High-speed aircraft preset time formation cooperative guidance method with double constraints

Abstract

The invention discloses a high-speed aircraft preset time formation cooperative guidance method with double constraints. The method comprises the following steps: 1, constructing a three-channel decoupling cooperative guidance motion system; 2, constructing a disturbance observer based on preset time; 3, constructing a consistency guidance protocol; 4, constructing a sight angle control protocol based on preset time; and 5, controlling the high-speed aircraft to intercept the maneuvering target by applying the preset time disturbance observer, the preset time consistency protocol and the preset time sight angle control protocol, and outputting a state response diagram. The method has the advantages that three-channel decoupling of the leader following system is achieved through geometric analysis, and then a high-speed aircraft preset time control task suitable for a leader following framework is constructed; 2, the estimation of the residual flight time of the high-speed aircraft is avoided, and the stability of the high-speed aircraft is proved; and 3, designing a lateral angle constraint control algorithm based on preset time, and realizing preset time stability of leader-follower transverse and lateral system states.

Description

Technical Field

[0001] The present invention is a preset-time formation cooperative guidance method for high-speed aircraft with dual constraints, belonging to the technical field of unmanned aircraft. Background Technique

[0002] High-speed aircraft generally refer to a type of offensive unmanned aircraft with a speed in the subsonic range and equipped with a tactical unit, which can achieve target locking, high-speed course change, and long-range strike. With the rapid development of flight control technology and target indexing technology, the interception ability of a single high-speed aircraft shows significant limitations when dealing with high-speed maneuvering targets. Multi-aircraft guidance technology, by introducing multiple combat individuals with the same combat performance, forms a "multiple-to-one" strike formation, and finally achieves a coordinated strike on a single target from multiple directions at the same moment in the terminal guidance stage. This technology improves the overall interception ability of the formation and reduces the performance cost of a single aircraft by instantaneous saturation interception and blocking the target escape route. Therefore, the research on multi-aircraft guidance technology has important practical engineering significance and great development potential, and has received extensive attention in recent years.

[0003] The primary task of multi-aircraft guidance technology is to achieve the time and space unity of different individuals. Currently, the mainstream methods can be divided into attack-time constraint guidance and cooperative guidance. Attack-time constraint guidance relies on the accurate estimation of the remaining flight time by each high-speed aircraft and does not involve the sharing of target situation information. Therefore, it is essentially an independent homing strategy. Independent homing cannot reduce the performance requirements for individual high-speed aircraft and is difficult to autonomously adjust the attack time according to the dynamic battlefield environment. Cooperative guidance methods require forming a communication network with individuals as nodes during the guidance process, dynamically adjusting their own states by sharing situation information, and finally achieving consistent interception. Currently, most cooperative guidance methods use the global remaining flight time error as the expected convergence term, and the actual application effect is still affected by the accuracy of the individual's estimation of the remaining time. However, through the research on the cooperative guidance system based on the global remaining time, the academic community has gradually linked cooperative guidance with the second-order system consensus theory, making it possible to analyze cooperative guidance through advanced control theory.

[0004] As an effective advanced control theory, the finite-time convergence theory has been widely applied to multiple scenarios. The finite-time theory features fast convergence, which can meet the response requirements even during high-speed combat. Meanwhile, a finite-time controller designed and implemented by adopting specific nonlinear control methods, such as sliding mode control, can cope with external disturbances and internal nonlinear links of the system, and performs well in dealing with various guidance constraints including the attack angle constraint. Therefore, it has become a research hotspot. However, the upper bound of the finite-time theory's convergence is sensitive to the initial values and parameters, and it performs poorly when dealing with the attack angle constraint with large deviation values. Therefore, the fixed-time and predefined-time methods are introduced into cooperative guidance as subsequent improvement means. Compared with the finite-time control method, the upper bound of the fixed-time control convergence is independent of the initial value, but its relationship with the control parameters is complex and difficult to adjust. The predefined-time theory further simplifies this relationship and can meet most guidance occasions, but its convergence time domain still needs to be adjusted through parameters and cannot be directly set. Due to the strict requirements of high-speed aircraft guidance in convergence time management, it inspired the emergence of the Prescribed Time (PT) control theory. By introducing a specific monotonically increasing time-varying function, it maps the time domain of a preset length to an infinite time domain and then stabilizes the system, enabling the original system to achieve convergence within the preset time domain. Up to now, there is little work on cooperative guidance based on the prescribed-time control, mainly because the solution method of the prescribed-time control for nonlinear systems was proposed relatively late, and the involved time-domain transformation increases the difficulty of the stability proof process, making the relevant work more concentrated in the control field in practical applications.

[0005] Another key to constructing a cooperative guidance method is to design a suitable communication architecture network. As a classic communication architecture, the "leader-follower" communication architecture requires that there is always a leading individual among the high-speed aircraft participating in the interception mission. It directly observes and obtains the target situation information. Other individuals, as followers, exchange their information through the communication network and finally achieve the consensus convergence of the situation with the followers under the guidance of the guidance protocol. The "leader-follower" communication architecture has a small communication burden and low requirements for the perception ability of non-leader individuals, and has good engineering application value.

