Intelligent fault-tolerant formation method of sea-air heterogeneous unmanned system triggered by preset time event

Abstract

The invention provides an intelligent fault-tolerant formation method for triggering a sea-air heterogeneous unmanned system by a preset time event. According to the technical scheme, the method comprises the following steps: step 1, converting an under-actuated heterogeneous USV-UAV system into a full-driven second-order dynamic system by using coordinate transformation; 2, designing a self-adaptive preset time dynamic event triggering mechanism; 3, designing a preset time sliding mode intelligent fault-tolerant formation control algorithm based on distributed errors; 4, designing an event triggering preset time intelligent fault-tolerant formation control algorithm based on a radial basis function neural network minimum learning parameter method; and step 5, carrying out stability proving on the designed intelligent fault-tolerant formation control algorithm, and eliminating a sesame phenomenon. The method has the beneficial effect that the communication efficiency is greatly improved through a self-adaptive dynamic event triggering mechanism.

Description

Technical Field

[0001] The present invention relates to the technical field of formation control of unmanned systems, and in particular to an intelligent fault-tolerant formation method for a heterogeneous sea-air unmanned system triggered by a preset time event. Background Art

[0002] With the ocean power becoming a major strategic focus of national scientific and technological development, heterogeneous sea-air unmanned systems have become a research hotspot. Heterogeneous sea-air unmanned systems integrate the respective advantages of unmanned aerial vehicles and unmanned surface vehicles, have excellent payload and mission configuration capabilities, and are an indispensable part of cross-domain cooperative operations in the sea and air. However, due to the different dynamic characteristics, structural differences, spatial dimensions, and model parameter differences between unmanned aerial vehicles and unmanned surface vehicles, their cooperative operation and control are difficult, and there are still many challenges to be overcome.

[0003] For example, with the increase in the number of unmanned surface vehicles and unmanned aerial vehicles, actuator and sensor failures will inevitably occur during navigation or flight. Therefore, the introduction of fault detection and fault-tolerant control into the unmanned surface vehicle-unmanned aerial vehicle formation has gradually attracted attention. There are three common types of faults in actuators and sensors in industrial processes: partial faults, power outages, and jams. In the latter two cases, the control system is completely out of control, and it is meaningless to consider any controller design. Therefore, it is of great significance to find a suitable control method to solve the partial loss of effectiveness caused by actuator and sensor failures, and extensive research has been carried out in this regard in recent years. In the article "Finite-time fault-tolerant control of unmanned surface vehicles based on a finite-time observer", the author designed a finite-time observer for fault compensation and detection, which solved the problem of partial actuator and sensor faults to a certain extent. However, this article is based on a finite-time framework and does not solve the problems of preset time and fault estimation. In addition, this article focuses on the fault-tolerant control strategy of fault compensation and does not explore the time-varying fault estimation strategy of adaptive fault tolerance control. Although some progress has been made in the fault-tolerant control of multi-USV and multi-UAV formations, there are not many implementation strategies for USV-UAV fault-tolerant formation control.

[0004] During the flight or navigation of USVs and UAVs, control signals are typically updated at discrete sampling intervals. Generally, relatively short sampling times are adopted to ensure system performance and stability. Excessively high sampling frequencies may cause the controller to be updated frequently, thereby wearing out the actuators and wasting energy. To address this issue, event-triggered control has been proposed, where data updates and transmissions occur when preset conditions are met. This minimizes resource consumption while maintaining system efficiency. For multi-agent systems, static event-triggered control techniques have been developed to achieve consensus. For example, in the paper "Distributed dynamic event-triggered control method for linear multi-agent system consensus with directed networks", the authors have proposed dynamic event-triggered control techniques to achieve leader-follower consensus in multi-agent systems. According to current findings, dynamic internal variables can significantly reduce the number of event triggers and avoid the Zeno phenomenon. The adaptive dynamic event-triggered control technique combines the advantages of adaptive control strategies and dynamic event-triggered control and has currently become a popular new trend in the development of dynamic event-triggered control. Therefore, the adaptive dynamic event-triggered control strategy provides a feasible method to enhance the effectiveness and versatility of heterogeneous USV-UAV systems in various scenarios and applications.

[0005] It is worth noting that some of the strategies mentioned above are created based on assumptions, and many scholars have full access to each dynamic parameter. Obtaining such accurate information during system operation is a challenge because it may change gradually and be affected by actuator and sensor failures. Therefore, it is crucial to develop strategies that do not rely on accessing all dynamic parameters. To address uncertain parameters and unknown dynamics, estimators based on Fourier series and radial basis function neural networks are commonly used. Although these methods effectively mitigate the adverse effects of uncertain dynamics, determining the weights of neural nodes requires a large amount of computational resources, increasing the system's computational load and slowing down the algorithm execution speed. Fortunately, the minimum learning parameter (MLP) strategy provides an effective remedy to overcome this challenge. The MLP method compresses the weights of multiple neural nodes into a weight matrix during the parameter identification process. Therefore, on-board computing becomes less difficult, significantly saving computational resources, which highlights a promising area for future research. Summary of the Invention

[0006] The purpose of the present invention is to provide a preset-time event-triggered intelligent fault-tolerant formation method for heterogeneous sea-air unmanned systems, which solves the technical problems of formation control of heterogeneous USV-UAV systems in the case of partial efficiency failures of actuators and sensors and the presence of uncertain dynamics. At the same time, through the adaptive dynamic event-triggered mechanism, the communication efficiency is greatly improved, and 60%-80% of communication resources can be saved.

