Fault-tolerant fuzzy formation control method for triggering predetermined time by dynamic events of multiple unmanned ships

Abstract

The invention provides a fault-tolerant fuzzy formation control method for preset time triggered by dynamic events of multiple unmanned ships, and belongs to the technical field of heterogeneous unmanned system formation control. Comprising the following steps of 1, establishing a heterogeneous multi-USV kinematics and dynamics model considering input hysteresis quantization, intermittent communication topology, execution mechanism intermittent faults and external disturbance; 2, constructing an execution mechanism intermittent fault model and an input hysteresis quantizer; 3, designing a fuzzy logic system based on a minimum learning parameter strategy; 4, proposing a predetermined time robust adaptive dynamic event triggering strategy; and 5, constructing a fault-tolerant formation control law based on predetermined time sliding mode control, and processing an unknown control gain by adopting a Nussbaum function. According to the method, the anti-interference capability and the engineering applicability of the USV system in a complex marine environment are remarkably improved while the consumption of communication and computing resources is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of heterogeneous unmanned system formation control, and particularly relates to a heterogeneous multi-USV predetermined time fault-tolerant fuzzy formation control method based on dynamic event triggering. BACKGROUND

[0002] With the rapid development of marine power strategy and intelligent equipment technology, USV has become an important research direction for maritime multi-task cooperation. USV has flexible maneuverability, strong task load capacity and wide application prospect. However, due to the significant differences in dynamic characteristics, structural parameters and operating environment of different USVs, there are still many technical challenges in cooperative operation and control accuracy.

[0003] In order to overcome these challenges, especially the limitations of fixed time scheme and limited time scheme, researchers have developed a predetermined time control strategy to ensure system convergence within the user-specified deadline. In the field of USV, this strategy has been extended to key tasks such as trajectory tracking and formation keeping, which need to be performed under strict time constraints. For example, the predetermined time control method has been tailored to deal with input amplitude and rate limitations in under-actuated passive USVs, where the inherent passivity and actuator limitations of USVs pose significant challenges. Similarly, a robust predetermined time formation controller is designed to cope with random disturbances and intermittent communication topologies in distributed multi-USV fleets, greatly improving the practical applicability in bandwidth-limited and disturbance-limited marine environments.

[0004] Although these control strategies have made progress, in the process of multi-USV cooperation, the actuator or sensor will inevitably have abnormality such as multiplicative failure, additive bias or sticking, which will affect the control accuracy and task completion quality, and even cause system instability. Existing research has proposed fault-tolerant control methods for partial failure, power failure or sticking of actuators and sensors, but most of them rely on complete dynamic parameter acquisition, which is often difficult to achieve in actual tasks, especially in environments with intermittent communication, information transmission delay and limited bandwidth, it is quite difficult to obtain complete and accurate information.

[0005] In order to further improve the reliability and resource utilization efficiency of the system, the event-triggered control method is widely proposed and applied. This method can significantly reduce communication resource occupation and energy consumption caused by frequent actuator action by transmitting data and updating control only when the triggering condition is met. However, the traditional static event-triggered strategy cannot adjust the triggering condition in real time according to the change of system operating state, which is prone to trigger too frequently or too sparsely, thereby affecting the control performance.

[0006] In recent years, adaptive dynamic event-triggered control strategy has become a research hotspot. By introducing adjustable triggering thresholds, this strategy optimizes the triggering frequency dynamically, effectively reducing unnecessary update times while maintaining system performance stability. However, existing research often lacks a unified modeling method and compensation mechanism when facing intermittent actuator faults, quantization errors, and external disturbances, making it difficult to balance fault tolerance and communication resource optimization. In addition, input hysteresis quantization further exacerbates system uncertainty. Input hysteresis quantization refers to the nonlinear hysteresis effect introduced by the quantizer during transmission and execution, resulting in an inability to accurately match the expected value of the input signal, thus generating additional errors and delays. This factor is particularly prominent in resource-constrained environments, amplifying the impact of faults and reducing the accuracy of event triggering and overall system stability. At the same time, intermittent switching topology is a key challenge, resulting from the intermittent interruption or dynamic changes of communication links in the marine environment, leading to frequent switching of the connection topology structure between USVs, thereby affecting the continuity of information exchange and the coordination of formation control. Existing methods often fail to adapt to such topology switching in real time, easily causing system response delays or inconsistencies. Therefore, there is an urgent need for an adaptive dynamic event-triggered fault-tolerant fuzzy formation control method that can balance control performance and communication efficiency in the presence of intermittent actuator faults, input hysteresis quantization, and intermittent switching topology. SUMMARY

[0007] The purpose of the present application is to provide a dynamic event-triggered heterogeneous multi-USV pre-determined time fault-tolerant fuzzy formation control method. For the formation control problem in a multi-USV system with intermittent actuator faults and the presence of input hysteresis quantization, external disturbances, and intermittent switching topology, a cooperative control strategy is proposed that can reduce communication and control resource consumption while ensuring system stability and tracking accuracy.