[0006] Based on the above problems, the present invention designs a prescribed-time formation cooperative guidance method for high-speed aircraft with dual constraints, aiming to construct a three-dimensional "leader-follower" cooperative guidance formation with a strict formation time under the prescribed-time control criterion for intercepting high-speed maneuvering targets with unknown states, and considering the prescribed-time convergence of the attack angle constraint. Summary of the Invention

[0007] 1. Object of the Invention:

[0008] The object of the present invention is to provide a preset-time formation cooperative guidance method for high-speed aircraft with dual constraints. The aim is to achieve cooperative guidance of multiple high-speed aircraft based on the "leader-follower" communication architecture within a preset time under multiple constraint conditions, while avoiding the estimation of the remaining flight time.

[0009] 2. Technical solution:

[0010] The present invention designs a preset-time formation cooperative guidance method for high-speed aircraft with dual constraints. By combining integral sliding mode control (ISMC) with second-order multi-agent (SMA) consensus strategy, a PT cooperative guidance law acting on the line-of-sight (LOS) direction is established, realizing consensus tracking guidance without the estimation of the remaining flight time. In addition, a two-level PT attack angle constraint strategy is designed to ensure the convergence of the impact angle before interception. The specific steps are as follows:

[0011] Step 1: Construct a three-channel decoupled cooperative guidance motion system

[0012] S11. Construct a three-dimensional cooperative guidance system under the leader-follower architecture

[0013] When there are N + 1 high-speed aircraft individuals in space, including N followers and 1 leader, attempting to intercept a high-speed maneuvering target T, their relative state relationships are as Figure 1 shown. At this time, a basic three-dimensional cooperative guidance system is formed between follower i and the leader, as follows:

[0014]

[0015] Among them, the subscript l represents the variables in the LOS coordinate system. For i ∈ {1,..., N}, R l,i represents the relative distance between follower i and leader L; γ l,i and ψ l,i represent the inclination angle and deflection angle in the LOS coordinate. and respectively represent the acceleration separation between the leader and the follower in the LOS coordinate; the superscript' represents the matrix transpose. The three-dimensional cooperative guidance system (1) not only shows the relationship between the leader and the follower, but also can be used to represent the relationship between target T and leader L. In the following text, for convenience, N + 1 is used to represent the relationship between the target and the leader.

[0016] It can be seen that the three-dimensional cooperative guidance system (1) is a typical non-linear system, and the system state variables are coupled, making it difficult to directly apply internal control means. Therefore, multi-model decoupling is required. Specifically, let x 1,i = R l,i , where and are the desired attack angles. Therefore, the three-dimensional cooperative guidance system (1) can be simplified to:

[0017]

[0018] where are considered fast time-varying mismatched perturbations in three directions, and these perturbations directly come from the leader. In the present invention, these external perturbations are considered unknown and bounded for this individual,

[0019] i.e., and

[0020] S12. Construct a three-dimensional preset-time cooperative guidance mission

[0021] Based on the leader-follower cooperative guidance model, the preset-time guidance targets of the leader and the follower can be obtained: within the user-defined time interval T s , the high-speed aircraft i = 1,..., N + 1 can intercept the maneuvering target T and achieve the PT convergence of the line-of-sight angle. Specifically, for the follower i = 1,..., N, the PT guidance target along the LOS direction is:

[0022]

[0023] where the subscript p = 1, 2. t1 represents the maximum convergence moment of the user-defined relative distance and relative speed. After the moment t1, if x p,N+1 both show asymptotic stability, and the leader satisfies:

[0024] x 1,N+1 = 0, t ≥ t2, (4)

[0025] then it is considered that the cooperative interception is achieved. In Equation (4), t2 is the interception time, which is determined by the actual guidance law of the leader. Then, the line-of-sight angle constraint control target is defined. For the high-speed aircraft i = 1,..., N + 1, the lateral PT cooperative guidance law is set as follows:

[0026]

[0027] where q = 3,..., 6. respectively represent the line-of-sight angle errors, where and respectively represent the desired line-of-sight angle and the desired line-of-sight angle rate. t3 represents the preset maximum convergence time, satisfying t3 ≤ t2. For t ≥ t3, all high-speed aircraft are expected to satisfy the specified line-of-sight angle.