[0007] To achieve the above-mentioned invention objectives, the technical solutions adopted in the present invention are specifically as follows: A method for intelligent fault-tolerant formation of a heterogeneous sea-air unmanned system triggered by preset time events, comprising the following steps:

[0008] Step 1: Transform the underactuated heterogeneous USV-UAV system into a fully actuated second-order dynamic system through coordinate transformation;

[0009] Step 2: Design an adaptive preset-time dynamic event-triggering mechanism to save communication resources;

[0010] Step 3: Design a preset-time sliding mode intelligent fault-tolerant formation control algorithm based on distributed error, and describe the communication topology between agent systems with the help of graph theory;

[0011] Step 4: Design an event-triggered preset-time intelligent fault-tolerant formation control algorithm based on the minimum learning parameter method of RBF neural network to estimate uncertain dynamics;

[0012] Step 5: Use the Lyapunov function and with the help of the Young inequality and the Nussbaum function, prove the stability of the above-designed control algorithm and eliminate the Zeno phenomenon.

[0013] Further, in the above Step 1, the kinematic model of the unmanned surface vehicle in the ground coordinate system can be expressed as:

[0014]

[0015] where, (x l (t), y l (t)) and are respectively the position and heading angle of the l-th unmanned boat in the ground coordinate system; (w i (t), v l (t)) and r l (t) are the linear velocity and angular velocity of the l-th unmanned boat.

[0016] The dynamic model of the unmanned boat is:

[0017]

[0018] where, τ l,ω (t) and τ l,r (t) represent the control inputs of the USV, m 11,l , m 22,l , m 33,l are mass parameters related to the rotation and movement of the USV. In addition, d 11,l , d 22,l and d 33,l correspond to the damping parameters related to the flow effect of the USV.

[0019] Since the kinematic model of the unmanned boat is a non - holonomic constraint model, new output state variables are defined as:

[0020]

[0021] where ∈ is a very small positive constant, representing the distance from the l - th reference point of the unmanned boat to the centroid.

[0022] From the above equation, its dynamic equation can be obtained as:

[0023]

[0024] where τ l (t)=[τ l,ω (t),τ l,r (t)] T ,

[0025]

[0026] The dynamic model of the quad - rotor UAV is:

[0027]

[0028] where the total thrust and control torque acting on the l - th UAV are τ l,1 (t),τ l,2 (t),τ l,3 (t) and τ l,4 (t), represents the propeller speed margin. The position and attitude of the l - th UAV are described by and respectively. The moment of inertia of the quad - rotor UAV is I x,l ,I y,l and I z,l . g represents the acceleration due to gravity, M l is the mass of the UAV, the air damping coefficient is d θ,l , d x,l ,d y,l and d z,l , corresponding to the appropriate directional damping effects, I r,l is the moment of inertia of the rotor.

[0029] Introduce three control variables u x,l (t),u y,l (t) and u z,l (t), that is, the horizontal position, vertical position and altitude of the l - th UAV. The UAV displacement subsystem can be rewritten as:

[0030]

[0031] Among them, A l = diag(1 / M l , 1 / M l , 1 / M l ), F x,l (t), F y,l (t) and F z,l (t) are non - linear uncertain dynamics.

[0032]

[0033] It can be seen from the above conversion process that the under - actuated system is transformed into a fully - actuated system.

[0034] Only considering the formation in the XOY plane, the equivalent state equations of each USV and UAV system are expressed as:

[0035]

[0036] Furthermore, in the second step, to save communication resources, an adaptive preset - time dynamic event - triggering mechanism is designed:

[0037] Introduce a time - varying scalar function:

[0038]

[0039] where b > 1 is an arbitrary real number, t1 = t0+T, T > 0 is a specific constant. ψ -d (t)(d > 0) is monotonically decreasing on [t0, t1), ψ(t0) -d = 1 and

[0040]

[0041] For the convenience of the following analysis, a preset - time stability lemma is given:

[0042] Lemma 1 For the system

[0043] g(0) = 0,

[0044] where the function g(·) is continuous. Let the convergence time T be a predetermined constant. If the following conditions are satisfied:

[0045]

[0046] Then for t ∈ [t0, t1), where V(t) is a continuous positive - definite radially unbounded function, λ and K are positive constants.

