Sea-air heterogeneous unmanned system predetermined time formation method based on event trigger output constraint

Abstract

The invention provides an event-triggered output-constrained sea-air heterogeneous unmanned system predetermined time formation method. According to the technical scheme, the method comprises the following steps that 1, coordinate transformation is used for converting an under-actuated heterogeneous USV-UAV system into a second-order full-drive system; 2, designing a dynamic observer based on preset time; 3, designing a preset time control algorithm with asymmetric output constraints; 4, in order to save communication resources, a self-adaptive preset time event triggering mechanism is provided; and step 5, proving error convergence through Lyapunov stability analysis, and eliminating a sesame phenomenon. According to the invention, 60%-80% of communication resources can be saved, and the formation task can be completed within the preset time under the condition that the output is limited.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned system formation control, and in particular to a method for pre-setting time formation of sea and air heterogeneous unmanned systems with event-triggered output constraints. Background Art

[0002] As maritime superiority becomes a key strategic priority for national technological development, heterogeneous multi-agent systems consisting of UAVs and unmanned boats have become a research hotspot. This heterogeneous multi-agent system provides excellent payload and mission configuration capabilities by combining the unique advantages of UAVs and unmanned boats, making it invaluable in cross-domain collaboration in sea and air operations. However, the different dynamic characteristics, structural differences, spatial dimensions, and model parameter changes between UAVs and unmanned boats complicate their coordinated operation and control.

[0003] For example, when network bandwidth is limited, excessive data transmission can cause network congestion. Unlike the time-triggered mechanism with a fixed transmission cycle, event-triggered control updates the system according to specific trigger conditions, effectively reducing redundant information transmission and minimizing resource waste. In the article "Event Triggering Based on Finite Time for Second-Order Master-Slave Multi-Agent Systems with Uncertain Perturbations", the authors designed an event-triggered mechanism to solve the problem of communication resource waste to a certain extent and improve the efficiency of communication. However, this article is based on a finite time framework and does not solve the problem of event triggering mechanism and predefined time control. In addition, this article focuses on event triggering strategies with fixed thresholds and does not explore time-varying threshold strategies that adapt to system states.

[0004] Resolving output constraints is a critical but often overlooked issue. Output constraints, such as those on position and velocity, are derived from physical performance characteristics or external environmental factors. In the paper Event-Triggered Adaptive Control of Multi-Agent Systems with Saturated Inputs and Partial State Constraints, the authors only focused on input constraints, such as rotational speed and rudder angle, but output constraints, especially in heterogeneous UAV-UAV systems, have received less attention. However, constraining position errors and outputs is critical to ensure safety during formation missions, as excessive tracking errors caused by sudden load changes, current or voltage instability, or environmental disturbances can pose significant risks. Recently, barrier Lyapunov functions have been used to manage nonlinear systems with state and output constraints, and have shown advantages in resolving static symmetric constraints and time-varying asymmetric constraints through time-varying barrier Lyapunov functions. Despite their potential, barrier Lyapunov functions have rarely been applied to formation control of multi-agent systems of unmanned aerial vehicles under a predefined time-convergence framework, highlighting a promising area for future research. Summary of the invention

[0005] The purpose of the present invention is to provide a method for pre-determined time distributed formation control of sea and air heterogeneous unmanned systems with asymmetric output constraints based on event triggering, which solves the problem of realizing distributed formation control of heterogeneous unmanned boat-UAV systems within a predetermined time frame and with output constraints. At the same time, through the adaptive dynamic event triggering mechanism, the communication efficiency is greatly improved, which can save 60%-80% of communication resources.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a method for pre-determined time distributed formation control of a heterogeneous unmanned boat-unmanned aerial vehicle system with asymmetric output constraints based on event triggering, comprising the following steps:

[0007] Step 1: Use coordinate transformation to transform the underactuated heterogeneous USV-UAV system into a second-order fully dynamic system;

[0008] Step 2: To estimate the uncertain dynamics, an uncertain dynamic observer based on a preset time is designed;

[0009] Step 3: Design a preset time control algorithm with asymmetric output constraints;

[0010] Step 4: To save communication resources, an adaptive preset time event trigger mechanism is proposed;

[0011] Step 5: Prove the convergence of the error through Lyapunov stability analysis and eliminate the Zeno phenomenon.