[0028] Step 2: Construct a disturbance observer based on a preset time

[0029] To accurately obtain the fast time-varying information of connectable objects in the communication network, such as acceleration information, a disturbance observer with a preset time is used for state estimation to input the guidance model in real time. Taking the sub-model along the line-of-sight angle as an example, to observe the disturbance quantity d 1,i , i = 1,..., N. The observer is constructed as follows:

[0030]

[0031] where, at time time period T o1 = t o1 - t0. represents the estimated value, and the estimation error satisfies Δ1 is a sufficiently small positive real number, and the coefficients b1, κ1, r1, χ1 are positive real numbers respectively. When it is assumed that d 1,i is a bounded unknown, r1 needs to satisfy

[0032] In addition, without loss of generality, the function is defined as follows:

[0033]

[0034] where, ω m (t) is a time-varying function, satisfying:

[0035]

[0036] and m is a positive integer. The saturation function

[0037]

[0038] is used to replace the conventional sign function to reduce chattering during the convergence process. Furthermore, the sliding mode auxiliary variable is defined as:

[0039]

[0040] Therefore, for the sub-model along the line-of-sight angle, the mismatched disturbance quantity d can be realized within the time period T o1 by the observer (6)-(10)1,i , accurate estimation for \(i = 1,\cdots,N\), that is, the estimation error

[0041] Similarly, for the observation \(d\) q,i , \(q\in\{2,3\}\), \(i = 1,\cdots,N\), the forms of the preset time observer in the lateral direction are respectively expressed as follows:

[0042]

[0043] where The time interval \(T\) oq \(=t\) oq \(-t_0\), \(\Delta\) q is a sufficiently small positive number. The parameters \(b\) q , \(\kappa\) q , \(r\) q , \(\chi\) q are sufficiently small positive numbers, and \(r\) q satisfies Their auxiliary variables are respectively expressed as:

[0044]

[0045] Step 3: Construct the consensus cooperative guidance protocol

[0046] S31. Construct the consensus guidance protocol along the line-of-sight angle

[0047] By introducing the integral sliding mode theory and the second-order multi-agent theory, a PT consensus protocol in the LOS direction can be constructed, and this protocol can be described as:

[0048]

[0049] where and respectively represent the arrival guidance law and the nominal guidance law to the follower \(i\). Specifically, is used for the perturbed guidance stage with both external and internal disturbances, while is used for the ideal guidance stage without disturbances.

[0050] Therefore, based on the simplified three-dimensional cooperative guidance system (2), the auxiliary variable \(s\) based on integral sliding mode can be constructed 1,i as follows:

[0051]

[0052] Then can be expressed as:

[0053]

[0054] Among them, μ1>0, μ2>0. Coefficient is a positive real number, α i,j Directed spanning tree G formed by leader-follower E For a directed spanning tree consisting of N+1 nodes, the connectivity relationship between its followers can be expressed by the coefficient matrix A=[α i,j ], i, j∈1,..., N represents. When followers are connected, α i,j =1; otherwise, α i,j = 0. The relationship between the leader and the follower is represented by A N+1 =diag{α 1,N+1 ,...,α N,N+1} indicates that when the follower is connected to the leader, α i,N+1 =1; otherwise, α i,N+1 =0.

[0055] Then, the arrival guidance law can be obtained Control law

[0056]

[0057] The time domain parameter r c and and is a minimum value.

[0058] It can be seen that for a cooperative guidance system composed of N high-speed aircraft, when the guidance laws (13)-(16) are satisfied, and the coefficients μ1>0 and μ2>0 satisfy the following relationship:

[0059]

[0060] Among them, L E is the extended Laplace matrix of the communication system, then the entire cooperative guidance system can meet the PT guidance target along the LOS direction within time T1 (3).

[0061] S32. Prove the stability of the guidance protocol along the line of sight angle

[0062] In order to prove the stability of the consensus guidance protocol, the LOS direction system is introduced and the auxiliary variable s 1,i (14) Taking the derivative, we can get:

[0063]

[0064] By combining the arrival guidance law We can get:

[0065]

[0066] Therefore, choose the Lyapunov function and take the derivative within the time domain [t0, t c ) to obtain:

[0067]

[0068] Analyze the saturation function and the sign of s 1,i to find that -κ c sat(s 1,i , Δ c )s 1,i ≤ 0 and So

[0069]

[0070] Further transformation gives:

[0071]

[0072] Inequality (22) is in the form of the standard predefined-time control convergence formula. Therefore, the algorithm will achieve convergence before time t c . That is to say, when t ≥ t c , the following equation holds:

[0073]

[0074] Also, since the observer has achieved convergence within the time period t ∈ [t0, t o1 ), it can be considered that at this time the system in the LOS direction has been transformed into a standard linear multi-agent system as follows:

[0075]

[0076] At this time, the nominal guidance law begins to play a major control role.

