight speed, \(\alpha\) i represents the angle of attack, \(\gamma\) i represents the track angle, \(q\) i represents the pitch angular velocity, respectively represent their derivatives; \(g\) represents the gravitational acceleration, \(m\) i represents the mass of the \(i\)-th aircraft, \(I\) i represents the moment of inertia of the \(i\)-th aircraft; \(L\) i represents the lift, \(D\) i represents the drag, \(M\) i represents the torque, and is expressed by the following formula: Among them, δ ei represents the elevator of the aircraft and is one of the control inputs of the aircraft; represents the average aerodynamic parameter; S represents the reference area; z T represents the thrust moment coupling parameter; represents the dynamic pressure, which is a function of the air density ρ i and the flight speed V i and is defined as where ρ0 is the reference air density, h i is the flight altitude, h0 is the initial flight altitude, h e is the reference altitude; C in formulas (6) and (7) L is the lift coefficient, C D is the drag coefficient, C M,α is the torque coefficient related to the angle of attack, is the torque coefficient related to the elevator, and all are functions of the angle of attack α i and the elevator δ ei and are defined as wherein, c e are all steady parameters; The T in formulas (2), (3) and (7) i represents the thrust of the aircraft engine and is defined as T i = C T,Φ Φ i + C T Where Φ i represents the oil-gas ratio; C T,Φ and C T are both thrust coefficients and are functions of the angle of attack, defined as where β1, β2, …, β8 are all constant parameters; the engine air-fuel ratio Φ i is represented by a second-order system, i.e., where Φ ci is the fuel-air ratio command, which is one of the control inputs of the aircraft; is the derivative of the fuel-air ratio Φ i ; is the second derivative of the fuel-air ratio Φ i ; ξ is the damping ratio of the second-order system, and ω f is the natural frequency of the second-order system.

3. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that, The specific content of Step 2 is as follows: Step 2.1: The top-level subsystem is the decomposition of formula (1), and the position of the aircraft is defined as p i =(x i , h i ) T ; Since the track angle γ i is small enough, so sinγ i =γ i , the differential equation satisfied by the aircraft position is obtained according to formula (1) wherein, is the set of aircraft serial numbers, and u vi represents the virtual input of the top-level subsystem, defined as u vi = G i ·(V i , γ i ) T , and Step 2.2: The bottom-level subsystem is the decomposition of Formulas (2)-(5); In the formula 4. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that, The specific content of Step 3 is as follows: The directed graph is represented as where represents the set of nodes, and ε represents the set of edges; the edge from the j-th aircraft to the i-th aircraft is represented as (i, j); the neighbor set of the i-th aircraft is represented as is defined as Let the number of leaders be \(m\) and the total number of aircraft be \(n\). Then the leader set and the follower set is The nominal layout of the aircraft swarm is denoted as \(r=(r_1,\ldots,r n ) T , where \(r i represents the nominal position of the \(i\)-th aircraft; In the nominal formation, the relative position e between the i-th aircraft and the j-th aircraft ij is defined as e ij = r j - r i =(e ij,1 , e ij,2 ) T where e ij,1 and e ij,2 are the first - dimension and second - dimension coordinates of the relative position, respectively; The relative position constraint of the i-th vehicle is written as where, H ij and H ik are 2×2 weight matrices, calculated as where c1, c2, c3, c4 are calculated as where ‖·‖2 represents the 2-norm of the vector; The nominal formation consists of a directed graph and the nominal layout r, denoted as The set relationships included in the nominal formation are represented by the weight matrix R f ; the weight matrix R f is a block matrix composed of (n - m) rows and n columns of 2×2 matrices, and the sub-matrix [R f ij is​ Matrix R f is decomposed into R f =[R fl R ff , where R fl is a sub-matrix with n - m rows and m columns in blocks, and R ff is a sub-matrix with n - m rows and n - m columns in blocks.

5. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that, The specific content of Step 4 is as follows: Target formation p * (t) is designed as where p * (t) is a column vector composed of the target positions of the aircraft, which can be decomposed into the leader target position and the follower target position That is denotes the Kronecker product; I n is an n-dimensional identity matrix; 1 n is an n-dimensional vector with all elements equal to 1; β(t) is a scaling parameter; δ(t) is a translation parameter; A(t) is a 2D rotation matrix; represents the time-varying target shape parameter, satisfying R fl ·η l (t) + R ff ·η f (t) = 0 It should be noted that the geometric relationship between the vehicles is invariant to the transformation in the target formation, that is, there is 6. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that The specific content of Step 5 is as follows: According to Step 4, the target formation is written as Thus, the control objectives of the leader and the followers are where \(p\) l (t) is the position of the leader at time \(t\), and \(p\) f (t) is the position of the follower at time \(t\), \(I\) m is an \(m\times m\) identity matrix, and \(1\) m is an \(m -\)dimensional vector with all elements equal to \(1\).

7. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that The specific content of Step 6 is as follows: The motion state planning module calculates the target motion state required for the leader and the follower to maintain the target formation, where the target motion state refers to the flight speed V of the aircraft i and the flight path angle γ i , that is, the expected value of the subsystem virtual input u in formula (8) vi ; The motion state planner of the leader is designed as: where k1, k2, k3 > 0 are the designed control gains; v ∈ (0, 1) is a constant parameter; sat(·) represents the saturation function and satisfies Indicates the error between the leader position and the target position; Is the derivative of the leader target position and can be pre-calculated according to the designed target position trajectory; The motion state planner of the followers is designed as: where \(c_1 > 0\) is the designed control gain; represents the actual position change of the follower neighbor, i.e., the velocity; \(H\) ij is the submatrix of \(R\) in formula (9) f ; Calculate the expected value u of the virtual input pi After that, the expected value V of the flight speed can be calculated di and the expected value γ of the track angle di , that is 8. A multi-hypersonic vehicle formation maneuver control method based on a hierarchical control architecture according to claim 1, characterized in that, The specific content of Step 7 is as follows: The motion control module calculates the aircraft control signals that can make the flight speed V i and the flight path angle γ i follow the expected flight speed V di and the expected flight path angle γ di calculated in step 6, namely the fuel-air ratio command Φ ci and the elevator δ ei ; it includes two parts, speed control and flight path angle control; Step 7.1: Speed control; the speed of the aircraft is controlled by the fuel-air ratio command Φ ci . According to the subsystem obtained in Step 2.2, design the controller as where k v1 , k v2 , k v3 > 0 is the controller gain; e vi = V i - V di represents the flight speed tracking error; represents the derivative of the desired flight speed; Step 7.2: Track angle control; the track angle is controlled by the elevator δ ei According to the subsystem obtained in step 2.2, calculate the following controller; calculate the expected angle of attack α of the aircraft di as where, k γ1 , k γ2 , k γ3 > 0 is the controller gain; e γi = γ i - γ di represents the track angle tracking error; represents the derivative of the desired track angle; Calculate the expected value q of the pitch angular velocity of the aircraft di For where k α1 , k α2 , k α3 > 0 is the controller gain; e αi = α i - α di represents the angle of attack tracking error; represents the derivative of the desired angle of attack; Calculate the elevator command δ of the aircraft ei For where k q1 , k q2 , k q3 > 0 is the controller gain; e qi = q i - q di represents the pitch angular velocity tracking error; represents the derivative of the desired pitch angular velocity; Through the obtained fuel-air ratio command Φ ci and the elevator δ ei perform formation maneuver control on the multi-hypersonic vehicle.

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