[0012] Furthermore, in step 1, the kinematic model of the unmanned boat in the ground system can be expressed as

[0013]

[0014] In the formula, (x i (t),y i (t)) and ι i (t) are the position and heading angle of the i-th unmanned boat in the ground coordinate system; (w i (t),v i (t)) and o i (t) is the linear velocity and angular velocity of the i-th unmanned boat.

[0015] The dynamic model of the unmanned boat is

[0016]

[0017] where u i,w (t) and u i,o (t) represents the control input of USV, m 11,i ,m 22,i ,m 33,iis a mass parameter related to the rotation and motion of the USV. In addition, d 11,i ,d 22,i and d 33,i Corresponds to the damping parameter related to the USV flow effect.

[0018] Since the kinematic model of the unmanned boat is a non-holistic constraint model, a new output state variable p is defined. i (t) = [p i1 (t),p i2 (t)] T for

[0019]

[0020] Where ∈ is a very small positive constant, which represents the distance from the reference point of the i-th unmanned boat to the center of mass.

[0021] From the above formula, the kinetic equation can be obtained as follows:

[0022]

[0023] Among them, u i (t)=[u i,w (t),u i,o (t)] T

[0024]

[0025] The UAV dynamics model is

[0026]

[0027] Among them, the total thrust and control torque acting on the i-th UAV are u i1 ,u i2 ,u i3 and u i4 , represents the propeller speed margin. The position and attitude of the i-th UAV are p i =[x i ,y i ,z i ] T and Description. The moment of inertia of the quadcopter is l x ,l y and l z . The gravitational acceleration g is expressed as m i is the mass of the drone; the air damping coefficient is d y ,d z , d φ and Corresponding to the appropriate directional damping effect l r is the moment of inertia of the rotor.

[0028] Introduce three control variables u xi ,u yi u zi , that is, the horizontal position, vertical position and height of i drones.

[0029] The UAV displacement subsystem can be rewritten as

[0030]

[0031] in, J i =diag{1 / m i ,1 / m i ,1 / m i}

[0032] From the above conversion, it can be seen that the under-actuated system is transformed into a fully-actuated system.

[0033] Considering only the formation in the XY plane, the equivalent state equation of each USV and UAV system is expressed as

[0034]

[0035] Furthermore, in step 2, due to the complexity of the actual working environment of the heterogeneous USV-UAV system, the corresponding system internal dynamic F i (t) There is uncertainty. Uncertain dynamics is a vector-valued function of the actual physical internal state, so it is continuous and bounded, and satisfies: ||F i (t)||≤b i,F ,b i,F >0.

[0036] Introducing a time-varying scalar function

[0037]

[0038] In the formula, h>1 is an arbitrary real number, t 1 =t 0 +T, T>0 is a specific constant. μ -q (q>0) in [t 0 ,t 1 )

[0039] The specific design steps of the uncertain dynamic observer are as follows:

[0040] Step 1: Define a helper variable:

[0041] E i(t) = v i (t)-Λ i (t)

[0042] Among them, Λ i (t) satisfies the following dynamic estimation equation:

[0043]

[0044] In the formula, is a positive gain, and The gain value is greater than b i,F . tanh(·) is the hyperbolic tangent function, and Yes F i (t) is estimated.

[0045] Define the above formula according to the auxiliary variable, and its derivative satisfies

[0046]

[0047] Step 2: Define the dynamic estimation error as follows:

[0048]

[0049] From step 1 and the above formula, we can get

[0050]

[0051] Assume that in the bounded uncertain dynamic ||F i (t)||≤b i,F ,b i,F >0, the designed preset time dynamic observer can accurately estimate the uncertain dynamic F within the preset time. i (t), and the estimation error tends to zero.

[0052] Select the following Lyapunov function:

[0053]

[0054] V 2 (t) Find the derivative that satisfies:

[0055]

[0056] Further, we can get

[0057]

[0058] Where b F =max{b 1,F ,…,b 2,F}, And δ 1 is a suitable positive constant.