[0077] For convenience, set ζ 1,i = x 1,i - x 1,N+1 , ζ 2,i = x 2,i - x 2,N+1 . ζ1 = [ζ 1,1 , ζ 1,2 , …, ζ 1,N ′, ζ2 = [ζ 2,1 , ζ 2,2 , …, ζ 2,N ′, Then the multi-agent system in the LOS direction can be abbreviated as:

[0078]

[0079] wherein, is the Kronecker product, and 1 N is the unit vector of size N. Thus, the Lyapunov function V2(t) can be constructed as follows:

[0080]

[0081] where According to the Schur complement theorem, the conditions for the above function to hold are: ① ②② Condition ② can be rewritten as follows:

[0082]

[0083] Obviously, when μ1 > 0 and μ2 > 0, formula (17) can satisfy the Schur complement theorem. Then, the stability of V2(t) can be analyzed. By taking the derivative of V2(t) within [t0, t1), we can obtain:

[0084]

[0085] Since μ1 > 0, so Γ1 ≤ 0, and the coefficient matrix in Γ2 can be expressed as:

[0086]

[0087] Obviously, under formula (17), Γ2 ≤ 0 holds. At this time, equation (28) is transformed into:

[0088]

[0089] Furthermore, the inequality (30) can be transformed into:

[0090]

[0091] where ξ is a positive integer.

[0092] By analyzing (31), it can be seen that there exists a closed set For satisfies

[0093]

[0094] Therefore, The inequality (31) can be expressed as:

[0095]

[0096] Further substituting Equation (33) into Equation (31) gives:

[0097]

[0098] Obviously, it also satisfies the Lyapunov form of the preset time control. Therefore, the multi-agent system (25) in the LOS direction will converge within the time interval (t0, t1].

[0099] Step 4: Construct the lateral angle control protocol based on the preset time

[0100] After completing the proof of the longitudinal consensus protocol, it is necessary to construct a lateral line-of-sight angle control protocol based on the preset time. Taking the lateral line-of-sight angle control as the law, for individual i = 1,..., N, construct the following guidance law:

[0101]

[0102] The above process is similar to Step S31. For the arrival guidance law, For the nominal guidance law. Their forms are as follows:

[0103]

[0104] Among them, Coefficient [[ID=3②]]The variable s constructed based on the integral sliding mode 2,i Is expressed as:

[0105]

[0106] Furthermore, σ 2,i And Can be expressed as:

[0107]

[0108] Among them, g1 and g2 are positive real numbers. The general form of the threshold function h is:

[0109]

[0110] Among them, t p ∈[t0, t0 + T s ); Δ2 is a sufficiently small positive number. The members within the variable pair {t, s2} can be defined by themselves. Therefore, the threshold functions h γ1,i And h γ2,i Can be defined as h γ1,i ({t, [x 3,i , x 4,i}, T3, t p1 , Δ γ1 ) and hγ2,i ({t,s 2,i},T o2 ,t p2 ,Δ γ2 ). Among them, Δ γ1 and Δ γ2 is a sufficiently small positive integer.

[0111] Under the action of the lateral preset time control laws (35)-(39), the lateral system can achieve stability of the lateral sight angle and the lateral sight angle rate before the preset time t3.

[0112] Similarly, the lateral preset time sight angle control law can be expressed as:

[0113]

[0114]

[0115] in, is a positive real number. Parameters g3 and g4 are positive real numbers. Threshold function h ψ1,i and h ψ2,i Represented as h ψ1,i ({t,[x 5,i ,x 6,i ]},T3,t q1 ,Δ ψ1 )and

[0116] h ψ2,i ({t,s 2,i},T o3 ,t q2 ,Δ ψ2 ). Δ ψ1 , Δ ψ2 , β3, β4 are sufficiently small positive real numbers.

[0117] Step 5: Build a leader guidance protocol based on line of sight control

[0118] In leader-follower collaborative guidance, the leader's seeker must dynamically adjust its strike angle to ultimately achieve precise target interception. Therefore, it is necessary to control the leader's line of sight angle. The principle of the parallel approach method shows that when the line of sight angular rate approaches 0, a high-speed aircraft can achieve precise interception of the target. Therefore, the leader does not need to control the distance along the line of sight angle direction, but only needs to control the lateral and side line of sight angles using equations (35) to (43).

[0119] Step 6: Apply the preset time disturbance observer, preset time consistency protocol and preset time sight angle control protocol to control the high-speed aircraft to intercept the maneuvering target and output the state response diagram

[0120] S61. Obtain the information of the target and the inertial system of the high-speed aircraft, and convert it into relative motion state information

[0121] At time t = t0, initialize the initial positions and initial velocities of the target T, the leader L, and the follower i, i = 1,..., N in the relative coordinate system, and respectively use and They both conform to the standard second-order acceleration system. Taking the motion of the follower i in the x direction as an example:

[0122]

[0123] are the acceleration components of this follower in the inertial coordinate system. It should be noted that the conversion relationship between the state variables of the inertial coordinate system and the line-of-sight angle coordinate system satisfies the following:

[0124]

[0125] At time t0, the target is under the control of the acceleration command to generate the velocity and acceleration values in the inertial coordinate system at time t0 + t δ where t δ is the minimum step size. Then, after conversion through formula (45), by taking the difference between the state variables under the target line-of-sight angle and the state variables of the leader, the relative state variables can be obtained. Similarly, the relative motion information of the follower and the leader can be updated.