[0008] To achieve the above purpose, the present application introduces a fractional order pre-determined time sliding mode control method, combined with a minimum learning parameter fuzzy logic system to compensate for system nonlinear uncertainties, and adjusts the communication and control update times through an adaptive dynamic event-triggering mechanism to reduce invalid communication and control update times, thereby significantly reducing network load and energy consumption. During formation, the present application uses the pre-determined time mechanism to calculate the control input in advance, combined with the dynamic threshold condition to trigger the controller update, effectively addressing the comprehensive effects of intermittent actuator faults, input hysteresis quantization, external disturbances, and intermittent switching topology.

[0009] To achieve the above application purpose, the technical scheme adopted by the present application is as follows: a multi-unmanned surface vehicle dynamic event-triggered pre-determined time fault-tolerant fuzzy formation control method, comprising the following steps:

[0010] Step one: The kinematics and dynamics model of heterogeneous multi-USVs is established considering input quantized hysteresis, intermittent communication topology, intermittent actuator failure and external disturbance. By introducing auxiliary reference position variables, the under-actuated second-order USV system is equivalent to a fully-actuated system, and the formation error and control objectives are strictly defined.

[0011] Step two: The intermittent actuator failure model and input quantized hysteresis are constructed, and the additional fault term, quantization error and external disturbance are modeled as a comprehensive nonlinear uncertainty term, providing a theoretical basis for subsequent robust control design.

[0012] Step three: The FLS is designed based on the MLP strategy to achieve high-precision approximation of the comprehensive nonlinear uncertainty term; the weight parameters are updated online through the predetermined time adaptive law, which significantly reduces the computational complexity while ensuring approximation accuracy.

[0013] Step four: A predetermined time robust adaptive dynamic event-triggered strategy is proposed, which combines the input quantized hysteresis to compress the control signal transmission and dynamically adjusts the communication and controller update frequency. This mechanism effectively reduces the bandwidth occupation while ensuring system stability.

[0014] Step five: The fault-tolerant formation control law is constructed based on the predetermined time sliding mode control, and the Nussbaum function is used to handle unknown control gain. Through Lyapunov stability analysis, it is strictly proved that under the conditions of intermittent communication, actuator failure and input quantized hysteresis, the formation error can converge to the zero neighborhood within a predetermined time without Zeno phenomenon.

[0015] In step one, after ignoring the high-degree-of-freedom motion of USVs such as heave, roll and pitch, the kinematics and dynamics model of the ith USV in the horizontal plane is represented as:

[0016]

[0017] where i ∈ {1, 2, …, N} is the number of unmanned surface vehicle; ω i (t) = [x i (t), y i (t), φ i (t)] T is the position and heading angle in the earth-fixed coordinate system; ν i (t) = [p i (t), q i (t), r i (t)] T is the surge velocity, sway velocity and yaw angular velocity in the body coordinate system; M i = diag{m 1,i , m 2,i , m 3,iJ(ν i (t)) is the Coriolis and centripetal force matrix; D(ν i (t)) = diag{d 1,i ,d 2,i ,d 3,i} is the hydrodynamic damping matrix; τ i (t) = [τ i,p (t), 0, τ i,r (t)] T is the control input vector, where τ i,p (t) is the longitudinal thrust, τ i,r (t) is the steering moment; τ i,d (t) = [τ i,pd (t), 0, τ i,rd (t)] T is the unknown external disturbance caused by wind, wave, current and so on; R(φ i (t)) is the rotation matrix from the body coordinate system to the earth-fixed coordinate system.

[0018] To achieve the unified full-drive modeling of the underactuated USV, a virtual reference point located on the bow extension line of the USV is introduced and defined as an auxiliary output variable:

[0019]

[0020] wherein, is a constant. The second-order derivative of the above auxiliary position vector is obtained by combining the dynamics equation:

[0021]

[0022] In the formula, u i (t) = [u i,1 (t), u i,2 (t)] T is the equivalent control input; u i,d (t) = [u i1,d (t), u i2,d (t)] T is the equivalent external disturbance;

[0023] is the transformation matrix:

[0024]

[0025] and is the system nonlinear term:

[0026]

[0027] wherein,

[0028]

[0029] Thus, the underactuated USV dynamic system is equivalently transformed into a fully actuated second-order system.

[0030] In step two, an intermittent fault model of the actuator and an input hysteresis quantizer are constructed, and the additional fault terms, quantization errors and external disturbances are uniformly modeled as a comprehensive nonlinear uncertainty term:

[0031] First, for the j-th execution channel of the i-th USV, the actuator output and the expected input satisfy the following:

[0032]

[0033] Where, γ ij (t) represents the multiplicative fault term. This indicates additional fault items caused by additive deviations / interferences, etc.; typical cases include: 1. normal;

[0034] 2. The effectiveness is partially lost;

[0035] 3. Additive fault / bias;

[0036] 4. The actuator is stuck.

[0037] Secondly, regarding the control input u ij The l-th component of (t) is hysteresis quantized, and the quantized output is:

[0038]

[0039] in τ l,min >0 represents the dead zone width, η l ∈(0,1),

[0040] The hysteresis quantization output is decomposed into an equivalent gain F(u) ij,l (t) and residual f ij,l (t) form:

[0041]

[0042] in,

[0043] 1-ω l ≤F(u ij,l (t))≤1+ω l ,|f ij,l (t)|≤uij,l,min

[0044] Finally, by unifying actuator faults and hysteresis quantization, the actual input applied to the USV is obtained:

[0045]

[0046] In step three, an FLS is designed based on the MLP strategy to achieve high-precision approximation of the comprehensive nonlinear uncertainty term; the weight parameters are updated online through a predetermined time adaptive law, which significantly reduces computational complexity while ensuring approximation accuracy.