[0059] Therefore, the observation error is stable within a preset time. 2 (t) is defined as follows: when t ≥ t 0 +T, you can get V 2 (t)≡0, Further

[0060] Furthermore, in step 3, the preset time control algorithm with asymmetric output constraints is designed as follows:

[0061] For the convenience of analysis, the following assumptions are made:

[0062] Assumption 1: ‖p d ‖, They are all bounded. J i (t)‖≤α i ,r,r 1 and α i are all positive real numbers.

[0063] Hypothesis 2: F i (t),J i (t) satisfies Lipschitz under continuous conditions.

[0064] Define the formation tracking error ζ(t) = [ζ 1 (t),ζ 2 (t),...,ζ 2N (t)] T ,make

[0065] The barrier function is designed as follows:

[0066]

[0067] Among them, z 1i is the formation tracking error of the ith follower, k bi ,k ai is a restricted function, p ≥ 1.

[0068] k ai (t):

[0069] k bi (t):

[0070]

[0071] Coordinate transformation by error

[0072] ξ i (t) = q(z 1i )ξ bi (t)+(1-q(z 1i ))ξ ai (t) Obviously, V 3 is positive and continuously differentiable, and its derivative is:

[0073]

[0074] Design 1j for:

[0075]

[0076] Bring it in have to

[0077]

[0078] The time-varying gain is

[0079]

[0080] Combination

[0081]

[0082] And discussing q=0 and q≠0 separately, we get

[0083]

[0084] in

[0085] The control inputs for the design are as follows:

[0086]

[0087] Furthermore, in step 4, the design of the adaptive dynamic event triggering mechanism based on the predetermined time is as follows:

[0088] First define the event trigger error e i (t), which represents the error between the system triggering time and the system state at the current time.

[0089]

[0090] Design the following adaptive event triggering mechanism:

[0091]

[0092] Where:i (t) is a variable parameter, and its initial value satisfies 0<σ i (0)<1,ε>0,θ>0.

[0093] Under the event-triggered scheme, t i,k The last trigger time t i,k+1 is the current triggering moment, k=0,1,2,... is the number of times the event occurs. i (t) Only at t i,k+1 It is updated at all times, otherwise the zero-order holder will maintain t i,k The value at the moment, that is, u i (t) = u(t i,k ).

[0094] Furthermore, in step 5, the proof of stability and the elimination of the Zeno phenomenon are as follows:

[0095] Select the Lyapunov function:

[0096]

[0097] The derivative is:

[0098]

[0099] Substituting the control input u(t), we get

[0100]

[0101] in Combined with the assumptions, we can further obtain:

[0102]

[0103] Then, we can get V(t) = V 3 (t)+V 4 The derivative of (t) satisfies:

[0104]

[0105] Combined with the preset time lemma, it can be seen that the system can achieve the convergence of the formation error within the preset time without violating the output limit.

[0106] If the system initial value p i (0)Satisfaction but

[0107] (1) Formation error z 1 satisfy:

[0108]

[0109] in,

[0110] (2) Asymmetric output constraints always satisfy: Elimination of Zeno's phenomenon:

[0111] The control rate will be updated only when certain conditions are met, otherwise it will keep the value at the last trigger time. Under the condition that all assumptions are true, there is a minimum event trigger time interval:

[0112]

[0113] Depend on

[0114]

[0115] Known is bounded, so there exists a q i >0, so because right Integrating, we get:

[0116]

[0117] Therefore, the minimum event triggering time interval is:

[0118]

[0119] The present invention proposes a control algorithm with time-varying asymmetric output constraints based on predetermined time event triggering, which utilizes the event triggering mechanism to reduce the waste of communication resources and improve the anti-interference capability of heterogeneous unmanned aerial vehicle multi-agent systems in formation missions.

[0120] Compared with the prior art, the present invention has the following beneficial effects:

[0121] 1. The heterogeneous underactuated UAV-USV system is transformed into a fully actuated system by introducing auxiliary variables, and an uncertain dynamic observer with predefined time is constructed. The leader-follower method is used to estimate the uncertain dynamics of the unmanned boat and the drone within a predetermined time. Compared with the finite time and fixed time in other previous inventions, the predefined time control ensures stability and guarantees convergence within the predefined time, regardless of the initial conditions.