[0126] S62. Use a preset-time observer to observe the external disturbance quantity

[0127] Considering the acceleration disturbance from other high-speed aircraft in the three-dimensional cooperative guidance system (1) of the follower, a preset-time observer (6)-(12) is used to observe the accelerations on the three channels respectively and generate estimated values for subsequent consensus time control and line-of-sight angle control. In particular, the leader is considered to be equipped with corresponding sensing devices to sense the state variables and acceleration quantities of the target.

[0128] S63. Apply the preset-time method to control the leader and the follower to intercept the maneuvering target

[0129] After obtaining the relative motion state, the leader and the follower use different acceleration control strategies to control the target. For the leader, without loss of generality, its acceleration along the line-of-sight angle direction is fixed, that is and its lateral acceleration input conforms to the preset-time angle control protocol (35)-(39). For the follower i, its acceleration input along the line-of-sight angle direction It conforms to the consistency guidance protocol (13)-(17). Calculate the acceleration control quantity of each aircraft at t0 + t through the above process, and re-enter it into the second-order model (44) to update the state information of the leader and the follower. δ At the moment, update the state information of the leader and the follower by re-inputting it into the second-order model (44).

[0130] S64. Determine whether the interception is successful and output the state response diagram.

[0131] When the distance between the high-speed aircraft and the target is close to 5 m, it enters the terminal guidance stage. At this time, the acceleration variable no longer changes. When the distance between the individual and the target is less than 0.1 m, it is considered that the cooperative interception of the target has been achieved. At this time, the program terminates and outputs the state response diagram. When the relative distance does not meet the above conditions and the maximum simulation time t has not been reached, M the process of S51-S53 is still repeated. For the detailed task flow chart of the above process, refer to Figure 2 .

[0132] The present invention designs a preset-time formation cooperative guidance method for high-speed aircraft with dual constraints, and its advantages and effects are as follows: First, through geometric analysis, the three-channel decoupling of the leader-follower system is realized, and then a preset-time control task for high-speed aircraft suitable for the leader-follower architecture is constructed. Second, a preset-time cooperative guidance method based on relative distance and relative speed is provided, which avoids the estimation of the remaining flight time of high-speed aircraft and proves its stability. Third, a lateral angle constraint control algorithm based on preset time is set to achieve the preset-time stability of the lateral and side system states of the leader-follower. Description of the Drawings

[0133] Figure 1 It is a leader-follower guidance relationship diagram.

[0134] Figure 2 It is a task flow chart.

[0135] Figure 3 It is a communication topology structure diagram.

[0136] Figure 4 It is a three-dimensional motion state response diagram.

[0137] Figure 5 It is a disturbance observation error response diagram.

[0138] Figure 6 It is a relative distance response diagram.

[0139] Figure 7 It is a relative speed response diagram.

[0140] Figure 8 It is a relative line-of-sight inclination response diagram.

[0141] Figure 9It is a relative line-of-sight deviation angle response diagram.

[0142] Figure 10 It is a relative line-of-sight tilt angular velocity response diagram.

[0143] Figure 11 It is a relative line-of-sight deviation angle angular velocity response diagram.

[0144] The symbols in the figure and their explanations are as follows:

[0145] O —— The origin of the inertial coordinate system;

[0146] x e , y e , z e —— The position components of the inertial coordinate system;

[0147] x, y, z —— The position components of the three-dimensional legend;

[0148] T, L, Fi —— Target, leader, follower i;

[0149] —— The position information of the target in the inertial coordinate system;

[0150] —— The position information of the leader in the inertial coordinate system;

[0151] —— The position information of the follower in the inertial coordinate system;

[0152] [V T , γ T , ψ T —— Target velocity, ballistic inclination angle, ballistic deviation angle;

[0153] [V L , γ L , ψ L —— Leader velocity, ballistic inclination angle, ballistic deviation angle;

[0154] [V i , γ i , ψ i —— Follower velocity, ballistic inclination angle, ballistic deviation angle;

[0155] [R l,N+1 , γ l,N+1 , ψ l,N+1 —— Leader's relative distance to the target, line-of-sight inclination angle, line-of-sight deviation angle;;

[0156] [R l,i , γ l,i , ψ l,i —— Follower i's relative distance to the leader, line-of-sight inclination angle, line-of-sight deviation angle

[0157] —— Motions of the target, the leader, the follower F1, and the follower FN in the inertial coordinate system;

[0158] —— Desired line-of-sight inclination angle, desired line-of-sight deflection angle;

[0159] [x 1,i , x 2,i , x 3,i , x 4,i , x 5,i , x 6,i —— Relative state variables of the follower i and the leader;

[0160] d 1,i , d 2,i , d 3,i —— External disturbance quantities in each direction received by the follower i;

[0161] T o1 , T o2 , T o3 —— Upper bounds of the preset convergence times of the observer in three directions;

[0162] T1, T c —— Preset convergence upper bound in the line-of-sight angle direction;