[0047] The specific design of the adaptive preset time dynamic event triggering mechanism is as follows:

[0048] First, define the event triggering error e l (t), which represents the error between the triggering moment of the system and the system state at the current moment.

[0049]

[0050] Among them, η d (t) represents the desired trajectory, and h l (t) represents the desired formation of the l-th agent.

[0051] Design the following adaptive event triggering mechanism:

[0052]

[0053] In the formula: σ l (t) is a variable parameter, and its initial value satisfies 0 < σ l (0) < 1, ∈ > 0, q l > 0, γ1 > 0, and L l > 0 are positive constants. Under the event triggering scheme, t l,k is the previous triggering time, t l,k+1 is the current triggering time, and k = 0, 1, 2,... is the number of times the event occurs. τ l (t) is updated only at the moment of t l,k+1 , otherwise, under the action of the zero-order hold, it will maintain the value at the moment of t l,k , that is, τ l (t) = τ l (t l,k ).

[0054] Furthermore, in the third step, the communication topology between agent systems is described by graph theory. The specific design of a preset time sliding mode intelligent fault-tolerant formation control algorithm based on distributed error is as follows:

[0055] First, introduce the relevant descriptions of partial failures in actuator and sensor efficiency:

[0056]

[0057] It should be noted that: Let two vectors and Then the multiplication operator of each element is defined as where represents partial failure in sensor efficiency, represents partial failure in actuator efficiency. and represent the corresponding fault coefficients.

[0058] Define the formation error when the actuator and sensor efficiencies fail: And describe the communication topology among multi - agents by means of graph theory:

[0059]

[0060] Design a sliding surface based on the preset time as follows:

[0061]

[0062] where c > 0 is a positive constant, Take the derivative of s l (t) and simplify to get:

[0063]

[0064] where the equivalent fault coefficient of the sensor is defined and φ l =[φ l,1 ,φ l,2 T and u l (t)=J l (t)τ l (t) and the equivalent fault coefficient of the actuator Finally, s l (t) can be simplified to:

[0065]

[0066] Furthermore, in the fourth step, in order to estimate the uncertain dynamics, the specific design of an event - triggered preset - time intelligent fault - tolerant formation control algorithm based on the minimum learning parameter method of RBF neural network is as follows:

[0067] (1) Introduce the RBF neural network:

[0068] Any real - valued continuous function can be approximated to any desired accuracy by the following RBFNN on the compact set as follows.

[0069]

[0070] where, m is the number of neural nodes, W m =[w1, w2, …, w m T is the weight vector, and the vector X n (t)=[x1(t), x2(t), …, x n (t)] T ​​Is the input of the neural network. The estimation error is denoted by o. The Gaussian function vector Λ(X n ) = [Λ1(X n ), Λ2(X n ), …, Λ m (X n )] T is defined as

[0071]

[0072] where represents the center of the Gaussian distribution of X n (t), and represents the width of Λ i (X n (t)).

[0073] To further reduce the computational complexity, we propose the following MLP technique based on the RBF neural network:

[0074]

[0075] where is the compression adaptive gain, Ξ(X(t)) and R = ||o|| represent the Euclidean norms of the Gaussian function vector Λ m×2 (X(t)) and the approximation error vector o, respectively. This method can ensure that the unknown dynamics are well approximated while maintaining a controllable computational complexity, and the adaptive laws and for estimating D and R are as follows:

[0076]

[0077] where, γ j > 0 (j = 5, 6, 7, 8) are all positive constants.

[0078] (2) Introduce the Nussbaum function:

[0079] If the function satisfies the following two properties, then is a Nussbaum function

[0080]

[0081] In this patent, for the convenience of theoretical proof, the selected Nussbaum function is:

[0082]

[0083] By synthesizing the content in the above Step 1, Step 2, Step 3, and Step 4, the following control law and the adaptive fault-tolerant control law for actuator efficiency faults are designed:

[0084]

[0085] Among them, k1>0, k2>0, and γ4>0 are positive constants.

[0086] The parameter adaptive control law for sensor efficiency faults is designed as:

[0087]

[0088] Among them, γ2>0, γ3>0 are positive constants.

[0089] Furthermore, in the above Step 5, the proof of stability and the elimination of Zeno phenomenon are as follows:

[0090] First, introduce relevant lemmas:

[0091] (1) Lemma 2:

[0092] For any χ>0, the following inequality can be established: Among them, ε=0.2785.

[0093] (2) Lemma 3:

[0094] If V(t), y(t), and are smooth functions on

[0095] holds, then V(t), y(t), and are bounded, where c0>0 is a suitable constant. Design the following Lyapunov function:

[0096]

[0097] Take the derivative of V1(t) and write it in the form of a sum to get:

[0098]

[0099] Substitute the corresponding fault-tolerant control law and parameter adaptive law to get:

[0100]

[0101] Combining Lemma 2 and 3, we can further obtain:

[0102]

[0103] where \(K1 = \min\{2k1, 2\gamma1, 2\gamma2\gamma3, 2\gamma5\gamma6, 2\gamma7\gamma8\}\), \(\|\varphi\|\) represents the upper bound of \(\varphi\).