[0122] 2. A time-varying asymmetric output constraint control method based on scheduled time is proposed for heterogeneous sea and air unmanned systems. In order to avoid violating the output constraint, an asymmetric time-varying barrier Lyapunov function is used, and it is shown that the output can start from any point in the original constrained output region.

[0123] 3. A dynamic adaptive predefined time event trigger mechanism is constructed to reduce the waste of communication resources. It can dynamically adjust the threshold parameters in the trigger conditions with high flexibility and determine the minimum event trigger time interval to prevent the occurrence of Zeno phenomenon. Compared with the previous static event trigger, the adaptive dynamic event trigger mechanism has higher flexibility and higher resource saving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0124] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0125] Figure 1 The block diagram of the proposed controller of the heterogeneous unmanned boat-unmanned aerial vehicle system in the present invention.

[0126] Figure 2 It is a communication topology diagram between individuals of the heterogeneous unmanned boat-unmanned aerial vehicle system in the present invention.

[0127] Figure 3 It is a schematic diagram of the shape of the formation formed by multiple intelligent agents under the constant expected formation in the present invention.

[0128] Figure 4 It is a schematic diagram of formation error under the constant expected formation in the present invention.

[0129] Figure 5 It is a schematic diagram of the output position under the constant expected formation in the present invention.

[0130] Figure 6 It is a schematic diagram of event triggering interval under the constant expected formation in the present invention.

[0131] Figure 7 This is a schematic diagram of the shape of the formation formed by multiple agents under the time-varying expected formation in the present invention.

[0132] Figure 8 It is a schematic diagram of formation error under the time-varying expected formation in the present invention.

[0133] Fig. 9 It is a schematic diagram of the output position under the time-varying expected formation in the present invention.

[0134] Fig.10 The present invention is a schematic diagram of event triggering intervals under a time-varying expected formation.

[0135] Fig.11 A comparison chart of the effects of the trigger mechanism designed in the present invention and the traditional mechanism. DETAILED DESCRIPTION

[0136] To make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0137] Embodiment 1

[0138] The technical solution provided in this embodiment is a predefined-time distributed formation control method for a heterogeneous air-sea unmanned system with asymmetric output constraints based on event-triggering. To better illustrate this embodiment, Matlab numerical simulation is used to verify the proposed controller, and the results are as Figures 3 to 10 shown. The specific steps are as follows

[0139] Step 1: Establish the models of unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs), transform them into fully actuated systems by using coordinate transformation, and obtain

[0140]

[0141] Step 2: Design a predefined-time uncertain dynamic observer based on the predefined-time theorem to observe the uncertain dynamics of the system, and define a new variable

[0142] E i (t) = v i (t) - Λ i (t)

[0143] where Λ i (t) satisfies the following dynamic estimation equation:

[0144]

[0145] In the formula, is a positive gain, and the gain value of is greater than b i,F . tanh(·) is the hyperbolic tangent function, and is the estimation of F i (t).

[0146] Step 3: Design a predefined-time control algorithm with asymmetric output constraints.

[0147] Design the barrier function as follows:

[0148]

[0149] where z 1i is the formation tracking error of the i-th follower, k bi , k ai is a constrained function, p ≥ 1.

[0150] Take the derivative of it to get

[0151]

[0152] Design auxiliary variable α 1j for:

[0153]

[0154] Bring it in Yes, we get

[0155]

[0156] in The control inputs for the design are as follows:

[0157]

[0158] Step 4: Design an adaptive dynamic event triggering mechanism based on scheduled time.

[0159] First define the event trigger error e i (t), which represents the error between the system triggering time and the system state at the current time.

[0160]

[0161] Design the following adaptive event triggering mechanism:

[0162]

[0163] Where: i (t) is a variable parameter, and its initial value satisfies 0<σ i (0)<1,ε>0,θ>0.

[0164] Step 5: Stability analysis, select Lyapunov function:

[0165]

[0166] Combined with the assumptions, we can further obtain:

[0167]

[0168] Finally, we can get V(t) = V 3 (t)+V 4 The derivative of (t) satisfies:

[0169]

[0170] Combined with the preset time lemma, it can be seen that the system can achieve the convergence of the formation error within the preset time without violating the output limit.