[0163] T3—— Preset convergence upper bounds in the lateral and side directions;

[0164] —— Acceleration output of the follower i;

[0165] L E —— Extended Laplacian matrix of the communication network;

[0166] —— Acceleration vector in the inertial coordinate system at time t;

[0167] —— Acceleration vector in the inertial coordinate system at time t + t δ ;

[0168] —— Disturbance quantity errors of three followers in the LOS direction;

[0169] —— Disturbance quantity errors of three followers in the lateral direction;

[0170] —— Disturbance quantity errors of three followers in the transverse direction;

[0171] t—— Simulation time. Specific implementation manners

[0172] The effectiveness of a preset-time formation and cooperative guidance method for high-speed aircraft with dual constraints is demonstrated below. The experimental computer is an Intel(R) Core(TM) i7-7700 processor with a CPU main frequency of 3.60 GHz and 32G of memory. The simulation software version is MATLAB 2022. A preset-time formation cooperative guidance method for high-speed aircraft with dual constraints is as follows:

[0173] Step 1: Construct a cooperative guidance motion system with three-channel decoupling

[0174] S11. Construct a three-dimensional cooperative guidance system under the leader-follower architecture

[0175] Suppose there are four high-speed aircraft in space, with 3 being followers and 1 being the leader. At a certain moment, they detect a high-speed moving target T and attempt to intercept it. Set this moment as the initial moment and set the minimum simulation step size t δ = 0.01 s and the maximum simulation duration t M = 100 s. The target T is under the control of accelerations and . The initial states and desired line-of-sight angles of the high-speed aircraft and the target are as follows in the table:

[0176]

[0177] S12. Preset-time cooperative guidance task

[0178] To better conform to the actual combat situation, the acceleration input of the high-speed aircraft is restricted, and the maximum acceleration of the followers and the leader is set to ±300 m / s 2 . Starting from the moment t0, the leader and the followers need to complete the consensus convergence under the control of the communication topology network and form a stable strike formation before the set time t1 = 25 s, as shown in Figure 3 . At this time, A N+1 = diag{1, 0, 1}. At the same time, the line-of-sight angle of the high-speed aircraft needs to accurately track the expected value within the preset time t3 = 20 s.

[0179] Step 2: Construct a disturbance observer based on preset time

[0180] According to the guidance task mentioned in S12, set the preset-time observer as follows: The series m of the time-varying function ω m is set to 3. For q = 1, 2, 3, the observer parameters are set as: b q = 3, χ q = 1, κ q = 3. r1 = 12, r2 = r3 = 5. Their preset time t oq= 5s,

[0181] Step 3: Construct a consistency cooperative guidance protocol

[0182] The parameter settings of the line-of-sight angle direction consistency protocol are as follows: t c = 10s, μ1 = 0.232, μ2 = 1. r c = 5, κ c = 1, Δ c = 0.1. During the t c time, the line-of-sight angle direction system needs to complete the compensation of the non-linear term by adjusting the acceleration input, reduce the LOS direction system to a linear multi-agent system, and complete the convergence of the relative distance and relative velocity before the t1 moment.

[0183] Step 4: Construct a lateral and lateral angle control protocol based on a preset time

[0184] Set the preset time control protocol parameters of the line-of-sight angle and line-of-sight angle rate of the lateral and lateral systems as follows: t p1 = 3s, t p2 = 10s. Δ γq = Δ ψq = 0.001, q = 1, 2. g1 = g3 = 0.01, g2 = g4 = 5; β1 = β3 = 0.01, β2 = β4 = 0.2, and are applied to the leader L and followers F1 - F3 respectively, for observing fast time-varying mismatched disturbances from connected individuals.

[0185] Step 5: Construct a leader guidance protocol based on line-of-sight angle control

[0186] To verify the effectiveness of the algorithm, make the LOS direction acceleration of the leader L constant at 5m / s 2 , and the lateral control protocol is the same as that of the followers, and the parameters are consistent with those in Step 4. At the beginning of each simulation cycle, the leader senses the motion state of the target through its own sensors and calculates the error from the desired line-of-sight angle. The lateral and lateral acceleration control quantities are generated through a preset time angle observer to drive the leader closer to the target.

[0187] Step 6: Apply the preset time disturbance observer, preset time consistency protocol and preset time line-of-sight angle control protocol to control a high-speed aircraft to intercept a maneuvering target and output a state response diagram

[0188] S61. Obtain the inertial system information of the target and the high-speed aircraft and convert it into relative motion state information

[0189] At t = ts , t s ∈(t0, t M , the maneuvering target inputs the acceleration maneuvering command into the motion model (44) to obtain the position and velocity in the inertial coordinate system. The leader obtains the relative motion state of the target through its own sensing device, subtracts it from its own motion state, and converts it into the relative state quantity in the line-of-sight coordinate system through Equation (45), and transmits its own relative state information to the connected followers through the communication network.