[0047] First, the distributed formation error ψ of the i-th USV follower. i (t) is defined as

[0048]

[0049] Where, ω d (t) represents the desired trajectory of the virtual leader USV, and the topology parameters satisfy a ij =a ji And b i >0. The time-varying formation error of the i-th follower is determined by... Given, and the corresponding error vector is defined as δ(t)=[δ1(t),δ2(t),...,δ N (t)] T ,ψ(t)=[ψ1(t),ψ2(t),...,ψ N (t)] T Under intermittent communication conditions, the formation error dynamically satisfies in It is a Laplace matrix that describes the information exchange between followers. It is a diagonal matrix of direct links from the formation leader to the followers.

[0050] Then, based on the fractional-order formation error Θ(ψ) i (t) Construct a sliding surface S with a predetermined time. i (t)

[0051] S i (t)=ψ i (t)+Θ(ψ i (t)),

[0052] Where α1≥1, T ψ >0.

[0053] To further ensure that the sliding surface reaches zero within the predetermined time, the following predetermined time sliding function is selected:

[0054]

[0055] where α2≥1, T S >0.

[0056] Taking the derivative of S i (t) and writing it in scalar form S ij (t), the corresponding dynamic sliding surface equation is:

[0057]

[0058] where

[0059] The MLP-FLS is used to approximate the unknown nonlinear uncertain term:

[0060] O i (t) = W i T ξ i (Z i (t)) + e i ,‖O i (t)‖≤μ i Ψ i (Z i (t)) + σ i ,

[0061] where Ψ i (Z i (t)) =‖ξ i (Z i (t))‖, μ i =‖W i ‖, σ i =‖e i ‖.

[0062] To reduce the computational complexity, a predetermined time weight adaptive law is used to adaptively adjust the weight coefficients:

[0063]

[0064] where μ = [μ1, μ2,..., μ N ] T , and T μ , T σ >0 are normal numbers.

[0065] The predetermined time robust adaptive dynamic event-triggered strategy is proposed in step four, which combines the input hysteresis quantizer to compress the control signal transmission and dynamically adjusts the communication and controller update frequency. This mechanism effectively reduces the bandwidth occupation under the premise of ensuring system stability.

[0066] First, an adaptive pre-specified time dynamic event-triggered mechanism is designed as

[0067]

[0068] where is a set of time-varying robust parameter vectors, where each i (t) satisfies 0 < λ i (0) < 1, and let be a set of positive design constant vectors, and for all i ∈ {1, 2,..., N}, have b i > 0. In addition, let i > 0 (Γ = [Γ1, Γ2,..., Γ N ] T denote the scalar control gain. Define two fixed positive scalars θ1∈(0, 1) and ε > 0, which will be used in the construction of the robust triggering mechanism and stability analysis.

[0069] To prevent Zeno behavior, introduce a minimum triggering interval T i,k > 0. When the triggering condition is satisfied and the interval from the last triggering time is greater than T i,k > 0, update the control input immediately and send it to the actuator side through the communication network. This event-triggered mechanism remains silent when the error is small and only triggers when the error increases to a certain extent, thus significantly reducing the communication and computation load while guaranteeing the pre-specified time convergence performance of the system, and maintaining robustness to faults and quantization uncertainty.

[0070] In step five, the designed control law is strictly proved by Lyapunov function and Nussbaum function that under the conditions of intermittent communication, actuator failure and input hysteresis quantization, the formation error can converge to the zero neighborhood within a pre-specified time without Zeno phenomenon.

[0071] Before proceeding with the theoretical proof, the following lemma is introduced:

[0072] Lemma 1. For the system if there exists a positive definite continuous Lyapunov function V(y) such that

[0073]

[0074] where λ > 0, β > 0, 0 < p < 1, Therefore, the system is pre-specified time stable, and the convergence time satisfies

[0075] Lemma 2. Assume V(·) and ζ i(·) is a specified smooth function on [0,∞) and V(t)≥0 K(·) is a Nussbaum function. G i (t) is a parameter varying on a closed interval. If there exist two parameters p>0 and c>0 such that the following inequality holds

[0076]

[0077] where V(t) and are bounded on t∈[0,∞).

[0078] By synthesizing the above-mentioned step one, step two, step three and step four, the adaptive pre-determined time fault-tolerant control law is designed as follows:

[0079]

[0080] where i∈{1,2,...,N}, j∈{1,2}, and and are the estimation values of μ and σ, respectively.

[0081] The Lyapunov function is selected as follows

[0082]

[0083] where S(t) is the sliding mode surface vector, is the parameter estimation error.

[0084] Substituting the above fault-tolerant control law and weight adaptive law into the system closed-loop dynamics and combining the fault and quantization model, the following equation can be obtained

[0085]

[0086] where is a positive constant, m=min{β2,θ1,θ2,θ3},

[0087] Combined with Lemma 2, it can be further obtained that

[0088]

[0089] where

[0090] By using Lemma 1 and the above theoretical derivation and analysis, it is proved that the controlled multi-USV system realizes the pre-determined time stability under the fixed communication topology structure.