[0104] Integrating the above equation and according to Lemma 1 and Lemma 3, we can obtain:

[0105]

[0106] where \(\Delta2=\Delta1 + \varepsilon1\), is a bounded constant.

[0107] Then, combined with Lemma 1, i.e., the preset-time lemma, it can be known that even in the case of partial failures of the system actuator and sensor efficiency, the convergence of the sliding surface can still be achieved within a predetermined time, thus ensuring the practical preset-time stability (PPTS) of \(\|s(t)\|\), and specifying the region set of \(\|s(t)\|\):

[0108]

[0109] Subsequently, the preset-time stability analysis of the formation error \(\|p1(t)\|\) was carried out. According to the preset-time sliding surface \(s(t)\), reconstructing its structure can obtain:

[0110]

[0111] Design the following Lyapunov function:

[0112]

[0113] Taking the derivative of \(V2(t)\) gives:

[0114]

[0115] And according to the Young inequality, we can obtain:

[0116]

[0117] where \(\chi2\) is an adjustable parameter, and the control gain \(c\) satisfies \(c - \chi2>0\),

[0118] Finally, combined with Lemma 1, i.e., the preset-time lemma, it can be known that even in the case of partial failures of the system actuator and sensor efficiency, the convergence of the formation error can still be achieved within a predetermined time, thus ensuring the practical preset-time stability (PPTS) of \(\|p1(t)\|\), and specifying the region set of \(\|p1(t)\|\):

[0119]

[0120] Exclusion of Zeno phenomenon:

[0121] The control rate will be updated only when certain conditions are met, otherwise it will maintain the value at the previous triggering moment. Under the condition that all assumptions hold, there exists a minimum event triggering time interval:

[0122]

[0123] where T l,k > 0 and are positive parameters.

[0124] The proof is as follows:

[0125]

[0126] It is known that is bounded, so there exists a such that Note that Then integrate from t l,k to t l,k+1 , and we can get:

[0127]

[0128] Therefore, the minimum event triggering time interval is:

[0129]

[0130] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0131] 1. By introducing an auxiliary reference position variable, the heterogeneous USV-UAV system is converted into a fully actuated system. Considering the characteristics of partial failures of actuators and sensors and nonlinear uncertain dynamics, the heterogeneous USV-UAV system is made more practical and has engineering and practical significance.

[0132] 2. Compared with other prior art of finite time and fixed time, the predefined time control ensures stability and guarantees convergence within the preset time, regardless of the initial conditions. In addition, by equivalently transforming the nonlinear dynamics of the heterogeneous USV-UAV system, a preset time sliding mode control strategy based on MLP is proposed, which makes the control structure of this scheme simple and easy to apply.

[0133] 3. The present invention proposes a preset time-based adaptive dynamic event triggering mechanism, which realizes communication resource constraints through dynamic interaction and information sharing among agents, thereby dynamically adjusting the communication times among agents and the update frequency of the controller, so as to improve the resource utilization rate.

[0134] 4. The present invention proposes an intelligent fault-tolerant formation method for a heterogeneous sea-air unmanned system triggered by preset time events, which uses an adaptive dynamic event-triggering mechanism to reduce waste of communication resources; uses the minimum learning parameter strategy to estimate uncertainties dynamically, greatly saving computing resources; and improves the anti-interference ability of the heterogeneous sea-air unmanned system in the formation task. Description of the Drawings

[0135] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention.

[0136] Figure 1 It is a block diagram of the proposed controller for the heterogeneous unmanned boat - unmanned aerial vehicle system in the present invention.

[0137] Figure 2 It is a communication topology diagram among individuals of the heterogeneous unmanned boat - unmanned aerial vehicle system in the present invention.

[0138] Figure 3 It is a schematic diagram of the shape formed by multi-agent systems in a steady-state desired formation in the present invention.

[0139] Figure 4 It is a schematic diagram of formation error under a steady-state desired formation in the present invention.

[0140] Figure 5 It is a schematic diagram of event-triggering intervals under a steady-state desired formation in the present invention.

[0141] Figure 6 It is a schematic diagram of the shape formed by multi-agent systems in a time-varying desired formation in the present invention.

[0142] Figure 7 It is a schematic diagram of formation error under a time-varying desired formation in the present invention.

[0143] Figure 8 It is a schematic diagram of event-triggering intervals under a time-varying desired formation in the present invention.

[0144] Figure 9 It is a comparison diagram of the effects of the designed triggering mechanism and the traditional mechanism in the present invention. Detailed Embodiments

[0145] In order to make the objectives, technical solutions and advantages of the present invention clearer, the following further details the present invention in conjunction with the 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.