[0190] S62. Observe the external disturbance quantity using a preset-time observer

[0191] After the high-speed aircraft individual obtains the relative state quantity, it respectively uses the preset-time observers (6)-(12) to observe the acceleration disturbances d 1,i , d 2,i , d 3,i from the leader in three directions, and generates disturbance observation values

[0192] and inputs them as reference values into the corresponding channel guidance laws.

[0193] S63. Apply the preset-time method to control the leader and followers to intercept the maneuvering target

[0194] In three directions, respectively apply the corresponding line-of-sight angle direction preset-time guidance laws (13)-(17), lateral preset-time guidance laws (35)-(39), and transverse preset-time guidance laws (40)-(43) to the followers to generate the next t + t δ acceleration input quantity Specifically, apply the preset-time guidance laws (35)-(43) to the transverse and lateral directions of the leader, and fix the longitudinal acceleration of the leader at 5 m / s 2 to show the guidance situation of the leader in general cases. At this time, the acceleration input quantity of the leader at the next moment is Input the input quantity into the corresponding second-order model (44) for simulation at the t + t δ moment, and update and record the states of each aircraft.

[0195] S64. Judge whether the interception is successful and output the state response diagram

[0196] When the distance between the high-speed aircraft and the target is close to 5 m, it enters the terminal guidance stage. At this time, the acceleration input quantity remains unchanged. When the distance between the individual and the target is less than 0.1 m, it is considered that the individual has achieved the interception of the target. At this time, the simulation ends, and the state response diagram is output, such as Figures 4 - 10When the simulation does not reach the maximum simulation duration and the demand conditions are not met, steps S61 - S63 are repeated. When the simulation reaches the maximum simulation duration and the demand conditions are still not met, the simulation stops. The simulation lasted for 37.97 s, as Figure 3 The response diagram of the three - dimensional motion state is as Figure 4 shown. It can be seen that even if there are differences in the initial states among individuals, the proposed method can achieve accurate connection to the target. Figure 5 is the response diagram of the disturbance quantity observation error. Within the specified convergence time of 5 s, the observation errors in the three directions are stable at zero. It should be noted that as the relative distance R l,i rapidly converges to 0, d 2,i and d 3,i increase to infinity, and at this time the prerequisite of boundedness is no longer satisfied. Therefore, near the end of the guidance mission, the error estimators in the lateral and side - ways directions increase rapidly. However, since the aircraft has entered the terminal guidance stage and the control input is constant, this change has little impact on the guidance system. Figure 6 and Figure 7 are the response diagrams of the relative distance and relative velocity respectively. Within 25 s, R l reaches consistency and continues to decrease with time. A similar observation is also found in R l . Finally, the maximum relative distance of the four high - speed aircraft decreases to 0.0617 m, and the maximum relative change rate decreases to 1.5 m / s, meeting the guidance requirements. Figures 8 - 11 The response diagrams of the lateral and side - ways line - of - sight angles and their angular velocities are given. It can be seen that within 20 s, the attack angles of all high - speed aircraft converge to the desired angles and remain stable throughout the mission. In addition, the attack angles of all high - speed aircraft converge within 0.01° / s of the desired values within 20 s. From the above results, it can be known that the method designed by the present invention is overall effective.

Claims

1. A preset-time formation cooperative guidance method for a high-speed aircraft with dual constraints, characterized in that: The method includes the following steps: Step 1: Construct a three-channel decoupled cooperative guidance motion system S11. Construct a three-dimensional cooperative guidance system under a leader-follower architecture; S12. Construct a three-dimensional preset-time cooperative guidance task; Step 2: Construct a disturbance observer based on preset time To accurately obtain the fast time-varying information of connectable objects in the communication network, a disturbance observer with preset time is used for state estimation to input the guidance model in real time; Step 3: Construct a consensus cooperative guidance protocol; S31. Construct a consensus guidance protocol along the line-of-sight angle: By introducing the integral sliding mode theory and the second-order multi-agent theory, construct a preset-time consensus protocol in the line-of-sight angle direction; S32. Prove the stability of the consensus guidance protocol along the line-of-sight angle; Step 4: Construct a lateral angle control protocol based on preset time; S41. Construct a lateral preset time control: After proving the longitudinal consensus protocol, it is necessary to construct a lateral line-of-sight angle control protocol based on preset time; S42. Construct a lateral preset-time guidance law; Step 5: Construct a leader guidance protocol based on line-of-sight angle control; Step 6: Apply the preset-time disturbance observer, the preset-time consensus protocol, and the preset-time line-of-sight angle control protocol to control a high-speed aircraft to intercept a maneuvering target and output a state response diagram; S61. Obtain the inertial system information of the target and the high-speed aircraft and convert it into relative motion state information; S62. Use a preset-time observer to observe the external disturbance quantity; S63. Apply the preset-time method to control the leader and follower to intercept the maneuvering target; S64. Judge whether the interception is successful and output a state response diagram.