[0091] The boundedness of the dwell time under the intermittent switching topology needs to be analyzed.

[0092] According to the scaling relationship of Young's inequality and the structure of Lyapunov function, the following conclusions can be drawn:

[0093]

[0094] where χ > 0 is a positive constant defined as and

[0095] By recursively applying, for the o-th switching time t o , we have

[0096]

[0097] where the minimum dwell time condition is satisfied as

[0098] Regarding the boundedness established in the above, based on the same control and switching conditions, the convergence characteristics of the sliding surface S i (t) and the formation error ψ i (t) within a predetermined time will be derived.

[0099] First, define the Lyapunov function as

[0100]

[0101] Then, taking the derivative of V2(t) gives

[0102]

[0103] where there exists a positive constant ζ > 0 satisfying

[0104] Therefore, we can further obtain

[0105]

[0106] where

[0107] According to Lemma 1-2, the Lyapunov function V2(t) and the sliding surface S(t) are bounded, and the predetermined time sliding compact set of S(t) is as follows:

[0108]

[0109] where the predetermined time is T S .

[0110] Similarly, it can also be obtained that ψ(t) is pre-defined time stable, and the corresponding ψ(t) compact set is as follows:

[0111]

[0112] where T is the predetermined time ψ .

[0113] Finally, the total predetermined time is T = T S + T ψ .

[0114] Therefore, under the designed controller and event-triggered mechanism, all closed-loop signals are bounded and convergent in the predetermined time, and the sliding surface S(t) and the formation error ψ i (t) tend to zero in the predetermined time T ψ + T S , thus realizing the stable formation control of the system and having the robust fault-tolerant capability to intermittent faults of actuators, quantization of hysteresis and external disturbances.

[0115] Exclusion of Zeno phenomenon:

[0116] The control law is updated only when certain conditions are met, otherwise the value at the last triggering time is maintained. Under the condition that all assumptions are true, there is a minimum event-triggering time interval:

[0117]

[0118] where ε > 0, and θ > 0 are designed normal numbers. The positive duration between adjacent triggers can avoid the occurrence of Zeno phenomenon. The relevant theoretical proof is as follows:

[0119]

[0120] Since the vector is bounded, there is a positive constant θ > 0 such that Note that ‖l i (t i,k )‖ = 0 and Integrating over the interval [t i,k , t i,k+1 ) gives

[0121]

[0122] Therefore, the minimum event-triggering time interval is:

[0123]

[0124] The application proposes a heterogeneous multi-USV predetermined time fault-tolerant fuzzy formation control method based on dynamic event triggering, which reduces communication resource waste by using an adaptive dynamic event triggering mechanism; estimates the comprehensive uncertain dynamics by using the MLP-FLS strategy, greatly saving the computing resources; and improves the anti-interference ability of the multi-USV system in the formation task.

[0125] Compared with the prior art, the core advantages of the application are reflected in the following aspects:

[0126] 1. Efficient resource management and performance guarantee: The application innovatively proposes a cooperative control method that combines a predetermined time adaptive dynamic event triggering mechanism to address the key challenges of nonlinearity, dynamic uncertainty, and limited communication resources in multi-USV formation control. This method ensures stable convergence within a predetermined time window and maintains excellent performance while significantly reducing the frequency of redundant communication and control instruction updates, thereby greatly optimizing the overall resource utilization efficiency of the system and demonstrating significant engineering application potential and practical operational benefits.

[0127] 2. Superiority of adaptive triggering mechanism: The adaptive dynamic event triggering strategy designed in the application has the ability to conditionally determine the triggering threshold based on the real-time state error and dynamic adjustment of the system. Compared with traditional static event triggering strategies, this mechanism can significantly reduce the event triggering frequency of data transmission and control updates without sacrificing the performance of the control system, thereby significantly improving the utilization of communication bandwidth and computing resources.

[0128] 3. Robust cooperation in complex environments: The application constructs a multi-agent cooperative information interaction architecture, enabling efficient information cooperation and distributed cooperative control in a resource-limited communication environment. This ensures that the multi-USV system can maintain excellent formation stability and high-precision trajectory tracking capability when facing external environmental disturbances, intermittent actuator failures, input hysteresis quantization, and intermittent communication topology switching.

[0129] 4. Reinforced robustness and fault tolerance: The application ingeniously combines nonlinear dynamic compensation and forward-looking robust control paradigms in the control law design. This design significantly enhances the system's adaptability and resilience in dealing with model uncertainty, external disturbances, and intermittent failures in complex working conditions, thereby significantly improving the reliability and anti-external disturbance ability of the multi-USV system. BRIEF DESCRIPTION OF DRAWINGS

[0130] The accompanying drawings are included to provide a further understanding of the application, and constitute a part of the specification, together with the embodiments of the application, to explain the application, and do not constitute a limitation on the application.

[0131] Figure 1The control block diagram is designed for the fault-tolerant fuzzy formation control under the scheduled time dynamic event trigger mechanism of the heterogeneous multi-USV system in the application.