[0146] Embodiment 1

[0147] The technical solution provided by this embodiment is that a preset time event triggers an intelligent fault-tolerant formation method for a heterogeneous sea-air unmanned system. To better illustrate the present invention, MATLAB numerical simulation is used to verify the proposed controller, and the results are as Figures 3 to 9 shown, and the specific steps are as follows

[0148] Step 1: Establish the models of unmanned aerial vehicles and unmanned surface vessels, transform them into fully actuated systems by using coordinate transformation, and based on the leader-following method, obtain:

[0149]

[0150] Step 2: To save communication resources, design an adaptive preset time dynamic event-triggering mechanism:

[0151] First, define the event-triggering error e l (t), which represents the error between the triggering moment of the system and the current system state.

[0152]

[0153] Among them, η d (t) represents the desired trajectory, and h l (t) represents the desired formation of the l-th agent.

[0154] Design the following adaptive event-triggering mechanism:

[0155]

[0156] In the formula: σ l (t) is a variable parameter, and its initial value satisfies 0 < σ l (0) < 1, ∈ > 0, q l > 0, γ1 > 0 and L l > 0 are positive constants. Step 3: Describe the communication topology between agent systems with the help of graph theory, and design a preset time sliding mode intelligent fault-tolerant formation control algorithm based on distributed error:

[0157] Design the sliding mode surface based on preset time as follows:

[0158]

[0159] Among them, c > 0 is a positive constant, Derive s l (t) and simplify to get:

[0160]

[0161] Among them, define the equivalent fault coefficient of the sensor And φ l =[φl,1 , φ l,2 T and u l (t) = J l (t)τ l (t) and the equivalent fault coefficient of the actuator Finally, s l (t) can be simplified to:

[0162]

[0163] Step 4: To estimate the uncertain dynamics, design an event-triggered preset-time intelligent fault-tolerant formation control algorithm based on the minimum learning parameter method of RBF neural network:

[0164] By comprehensively using the contents of the above Step 1, Step 2, Step 3, and Step 4, we design the following control law and the adaptive fault-tolerant control law for the actuator efficiency fault:

[0165]

[0166] where k1 > 0, k2 > 0, and γ4 > 0 are positive constants.

[0167] The parameter adaptive control law for the sensor efficiency fault is designed as:

[0168]

[0169] where γ2 > 0, γ3 > 0 are positive constants.

[0170] Step 5: Stability analysis, select the Lyapunov function:

[0171] Design the following Lyapunov function:

[0172]

[0173] Combined with Lemma 2 and 3, we can further obtain:

[0174]

[0175] where K1 = min{2k1, 2γ1, 2γ2γ3, 2γ5γ6, 2γ7γ8}, ||φ|| represents the upper bound of φ.

[0176] Integrate the above formula, and according to Lemma 1 and Lemma 3, we can get:

[0177]

[0178] where Δ2 = Δ1 + ε1, ​is a bounded constant.

[0179] Next, combined with Lemma 1, i.e., the preset-time lemma, it can be seen that even when there are partial failures in the system actuator and sensor efficiency, the convergence of the sliding mode surface can still be achieved within a predetermined time, thus ensuring the practical preset-time stability (PPTS) of ||s(t)||, and specifying the region set of ||s(t)||:

[0180]

[0181] Subsequently, the preset-time stability analysis of the formation error ||p1(t)|| was carried out. According to the preset-time sliding mode surface s(t), reconstructing its structure gives:

[0182]

[0183] Design the following Lyapunov function:

[0184]

[0185] And according to the Young inequality, we have:

[0186]

[0187] where χ2 is an adjustable parameter, and the control gain c satisfies c - χ2 > 0. Finally, combined with Lemma 1, i.e., the preset-time lemma, it can be seen that even when there are partial failures in the system actuator and sensor efficiency, the convergence of the formation error can still be achieved within a predetermined time, thus ensuring the practical preset-time stability (PPTS) of ||p1(t)||, and specifying the region set of ||p1(t)||:

[0188]

[0189] The specific simulation process and parameters are as follows:

[0190] A heterogeneous USV-UAV system consisting of a virtual leader i = 0, two follower unmanned surface vehicles (USVs) (l = 1, 2), and two follower unmanned aerial vehicles (UAVs) (l = 3, 4), with the following parameters:

[0191] USV:

[0192]

[0193] UAV: The relevant parameters of the MLP are selected as: Gaussian function are evenly distributed in the center on [-1, -3]×[-2, 4]×[-5, 10]×[-6, 12]×[-3, 6]×[-4, 8]×[-7, 14]×[-8, 16], and the width of the Gaussian function is The number of nodes in the neural network is set to 30. The adaptive parameters of the MLP follow γ j = 0.01 (j ∈ 5, 6, 7, 8).