[0171] The specific simulation process and parameters are as follows:

[0172] The heterogeneous unmanned vehicle-unmanned aerial vehicle system consists of a virtual leader i=0, two follower unmanned vehicles (USVs) i=1,2 and two follower unmanned aerial vehicles (UAVs) (i=3,4), and its parameters are

[0173] m 11,i =0.01×i+1.965,kg,m 22,i =0.01×i+2.315kg,m 33,i =0.01×i+0.038kg,

[0174] d 11,i =0.01×i+2.364kg / s,d 22,i =0.01×i+12.277kg / s,d 33,i =0.01×i+0.0456kg / s,

[0175] i=1,2.l x = l y = l z =0.01×i+1.2×10 -3 kg·m 2 ,

[0176] d 11 =d 22 =d 33 =0.01×i+1.3×10 -2 N·m·s 2 ,m i =0.01×i+2.0kg,i=3,4.

[0177] The parameters of the controller are as follows

[0178] ρ 1 =2,ρ 2 =2,θ=3,b=0.1,K 1 =280,α=2,

[0179] c=2,ε=1,κ 1 =10,κ 2 =20,L i =0.9,i=1,2,3,4.

[0180] The desired position and speed of the virtual leader 1 are as follows

[0181] p d (t) = [1.5cos(t), 1.5sin(t)] T ,v d(t) = [-1.5sin(t), 1.5cos(t)] T

[0182] The initial positions of the four followers are as follows

[0183] p 1 (0) = [0.7, 2.4] T ,p 2 (0) = [0.7, 2.9] T ,p 3 (0) = [0.5, 3.4] T ,p 4 (0) = [1.4, 4.9] T

[0184] The initial velocity is zero. Choose the following time-invariant expected formation function

[0185] h 1 (t)=[-1,1] T ,h 2 (t) = [-2, 2] T ,h 3 (t) = [-3, 3] T ,h 4 (t) = [-4, 4] T

[0186] The asymmetric output constraint function is as follows

[0187] k c1 (t) = k c2 (t)=4sin(t)-5.55,k c3 (t) = k c4 (t) = 3.8sin(t) - 6.25,

[0188] k c5 (t) = k c6 (t)=2.5sin(t)-7.5,k c7 (t) = k c8 (t) = 7sin(t) - 10.75,

[0189]

[0190] Results show that: Under the constant expected formation, Figure 3 is the formation shape of the heterogeneous system at different times, Figure 4 and Figure 5 The formation error and position of two unmanned boats and two drones are described. It can be seen that the error converges within the preset time, and the output position is always within the restricted function. Figure 6This shows that this event triggering mechanism flexibly and effectively reduces the number of communications and improves communication efficiency.

[0191] Example 2

[0192] The parameters of the unmanned boat and the unmanned aerial vehicle system are the same as those in Example 1.

[0193] The parameters of the controller are as follows

[0194] ρ 1 =3,ρ 2 =2,θ=3,b=0.1,K 1 =200,α=2,

[0195] c=2,ε=1,κ 1 =15,κ 2 =10,L i =0.85,i=1,2,3,4.

[0196] The expected position and speed of the virtual leader are as follows

[0197] p d (t) = [cos(t)-1, sin(t)] T ,v d (t) = [-sin(t), cos(t)] T

[0198] The initial positions of the four followers are as follows

[0199] p 1 (0) = [0.7, 2.4] T ,p 2 (0) = [0.7, 2.9] T ,p 3 (0) = [0.5, 3.4] T ,p 4 (0) = [1.4, 4.9] T

[0200] The initial velocity is zero. Choose the following time-invariant expected formation function

[0201] h 1 (t) = [0, -0.2t] T ,h 2 (t) = [0.2t, 0] T ,h 3 (t) = [-0.2t, 0] T ,h 4 (t) = [0, 0.2t] T

[0202] The asymmetric output constraint function is as follows

[0203] k c1 (t) = k c2 (t)=2sin(t)-4.55,k c3 (t) = k c4 (t) = 1.2sin(t) - 3.25,

[0204] k c5 (t) = k c6 (t)=1.5sin(t)-4.8,k c7 (t) = k c8 (t) = 2sin(t) - 4.25,

[0205]

[0206] Results show that: Under the time-varying expected formation, the formation shapes of heterogeneous systems at different times are as follows Figure 7 As shown, Figure 8 and Fig. 9 The formation errors and positions of two groups of unmanned boats and drones are shown, even in a relatively complex time-varying expected formation. These errors can still be successfully converged within the preset time, and all output positions remain within the range of the limited function. At the same time, Fig.10 It shows that the event triggering mechanism is both flexible and efficient, significantly reducing the number of communications and thus improving communication efficiency.