[0132] Figure 2 The communication switching topological structure diagram of the heterogeneous multi-USV system in the application is shown.

[0133] Figure 3 The formation trajectory of the multi-USV in the time-varying pentagon formation in the application is shown Figure 1

[0134] Figure 4 The formation trajectory of the multi-USV in the time-varying pentagon formation in the application is shown Figure 2 .

[0135] Figure 5 The two-dimensional trajectory change diagram of the multi-USV in the time-varying pentagon formation task in the application at different times is shown.

[0136] Figure 6 The lateral and longitudinal formation error diagram of the multi-USV in the time-varying pentagon formation task in the application is shown Figure 1 .

[0137] Figure 7 The lateral and longitudinal formation error diagram of the multi-USV in the time-varying pentagon formation task in the application is shown Figure 2 .

[0138] Figure 8 The event trigger time interval diagram of the first USV in the time-varying pentagon formation task in the application is shown Figure 1 .

[0139] Figure 9 The event trigger time interval diagram of the second USV in the time-varying pentagon formation task in the application is shown Figure 2 .

[0140] Figure 10 The event trigger time interval diagram of the third USV in the time-varying pentagon formation task in the application is shown Figure 3 .

[0141] Figure 11 The event trigger time interval diagram of the fourth USV in the time-varying pentagon formation task in the application is shown Figure 4 .

[0142] Figure 12 The event trigger time interval diagram of the fifth USV in the time-varying pentagon formation task in the application is shown Figure 5 .

[0143] Figure 13Fig. 1 is a schematic diagram of the control input of the first USV in the application compared with the hysteresis quantization control input Figure 1 .

[0144] Figure 14 Fig. 2 is a schematic diagram of the control input of the second USV in the application compared with the hysteresis quantization control input Figure 2 .

[0145] Figure 15 Fig. 3 is a schematic diagram of the control input of the third USV in the application compared with the hysteresis quantization control input Figure 3 .

[0146] Figure 16 Fig. 4 is a schematic diagram of the control input of the fourth USV in the application compared with the hysteresis quantization control input Figure 4 .

[0147] Figure 17 Fig. 5 is a schematic diagram of the control input of the fifth USV in the application compared with the hysteresis quantization control input Figure 5 .

[0148] Figure 18 Fig. 6 is a bar chart of the total number of triggers of each USV under different trigger strategies in the application. DETAILED DESCRIPTION

[0149] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below in combination with the drawings and examples. Of course, the specific examples described here are only used to explain the application and not to limit the application.

[0150] Example 1

[0151] This example provides a technical scheme of a heterogeneous multi-USV predetermined time fault-tolerant formation control method based on dynamic event triggering. In order to better illustrate the application, MATLAB numerical simulation is used to verify the proposed controller, and the results are shown in Figures 3 to 10 , and the specific steps are as follows

[0152] Step one: establish a multi-USV model, convert it to a full-drive system by using coordinate transformation, and unify the actuator fault and hysteresis quantization to obtain the actual input applied to the USV:

[0153]

[0154] Step two: in order to save communication resources, an adaptive predetermined time dynamic event triggering mechanism is designed:

[0155] First, the adaptive predetermined time dynamic event triggering mechanism is designed as

[0156]

[0157] where, is a set of time-varying robust parameter vectors, where each i (t) satisfies 0 < λ i (0) < 1, and let be a set of positive design constant vectors, and for all i ∈ {1, 2,..., N}, have b i > 0. Furthermore, let Γ i > 0 (Γ = [Γ1, Γ2,..., Γ N ] T denote the scalar control gain. Define two fixed positive scalars θ1∈(0, 1) and ε > 0, which will be used in the construction of the robust triggering mechanism and stability analysis.

[0158] To prevent Zeno behavior, introduce a minimum triggering interval T i,k > 0, when the triggering condition is satisfied and the interval between the current time and the last triggering time is greater than T i,k > 0, immediately update the control input and send it to the actuator side through the communication network. This event-triggered mechanism remains silent when the error is small, and only triggers when the error increases to a certain extent, thereby significantly reducing the communication and computational load while ensuring the predetermined time convergence performance of the system, and maintaining robustness to faults and quantization uncertainties.

[0159] Step three: propose a predetermined time robust adaptive dynamic event-triggered strategy, combined with input hysteresis quantizer to compress control signal transmission, dynamically adjust the communication and controller update frequency. This mechanism effectively reduces the bandwidth occupation while ensuring the stability of the system.

[0160] First, the distributed formation error ψ i (t) of the i-th USV follower is defined as

[0161]

[0162] Then, based on the fractional order formation error Θ(ψ i (t)), the predetermined time sliding surface S i (t) is constructed

[0163] S i (t) = ψ i (t) + Θ(ψ i (t)),

[0164] where α1≥ 1, T ψ > 0.

[0165] Further, to ensure that the predetermined time sliding surface reaches zero within the predetermined time, the following predetermined time sliding surface function is selected,

[0166]

[0167] where α2≥ 1, T S > 0.