[0194] The actuator and sensor fault coefficients are selected as:

[0195]

[0196] The relevant event trigger parameters are set to γ1 = 0.01, ∈ = 1, L = [0.85, 0.85, 0.85, 0.85] T and q = [0.3, 0.3, 0.3, 0.3] T . The fault-tolerant adaptive parameters are set to γ2 = 1, γ3 = 0.01, γ4 = 0.1. The control gains are set to c = 4.5, k1 = 7, k2 = 6.

[0197] The expected position and velocity of the virtual leader 0 are as follows

[0198] η d (t) = [cos(1.5t) - 1, sin(1.5t)] T , v d (t) = [-1.5sin(1.5t), 1.5cos(1.5t)] T

[0199] The initial positions of the four followers are as follows

[0200] η1(0) = [0.85, 2.45] T , η2(0) = [0.85, 3.65] T , η3(0) = [0.65, 3.55] T , η4(0) = [1.55, 5.45] T

[0201] The initial velocity is zero. The following time-invariant expected formation function is selected

[0202] h1(t) = [0, -1] T , h2(t) = [0, 1] T , h3(t) = [-1, 0] T , h4(t) = [1, 0] T

[0203] Result description: Under the steady-state expected formation, Figure 3The formation shapes of the heterogeneous USV-UAV system at different times Figure 4 describe the formation errors and positions of two unmanned surface vehicles and two unmanned aerial vehicles Figure 5 indicating that the designed preset-time adaptive dynamic event-triggering mechanism flexibly and effectively reduces the number of communications, saves communication resources, and improves communication efficiency

[0204] Example 2

[0205] The parameters related to the unmanned surface vehicle and unmanned aerial vehicle systems are the same as those in Example 1

[0206] The relevant event-triggering parameters are set as γ1 = 0.01, ∈ = 1, L = [0.85, 0.85, 0.85, 0.85] T and q = [0.3, 0.3, 0.3, 0.3] T . The fault-tolerant adaptive parameters are set as γ2 = 1, γ3 = 0.01, γ4 = 0.1. The control gains are set as c = 4.5, k1 = 7, k2 = 6

[0207] The desired position and velocity of the virtual leader 0 are as follows

[0208] η d (t) = [cos(1.5t) - 1, sin(1.5t)] T , v d (t) = [-1.5sin(1.5t), 1.5cos(1.5t)] T

[0209] The initial positions of the four followers are as follows

[0210] η1(0) = [0.85, 2.45] T , η2(0) = [0.85, 3.65] T , η3(0) = [0.65, 3.55] T , η4(0) = [1.55, 5.45] T

[0211] The initial velocity is zero. Select the following time-varying desired formation function

[0212] h1(t) = [-0.3t, 0] T , h2(t) = [0.3t, 0] T , h3(t) = [0, -0.3t] T , h4(t) = [0, 0.3t] T

[0213] Result description: Under the time-varying desired formation, the formation shapes of the heterogeneous USV-UAV system at different times are as shown in Figure 6As shown Figure 7 It shows the formation errors and their positions of two groups of unmanned boats and unmanned aerial vehicles, and these errors converge within the preset time. At the same time, Figure 8 It shows that the event triggering mechanism is both flexible and efficient, significantly reducing the number of communications, saving communication resources, and thus improving the communication efficiency.

[0214] Embodiment 3

[0215] The parameters of the unmanned boat and unmanned aerial vehicle system and the controller are the same as those in Embodiment 2.

[0216] In Step 4 of the implementation steps, the adaptive dynamic event triggering mechanism is replaced with a traditional static event triggering mechanism, that is, the threshold parameter is a fixed constant, and the size of the threshold parameter is selected to be 0.5.

[0217] Design a static event triggering mechanism:

[0218] t i,k+1 = inf{t > t i,k |L i ||e i (t)||≥0.5}

[0219] The desired position and speed of the virtual leader 0 are as follows

[0220] η d (t) = [cos(1.5t) - 1, sin(1.5t)] T ,v d (t) = [1.5sin(1.5t), 1.5cos(1.5t)] T

[0221] The initial positions of the four followers are as follows

[0222] η1(0) = [0.85, 2.45] T ,η2(0) = [0.85, 3.65] T ,η3(0) = [0.65, 3.55] T ,η4(0) = [1.55, 5.45] T

[0223] The initial speed is zero. Select the following time-varying desired formation function

[0224] h1(t) = [-0.3t, 0] T ,h2(t) = [0.3t, 0] T ,h3(t) = [0, -0.3t] T ,h4(t) = [0, 0.3t] T

[0225] The final trigger count is as follows Figure 9 As shown, by comparing the traditional static event trigger mechanism and the adaptive dynamic event trigger 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 individual agents in the intelligent agent system while ensuring the convergence of errors, and has a higher resource saving efficiency.