[0207] Example 3

[0208] The parameters of the unmanned boat, unmanned aerial vehicle system and controller are the same as those in Example 2.

[0209] In the fourth step, the adaptive dynamic event trigger mechanism is replaced by the traditional static event trigger mechanism, that is, the threshold parameter is a fixed constant, and the threshold parameter size is selected as 0.1.

[0210] Design static event triggering mechanism.

[0211] t i,k+1 = inf{t>t i,k |L i ||e i (t)||≥0.1}

[0212] The expected position and speed of the virtual leader are as follows

[0213] p d (t) = [cos(t)-1, sin(t)] T ,v d (t) = [-sin(t), cos(t)] T

[0214] The initial positions of the four followers are as follows

[0215] p 1 (0) = [0.7, 2.4] T ,p 2 (0) = [0.7, 2.9] T ,p 3 (0) = [0.5, 3.4] T ,p 4 (0) = [1.4, 4.9] T

[0216] The initial velocity is zero. Choose the following time-invariant expected formation function

[0217] h 1 (t) = [0, -0.2t] T ,h 2 (t) = [0.2t, 0] T ,h 3 (t) = [-0.2t, 0] T ,h 4 (t) = [0, 0.2t] T

[0218] The asymmetric output constraint function is the same as that in the second embodiment.

[0219] Result description:

[0220] The final trigger count is Fig.11 As shown, by comparing the traditional static event triggering mechanism and the adaptive dynamic event triggering mechanism based on preset time designed in this paper, it can be seen that the method proposed in this paper can more effectively reduce the communication between individuals in the unmanned system while ensuring error convergence, and the resource saving efficiency is higher.

[0221] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for pre-setting time formation of heterogeneous sea and air unmanned systems with event-triggered output constraints, characterized in that: The following steps are involved: Step 1: Convert the underactuated heterogeneous USV-UAV system into a second-order fully actuated system through coordinate transformation; Step 2: To estimate the uncertain dynamics, an uncertain dynamic observer based on a preset time is designed; Step 3: Design a preset time control algorithm with asymmetric output constraints; Step 4: To save communication resources, an adaptive preset time event trigger mechanism is proposed; Step 5: Prove the convergence of the error through Lyapunov stability analysis and eliminate the Zeno phenomenon.

2. The method for pre-setting time formation of heterogeneous sea and air unmanned systems with event-triggered output constraints as claimed in claim 1 is characterized in that: In step 1, the kinematic model of the unmanned boat in the ground system is expressed as In the formula, (x i (t),y i (t)) and ι i (t) are the position and heading angle of the i-th unmanned boat in the ground coordinate system; (w i (t),r i (t)) and o i (t) is the linear velocity and angular velocity of the i-th unmanned boat; The dynamic model of the unmanned boat is: where u i,w (t) and u i,o (t) represents the control input of USV, m 11,i ,m 22,i ,m 33,i is the mass parameter related to the rotation and motion of the USV, d 11,i ,d 22,i and d 33,i corresponds to the damping parameters related to the USV flow effect; Since the kinematic model of the unmanned boat is a non-holistic constraint model, a new output state variable p is defined. i (t) = [p i1 (t),p i2 (t)] T for: In the formula, ∈ is a very small positive constant, which represents the distance from the reference point of the i-th unmanned boat to the center of mass; From the above formula, the kinetic equation is: among them,in i (t)=[u i,w (here i,o (t)] T The UAV dynamics model is: Among them, the total thrust and control torque acting on the i-th UAV are u i1 ,u i2 ,u i3 and u i4 , represents the propeller speed margin, and the position and attitude of the i-th UAV are p i =[x i ,y i ,z i ] T and Description, the moment of inertia of the quadcopter is l x ,l y and l z ; gravitational acceleration g represents, m i is the mass of the drone; the air damping coefficient is d y ,d z , d φ and Corresponding to the appropriate directional damping effect l r is the moment of inertia of the rotor; Introduce three control variables u xi ,u yi u zi , i.e., the horizontal position, vertical position and height of the i-th UAV; The drone displacement subsystem is rewritten as: in, J i =diag{1 / m i ,1 / m i ,1 / m i }; From the above transformation, it can be seen that the underactuated system is transformed into a fully actuated system; Considering only the formation in the XY plane, the equivalent state equations for each USV and UAV system are expressed as:

3. The method for pre-time formation of sea and air heterogeneous unmanned systems with event-triggered output constraints according to claim 1 is characterized in that: In step 2, due to the complexity of the actual working environment of the heterogeneous USV-UAV system, the corresponding system internal dynamic F i (t) There is uncertainty. Since the uncertain dynamics is a vector-valued function of the actual physical internal state, it is continuous and bounded and satisfies: ||F i (t)||≤b i,F ,b i,F >0; introduce time-varying scalar function In the formula, h>1 is an arbitrary real number, t1=t0+T, T>0 is a specific constant, μ -q (q>0) is monotonically decreasing on [t0,t1), μ(t0) -q =1 and The specific design steps of the uncertain dynamic observer are as follows: Step 1: Define a helper variable: E i (t)=v i (t)-Λ i (t) Among them, Λ i (t) satisfies the following dynamic estimation equation: In the formula, is a positive gain, and The gain value is greater than b i,F , tanh(·) is the hyperbolic tangent function, and Yes F i (t) estimate; According to the auxiliary variable definition above, its derivative satisfies: Step 2: Define the dynamic estimation error as follows: From step 1 and the above formula, we get: Assume that in the bounded uncertain dynamic ||F i (t)||≤b i,F ,b i,F >0, the designed preset time dynamic observer accurately estimates the uncertain dynamic F within the preset time. i (t), and the estimation error tends to zero.

4. The method for pre-setting time formation of heterogeneous sea and air unmanned systems with event-triggered output constraints according to claim 1 is characterized in that: In step 3, the preset time control algorithm with asymmetric output constraints is designed as follows: Define the formation tracking error ζ(t) = [ζ1(t),ζ2(t),...,ζ 2N (t)] T ,make The barrier function is designed as follows: Among them, z 1i is the formation tracking error of the ith follower, k bi ,k ai is a restricted function, p≥1; Coordinate transformation by error V3 is positive and continuously differentiable, and its derivative is: Design 1j for: Bring it in have to: The time-varying gain is: Combination And discuss q=0 and q≠0 respectively, and get: in The control inputs for the design are as follows:

5. The method for pre-setting time formation of heterogeneous sea and air unmanned systems with event-triggered output constraints according to claim 1 is characterized in that: In step 4, the design of the adaptive dynamic event triggering mechanism based on the predetermined time is as follows: First define the event trigger error e i (t), which represents the error between the system triggering time and the system state at the current time; Design the following adaptive event triggering mechanism: Where: i (t) is a variable parameter, and its initial value satisfies 0<σ i (0)<1,ε>0,θ>0; Under the event-triggered scheme, t i，k The last trigger time t i，k+1 is the current triggering moment, k=0,1,2,... is the number of times the event occurs, u i (t) Only at t i，k+1 It is updated at all times, otherwise the zero-order holder will maintain t i,k The value at the moment, that is, u i (t) = u(t i,k ).

6. The method for pre-time formation of sea and air heterogeneous unmanned systems with event-triggered output constraints according to claim 1 is characterized in that: In step 5, the proof of stability and the elimination of the Zeno phenomenon are as follows: Select the Lyapunov function: The derivative is: Substituting the control input u(t), we get in Combining the assumptions, we get: The derivative of V(t)=V3(t)+V4(t) satisfies: Combined with the preset time lemma, it can be seen that the system achieves the convergence of the formation error within the preset time without violating the output limit; Elimination of Zeno's phenomenon: The control rate will be updated only when certain conditions are met, otherwise it will keep the value at the last trigger time. Under the condition that all assumptions are true, there is a minimum event trigger time interval: Depend on Known is bounded, so there exists a q i >0, so because right Integrating, we get: Therefore, the minimum event triggering time interval is:

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