[0168] Taking the derivative of S i (t) and writing it in scalar form S ij (t), the corresponding dynamic sliding mode surface equation is:

[0169]

[0170] where

[0171] Step four: design FLS based on MLP strategy to achieve high-precision approximation of the comprehensive nonlinear uncertain term; update the weight parameters online through the predetermined time adaptive law, which significantly reduces the computational complexity while ensuring the approximation accuracy, and through the comprehensive use of the contents of the above step one, step two, step three and step four, the following weight coefficient adaptive law and predetermined time fault-tolerant control law are designed:

[0172] In order to reduce the computational complexity, the predetermined time weight adaptive law is used to adaptively adjust the weight coefficient:

[0173]

[0174] where μ = [μ1, μ2,..., μ N ] T , and T μ , T σ > 0 are normal numbers.

[0175] In order to realize the predetermined time formation control, the following predetermined time fault-tolerant control law:

[0176]

[0177] where i ∈ {1, 2,..., N}, j ∈ {1, 2}, and and are the estimated values of μ and σ, respectively.

[0178] Step five: stability analysis, select Lyapunov function:

[0179] Select the following Lyapunov function

[0180]

[0181] where S(t) is the sliding mode surface vector, is the parameter estimation error.

[0182] Substituting the fault-tolerant control law and the weight adaptive law into the system closed-loop dynamics and combining the fault and quantization models, we have

[0183]

[0184] where is a positive constant, m = min{β2, θ1, θ2, θ3},

[0185] Combining Lemma 2, we can further obtain

[0186]

[0187] where

[0188] Using Lemma 1 and the above theoretical derivation and analysis, it is proved that the controlled multi-USV system achieves the predetermined time stability under the fixed communication topology.

[0189] Then, define the Lyapunov function as

[0190]

[0191] Then, take the derivative of V2(t) to obtain

[0192]

[0193] where there exists a positive constant ζ > 0 satisfying

[0194] Therefore, we can further obtain

[0195]

[0196] where

[0197] According to Lemmas 1-2, the Lyapunov function V2(t) and the sliding surface S(t) are bounded, and the predetermined time sliding surface set of S(t) is as follows:

[0198]

[0199] where the predetermined time is T S .

[0200] Similarly, we can also obtain that ψ(t) is predetermined time stable, and the corresponding predetermined time sliding surface set of ψ(t) is as follows:

[0201]

[0202] where predetermined time is T ψ .

[0203] The specific simulation process and parameters are as follows:

[0204] A virtual leader i = 0, four follower unmanned surface vehicles (USVs) (i = 1, 2, 3, 4, 5) heterogeneous multi-USV system, the model parameters are:

[0205]

[0206] The related parameters of MLP-FLS are as follows:

[0207]

[0208] The related control parameters are as follows:

[0209] α1=2, β1=0.15, α2=2, β2=0.1, k λ =20, k θ =0.01, θ1=0.5,

[0210] θ2=0.5, θ3=0.5, T S =1.5, T ψ =1.5, T λ =1, T μ =1, T σ =1.

[0211] The initial state of the multi-USV system is

[0212] η1(0)=[-0.5, 0.5] T , η2(0)=[-1.0, 1.0] T , η3(0)=[-1.5, 1.5] T , η4(0)=[-2.0, 2.0] T , η5(0)=[-2.5, 2.5] T .

[0213] The initial speed of the multi-USV system is zero. The following time-varying pentagon desired formation function is selected:

[0214]

[0215] The results show that in the set time-varying pentagon desired formation scenario, Figure 1 The heterogeneous multi-USV predetermined time fault-tolerant fuzzy formation control block diagram based on dynamic event triggering is given, Figure 2 The communication switching topology of the heterogeneous multi-USV system is shown, Figure 3 and Figure 4The formation situation of the system at different times is depicted respectively, Figure 5 The trajectory of the heterogeneous multi-USV system in two-dimensional space is intuitively depicted. Further, Figure 6 With Figure 7 It shows that the control strategy can effectively suppress the formation error and achieve convergence. At the same time, Figures 8 to 12 It verifies that the designed pre-time adaptive dynamic event triggering mechanism can flexibly and efficiently reduce the communication triggering frequency under the condition of ensuring the control performance, significantly saving communication resources and improving communication efficiency. More importantly, from Figures 13 to 17 It can be seen that even under the adverse conditions of input hysteresis and quantization effect, the proposed method can achieve the desired formation goal, and has strong robustness and engineering applicability.

[0216] Embodiment 2

[0217] The parameters of the heterogeneous multi-USV system and the related controller are the same as in Embodiment 1. In step three, the adaptive pre-time dynamic event triggering mechanism is replaced by the traditional static event triggering mechanism and the time triggering mechanism

[0218] 1. Static event triggering mechanism: that is, set the triggering threshold parameter to a fixed constant, and select the threshold parameter size as 0.1.

[0219] Design the static event triggering mechanism:

[0220] t i,k+1 =inf{t i >t i,k ∣ξ i ‖l i (t i )‖≥0.1}

[0221] 2. Time triggering mechanism: select the timing triggering method with a step size of 0.001s, collect data and update the input control quantity every 0.001s.

[0222] The final total triggering times are shown in Figure 18 By comparing the traditional static event triggering mechanism, the time triggering mechanism and the pre-time adaptive dynamic event triggering mechanism proposed in this patent, it can be seen that the algorithm proposed in this invention can significantly reduce the communication frequency between individuals under the premise of ensuring the error convergence and stability of the system, thereby exhibiting better comprehensive performance in communication overhead and computational resource utilization, and embodying higher resource saving efficiency and engineering application value.