[0226] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for triggering an intelligent fault-tolerant formation of a heterogeneous sea-air unmanned system by a preset time event, characterized in that It includes the following steps: Step 1: Transform the underactuated heterogeneous USV-UAV system into a fully actuated second-order dynamic system through coordinate transformation; Step 2: Design an adaptive preset-time dynamic event-triggering mechanism; Step 3: Design a preset-time sliding mode intelligent fault-tolerant formation control algorithm based on distributed error, and describe the communication topology between agent systems with the help of graph theory; Step 4: To estimate the uncertain dynamics, design an event-triggered preset-time intelligent fault-tolerant formation control algorithm based on the minimum learning parameter method of RBF neural network; Step 5: Use the Lyapunov function and with the help of Young's inequality and Nussbaum function, prove the stability of the above-designed control algorithm and exclude the Zeno phenomenon.

2. The intelligent fault-tolerant formation method for the sea-air heterogeneous unmanned system triggered by a preset time event according to claim 1, wherein In the above Step 1, the kinematic model of the unmanned surface vehicle in the ground coordinate system is expressed as: where (x l (t), y l (t)) and are respectively the position and heading angle of the l-th unmanned boat in the ground coordinate system; (w i (t), v l (t)) and r l (t) are the linear velocity and angular velocity of the l-th unmanned boat; The dynamic model of the unmanned surface vehicle is: where τ l,ω (t) and τ l,r (t) represent the control inputs of the USV, m 11,l , m 22,l , m 33,l are mass parameters related to the rotation and motion of the USV, d 11,l , d 22,l and d 33,l represent the damping coefficients in surge, sway and yaw motions, respectively; Since the kinematic model of the unmanned boat is a non-holonomic constraint model, define a new output state variable as follows: In the formula, ∈ is a very small positive constant, representing the distance from the reference point of the l-th unmanned surface vehicle to the centroid; From the above formula, its dynamic equation can be obtained as: where τ l (t) = [τ l,ω (t), τ l,r (t)] T , The dynamic model of the quadrotor UAV is: Among them, the total thrust and control torque acting on the $l$-th drone are $\tau$ l,1 (t), $\tau$ l,2 (t), $\tau$ l,3 (t) and $\tau$ l,4 (t), representing the propeller speed margin, the position and attitude of the $l$-th drone are respectively and described, the moment of inertia of the quadrotor drone is $I$ x,l , $I$ y,l and $I$ z,l , the gravitational acceleration is denoted as $g$, $M$ l is the mass of the drone; the air damping coefficient is $d$ x,l , $d$ y,l and $d$ z,l , corresponding to the appropriate directional damping effect $I$ r,l is the moment of inertia of the rotor; Introduce three control variables u x,l (t), u y,l (t) and u z,l (t), namely the horizontal position, vertical position and altitude of the l-th drone; the drone displacement subsystem is as follows: Among them, A l = diag(1 / M l , 1 / M l , 1 / M l ), F x,l (t), F y,l (t) and F z,l (t) are nonlinear dynamics, From the above conversion process, the underactuated system is transformed into a fully actuated system; Only considering the formation in the XOY plane, the equivalent state equations of each USV and UAV system are expressed as:

3. The intelligent fault-tolerant formation method for the sea-air heterogeneous unmanned system triggered by the preset time event according to claim 1, wherein In the above Step 2, design an adaptive preset-time dynamic event-triggering mechanism: Introduce a time-varying scalar function: where b > 1 is an arbitrary real number, t1 = t0 + T, T > 0 is a specific constant, and ψ -d (t) (d > 0) is monotonically decreasing on [t0, t1), and ψ(t0) -d = 1 and Give the preset-time stability lemma: Lemma 1 For the system where the function g(·) is continuous, let the convergence time T be a predetermined constant. If the following conditions are satisfied: where, for \(t\in[t_0,t_1)\), where \(V(t)\) is a continuously positive definite radially function, and \(\lambda\) and \(K\) are positive constants; The design of the adaptive preset-time dynamic event-triggering mechanism is as follows: First, define the event-triggering error e l (t), which represents the error between the triggering time of the system and the current system state; where η d (t) represents the desired trajectory, and h l (t) represents the desired formation of the l-th agent; Design the following adaptive dynamic event-triggering mechanism: where: σ l (t) is a variable parameter, and its initial value satisfies 0 < σ l (0) < 1, ∈ > 0, q l > 0, γ1 > 0, and L l > 0 are positive constants. Under the event-triggering scheme, t l,k is the time at the previous trigger, t l,k+1 is the current trigger time, k = 0, 1, 2,... is the number of times the event occurs, and τ l (t) is updated only at time t l,k+1 , otherwise, under the action of the zero-order hold, the value at time t l,k will be maintained, that is, τ l (t) = τ l (t l,k ).