2. A preset-time formation cooperative guidance method for a high-speed aircraft with dual constraints according to claim 1, characterized in that: The three-dimensional preset-time cooperative guidance task constructed in Step 1 is specifically implemented as follows: Based on the leader-follower cooperative guidance model, the preset-time guidance objectives of the leader and the followers are obtained: within the user-defined time interval T s such that the high-speed vehicles i = 1, ..., N+1 can intercept the maneuvering target T and achieve the preset-time convergence of the line-of-sight angle; specifically, for the followers i = 1, ..., N, the PT guidance objective along the LOS direction is: where the subscript p = 1, 2; t1 represents the maximum convergence time of the user-defined relative distance and relative speed; after the moment t1, if x p,N+1 both show asymptotic stability, and the leader satisfies: x 1,N+1 = 0, t ≥ t2, Then it is considered that cooperative interception is achieved; where t2 is the interception time, which is determined by the actual guidance law of the leader; then define the line-of-sight angle constraint control target; for high-speed aircraft i = 1,..., N+1, the lateral PT cooperative guidance law is set as follows: where q = 3,..., 6; respectively represent the line-of-sight angle error, where and respectively represent the desired line-of-sight angle and the desired line-of-sight angle rate; t3 represents the preset maximum convergence time, satisfying t3 ≤ t2; for t ≥ t3, all high-speed aircraft are expected to satisfy the specified line-of-sight angle.

3. A preset-time formation cooperative guidance method for a high-speed aircraft with dual constraints according to claim 1, characterized in that: The consensus guidance protocol along the line-of-sight angle constructed in Step S31 is specifically implemented as follows: By introducing the integral sliding mode theory and the second-order multi-agent theory, construct a PT consensus protocol in the LOS direction, and this protocol is described as: Among them, and represent the arrival guidance law and the nominal guidance law to follower i, respectively; specifically, is used for the disturbed guidance phase with both external and internal disturbances, while is used for the ideal guidance phase without disturbances. Construct the auxiliary variable s based on integral sliding mode 1,i As follows: Then It is expressed as: where, μ1 > 0, μ2 > 0; the coefficient is a positive real number, α i,j is the connectivity parameter of the directed spanning tree G E formed by the leader - followers; for a directed spanning tree consisting of N + 1 nodes, the connectivity relationship among its followers can be represented by the coefficient matrix A = [α i,j , i, j ∈ 1,..., N; when the followers are connected, α i,j = 1; otherwise, α i,j = 0; the relationship between the leader and the followers is represented by A N+1 = diag{α 1,N+1 ,..., α N,N+1}; when a follower is connected to the leader, α i,N+1 = 1; otherwise, α i,N+1 = 0; Then, the arrival guidance law is obtained as the control law: Among them, the time domain t c > t o1 ; parameter r c and and is a minimum value; For a cooperative guidance system composed of N high-speed aircraft, when the guidance law is satisfied, and the coefficients μ1 > 0 and μ2 > 0 satisfy the following relationship: Among them, L E is the extended Laplacian matrix of the communication system, and the entire cooperative guidance system meets the guidance target within time T1.

4. A preset time formation cooperative guidance method for a high-speed aircraft with dual constraints according to claim 1, characterized in that: The specific process of Step 6 is as follows: S61. Obtain the inertial system information of the target and the high-speed aircraft and convert it into relative motion state information At time \(t = t_0\), initialize the initial positions and initial velocities of the target \(T\), the leader \(L\), and the followers \(i\), \(i = 1,\ldots,N\) in the relational coordinate system, and respectively use and They both conform to the standard second-order acceleration system. Taking the motion of follower \(i\) in the \(x\)-direction as an example: is the acceleration component of the follower in the inertial coordinate system; the state quantity conversion relationship between the inertial coordinate system and the line-of-sight angle coordinate system satisfies the following: At time t0, the target, under the control of the acceleration command , generates the velocity and acceleration values in the inertial coordinate system at time t0 + t δ , where t δ is the minimum step size; then, by taking the difference between the state quantity of the target's line of sight and that of the leader, the relative state quantity is obtained; similarly, the relative motion information of the follower and the leader is updated. S62. Use a preset-time observer to observe the external disturbance quantity Considering the acceleration disturbance from other high-speed aircraft in the follower system, a preset-time observer is used to observe the accelerations on three channels respectively and generate estimated values, which are used for subsequent consensus time control and line-of-sight angle control; S63. Apply the preset-time method to control the leader and follower to intercept the maneuvering target After obtaining the relative motion state, the leader and the follower adopt different acceleration control strategies to control the target. For the leader, its acceleration along the line-of-sight angle is fixed, i.e., and its lateral acceleration input conforms to the preset time-angle control protocol. For the follower i, its acceleration input along the line-of-sight angle conforms to the consensus guidance protocol. Through the above process, the acceleration control quantities of each aircraft at time t0 + t δ are calculated and re-input into the second-order model to update the state information of the leader and the follower. S64. Judge whether the interception is successful and output a state response diagram.

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