[0223] The above merely describes preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for fault-tolerant fuzzy formation control of multiple unmanned surface vessels (USVs) with dynamic event triggering at predetermined times, characterized in that, Includes the following steps: Step 1: Establish a heterogeneous multi-USV kinematic and dynamic model that considers input hysteresis quantization, intermittent communication topology, intermittent actuator failures and external disturbances. By introducing auxiliary reference position variables, the underactuated second-order USV system is equivalently transformed into a fully actuated system, and the formation error and control objective are defined. Step 2: Construct an intermittent failure model of the actuator and an input hysteresis quantizer, and model the additional failure terms, quantization errors and external disturbances into a unified comprehensive nonlinear uncertainty term; Step 3: Design a fuzzy logic system FLS based on the minimum learning parameter (MLP) strategy to approximate the comprehensive nonlinear uncertainty term; update the weight parameters online through a predetermined time adaptive law; Step 4: Propose a predetermined time robust adaptive dynamic event triggering strategy, which combines input hysteresis quantizer to compress control signal transmission and dynamically adjust the communication and controller update frequency; Step 5: Construct a fault-tolerant formation control law based on the predetermined time sliding mode control, use the Nussbaum function to handle the unknown control gain, and perform stability analysis using the Lyapunov function: under the conditions of intermittent communication, actuator failure and input hysteresis quantization, the formation error converges to the zero neighborhood within the predetermined time and there is no Zeno phenomenon.

2. The multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method according to claim 1, characterized in that, In step one, after neglecting the high-degree-of-freedom motions of the USV such as heave, roll, and pitch, the kinematic and dynamic model of the i-th USV in the horizontal plane is expressed as follows: In the formula, i∈{1,2,...,N} is the unmanned surface vessel number; ω i (t)=[x i (t),y i (t),φ i (t)] T The position and heading angle in the Earth-fixed coordinate system; ν i (t)=[p i (t),q i (t),r i (t)] T For the sway velocity, roll velocity, and yaw rate in body coordinates; M i =diag{m 1,i ,m 2,i ,m 3,i } represents the system inertia matrix including the added mass; C(ν) i (t)) is the Coriolis force and centripetal force matrix; D(ν) i (t))=diag{d 1,i ,d 2,i ,d 3,i } represents the hydrodynamic damping matrix; τ i (t)=[τ i,p (t),0,τ i,r (t)] T To control the input vector, where τ i,p (t) represents the longitudinal thrust, τ i,r (t) represents the steering torque; τ i,d (t)=[τ i,pd (t),0,τ i,rd (t)] T R(φ) represents unknown external disturbances caused by external environmental factors such as wind, waves, and currents. i (t) is the rotation matrix from the volume coordinate system to the Earth-fixed coordinate system; For the unified full-drive modeling of the underactuated unmanned surface vessel (USV), a virtual reference point located on the bow extension line of the USV is introduced and defined as an auxiliary output variable: in, Since is a constant, taking the second derivative of the above auxiliary position vector and combining it with the aforementioned dynamic equations, we obtain: In the formula, u i (t)=[u i,1 (t),u i,2 (t)] T For equivalent control input; u i,d (t)=[u i1,d (t),u i2,d (t)] T For equivalent external disturbance; Here is the transformation matrix: as well as For the system's nonlinear terms: in, Thus, the underactuated USV dynamic system is equivalently transformed into a fully actuated second-order system.

3. The multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method according to claim 1, characterized in that, In step two, an intermittent fault model of the actuator and an input hysteresis quantizer are constructed, and the additional fault terms, quantization errors and external disturbances are uniformly modeled as a comprehensive nonlinear uncertainty term: First, for the j-th execution channel of the i-th USV, the actuator output and the expected input satisfy the following: Where, γ ij (t) represents the multiplicative fault term. This indicates additional fault items caused by additive deviations or disturbances; including the following situations: 1) γ ij (t)=1, normal; 2) γ ij (t)∈(0,1), The effectiveness is partially lost; 3) γ ij (t)=1, Additive fault / bias; 4) γ ij (t)=0, Actuator stuck; Secondly, regarding the control input u ij The l-th component of (t) is hysteresis quantized, and the quantized output is: in τ l,min >0 represents the dead zone width, η l ∈(0,1), The hysteresis quantization output is decomposed into an equivalent gain F(u) ij,l (t) and residual f ij,l (t) form: in, 1-ω l ≤F(u ij,l (t))≤1+ω l ,|f ij,l (t)|≤u ij,l,min ; Finally, by unifying actuator faults and hysteresis quantization, the actual input applied to the USV is obtained:

4. The multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method according to claim 1, characterized in that, In step three, a fuzzy logic system (FLS) is designed based on the minimum learning parameter (MLP) strategy to approximate the comprehensive nonlinear uncertainty term; the weight parameters are updated online using a predetermined time adaptive law. First, the distributed formation error ψ of the i-th USV follower. i (t) is defined as: Where, ω d (t) represents the desired trajectory of the virtual leader USV, and the topology parameters satisfy a ij =a ji And b i >0, the time-varying formation error of the i-th follower is determined by Given, and the corresponding error vector is defined as δ(t)=[δ1(t),δ2(t),...,δ N (t)] T ,ψ(t)=[ψ1(t),ψ2(t),...,ψ N (t)] T Under intermittent communication conditions, the formation error dynamically satisfies in It is a Laplace matrix that describes the information exchange between followers. It is a diagonal matrix of direct links from the formation leader to the followers; Then, based on the fractional-order formation error Θ(ψ) i (t) Construct a sliding surface S with a predetermined time. i (t) Where α1≥1, T ψ >0; To ensure that the sliding surface reaches zero within the predetermined time, the following predetermined time sliding function is selected: Where α2≥1, T S >0; S i Differentiate (t) and write it in scalar form S ij (t), then the corresponding dynamic sliding surface equation is: in The fuzzy logic system MLP-FLS approximation for unknown nonlinear uncertainties using minimum learning parameters: O i (t)=W i T ξ i (Z i (t))+e i ,‖O i (t)‖≤μ i Ψ i (Z i (t))+σ i ,; among them i (Z i (t))=‖ξ i (Z i (t))‖,μ i =‖W i ‖,s i =‖e i ‖; The weighting coefficients are adaptively adjusted using a predetermined time-weighted adaptive law. Where μ = [μ1, μ2, ..., μ N ] T , And T μ ,T σ >0 is a positive number.

5. The multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method according to claim 1, characterized in that, In step four, a predetermined time robust adaptive dynamic event triggering strategy is proposed, which combines input hysteresis quantizer to compress control signal transmission and dynamically adjust the communication and controller update frequency. First, design an adaptive, pre-set time dynamic event triggering mechanism. In the formula, Let λ be a set of robust parameter vectors that vary with time, where each λ i (t) all satisfy 0 < λ i (0) < 1, let... Let b be a set of positive design constant vectors, and for all i∈{1,2,...,N}, we have b i >0; In addition, let Γ i >0, Γ=[Γ1,Γ2,...,Γ N ] T Let scalar control gain be defined, and then two fixed positive scalars θ1∈(0,1) and ε>0 are defined for the construction and stability analysis of the robust triggering mechanism; Introducing a minimum trigger interval T i,k >0, when the triggering condition is met and the time interval between the previous trigger and the current trigger is greater than T. i,k When the value is greater than 0, the control input is updated and sent to the actuator via the communication network.

6. The multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method according to claim 1, characterized in that, In step five, the Lyapunov and Nussbaum functions are used to prove that the designed control law, under the conditions of intermittent communication, actuator failure and input hysteresis quantization, ensures that the formation error converges to the zero neighborhood within a predetermined time and there is no Zeno phenomenon. Design the following adaptive predetermined time fault-tolerant control law: Where i∈{1,2,...,N}, j∈{1,2}, and and These are the estimated values ​​of μ and σ, respectively; Choose the following Lyapunov functions Where S(t) is the sliding mode surface vector, For parameter estimation error; Substituting the aforementioned fault-tolerant control law and weighted adaptive law into the system closed-loop dynamics and combining them with the fault and quantization model, we obtain... in Let m be a positive constant, and m = min{β2,θ1,θ2,θ3}. get In the formula, Based on the scaling relationship of Young's inequality and the structure of Lyapunov functions, the following conclusions can be drawn: The positive constant χ > 0 is defined as... and By recursively applying the method, for the o-th switching time t o ,get In the formula, the minimum dwell time condition is satisfied. γ≥1; Regarding the boundedness established above, the sliding surface S will be derived based on the same control and switching conditions. i (t) and formation error ψ i (t) Convergence characteristics within a predetermined time; First, define the Lyapunov function as follows: Then, taking the derivative with respect to V2(t), we get... In the formula, there exists a positive constant ζ > 0, satisfying The conclusion is In the formula, Since both the Lyapunov function V2(t) and the sliding surface S(t) are bounded, and the predetermined time sliding compact set of S(t) is as follows: The scheduled time is T. S ; We obtain that ψ(t) is predefined to be time-stable, and its corresponding compact set is as follows: The scheduled time is T. ψ ; Ultimately, the total scheduled time is T = T S +T ψ .; Under the designed controller and event triggering mechanism, all closed-loop signals are bounded and converge within a predetermined time. The sliding surface S(t) and the formation error ψ i (t) at the predetermined time T ψ +T S The internal tends to zero, achieving stable formation control of the system, and has robust fault tolerance to intermittent actuator failures, hysteresis quantization, and external disturbances; The control law will only update if preset conditions are met; otherwise, it will retain the value from the previous triggering time. Under the condition that all assumptions are true, there exists a minimum event triggering time interval: Where ε>0, Both θ > 0 are designed positive constants. The positive duration between adjacent triggers avoids the Zeno phenomenon. The relevant theoretical proof is as follows: Due to vectors It is bounded, and there exists a positive constant θ > 0 such that Note ||l i (t i,k )‖=0 and In the interval [t] i,k ,t i,k+1 ) on ||l i (t i Integrating the result yields... Therefore, the minimum event triggering time interval is:

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