4. The intelligent fault-tolerant formation method for the sea-air heterogeneous unmanned system triggered by the preset time event according to claim 1, wherein In the above Step 3, with the help of graph theory to describe the communication topology between agent systems, the specific design of a preset-time sliding mode intelligent fault-tolerant formation control algorithm based on distributed error is as follows: First, introduce the relevant descriptions of partial failures in the actuator and sensor efficiency: Let two vectors and Then the multiplication operator ′°′ for each element is defined as where represents a partial failure of the sensor efficiency, represents a partial failure of the actuator efficiency, and represent the corresponding failure coefficients; Define the formation error when the actuator and sensor efficiencies fail: And describe the communication topology among multi-agents with the help of graph theory: Design a sliding mode surface based on preset time as follows: where \(c>0\) is a positive constant, \(l\in\{1,2,\ldots,N\}\), Derive s l (t) and simplify to obtain: Among them, the equivalent fault coefficient of the sensor is defined and φ l = [φ l,1 , φ l,2 T and u l (t) = J l (t)τ l (t) and the equivalent fault coefficient of the actuator Then the final s l (t) is as follows:​ 5. The intelligent fault-tolerant formation method for the air-sea heterogeneous unmanned system triggered by the preset time event according to claim 1, wherein In the above Step 4, the specific design of the preset-time intelligent fault-tolerant formation control algorithm based on the minimum learning parameter method of RBF neural network is as follows: (1) Introduce the RBF neural network: Any real-valued continuous function can be approximated to any desired accuracy over a compact set by the following RBFNN; where m is the number of neural nodes, and W m = [w1, w2, …, w m T is the weight vector, the vector X n (t) = [x1(t), x2(t), …, x n (t)] T is the input of the neural network, the estimation error is denoted by o, and the Gaussian function vector Λ(X n ) = [Λ1(X n ), Λ2(X n ), …, Λ m (X n )] T is defined as​ Among them, represents the Gaussian distribution center of X n (t), represents Λ i (X n (t)); The following MLP technology is proposed based on the RBF neural network: Among them, is the compressed adaptive gain, and Ξ(X(t)) and R = ||o|| respectively represent the Gaussian function vector Λ m×2 (X(t)) and the Euclidean norm of the approximation error vector o, while maintaining a controllable computational complexity, and the adaptive laws for estimating D and R and are as follows: where, γ j > 0 (j = 5, 6, 7, 8) are all positive constants; (2) Introduce the Nussbaum function: If a function satisfies the following two properties, then is a Nussbaum function The selected Nussbaum function is: Through the integration of the above Step 1, Step 2, Step 3 and Step 4, the following control law and the adaptive fault-tolerant control law for actuator efficiency failure are designed: where, k1>0, k2>0 and γ4>0 are positive constants; The parameter adaptive law for sensor efficiency failure is designed as: where, γ2>0, γ3>0 are positive constants.

6. The intelligent fault-tolerant formation method for the sea-air heterogeneous unmanned system triggered by preset time events according to claim 1, wherein In the above Step 5, the proof of stability and the exclusion of the Zeno phenomenon are as follows: First, introduce the relevant lemmas: (1) Lemma 2: For any χ > 0, the following inequality is established: where ε = 0.2785; (2) Lemma 3: If V(t), y(t), and are smooth functions on If it holds, then V(t), y(t) and are bounded, where c0 > 0 is a suitable constant; Design the following Lyapunov function: Take the derivative of V1(t) and write it in the form of a sum to get: Substitute the corresponding fault-tolerant control law and parameter adaptive law to get: Combined with Lemma 2 and 3 to get: where K1 = min{2k1, 2γ1, 2γ2γ3, 2γ5γ6, 2γ7γ8}, ||φ|| represents the upper bound of φ; Integrate the above formula, and according to Lemma 1 and Lemma 3, obtain: where Δ2 = Δ1 + ε1, is a bounded constant; Next, combined with Lemma 1, i.e., the preset time lemma, even in the case of partial failures in the efficiency of the system actuators and sensors, the convergence of the sliding mode surface is still achieved at the preset time, thus ensuring the practical preset time stability of ||s(t)||, and defining the region set of ||s(t)||: Subsequently, the preset time stability analysis of the formation error ||p1(t)|| was carried out. According to the preset time sliding mode surface s(t), its structure was reconstructed to obtain: Design the following Lyapunov function: Take the derivative of V2(t) to get: And according to the Young inequality, we have: where χ2 is an adjustable parameter, controlling the gain c to satisfy c - χ2 > 0, Combined with Lemma 1, i.e., the preset time lemma, even when there are partial failures in the system actuator and sensor efficiency, the formation error still converges at the preset time, thus ensuring the PPTS of ||p1(t)||, and specifying the region set of ||p1(t)||: Exclusion of Zeno phenomenon: The control rate will be updated only when certain conditions are met, otherwise it will maintain the value at the previous triggering moment. Under the condition that all assumptions hold, there exists a minimum event triggering time interval: where T l,k > 0 and are positive parameters; The proof is as follows: Known is bounded, so there exists a such that Note that Then integrate from t l,k to t l,k+1 , we get: Therefore, the minimum event triggering time interval is:

Images