Multi-unmanned vehicle dynamic event triggered scheduled time fault-tolerant fuzzy formation control method

Abstract

This invention provides a fault-tolerant fuzzy formation control method for multiple unmanned surface vessels (USVs) with dynamic event triggering at predetermined times, belonging to the field of heterogeneous unmanned system formation control technology. The method includes the following steps: Step 1: Establishing a kinematic and dynamic model of heterogeneous multiple USVs considering input hysteresis quantization, intermittent communication topology, intermittent actuator failures, and external disturbances; Step 2: Constructing an intermittent actuator failure model and an input hysteresis quantizer; Step 3: Designing a fuzzy logic system based on a minimum learning parameter strategy; Step 4: Proposing a predetermined-time robust adaptive dynamic event triggering strategy; Step 5: Constructing a fault-tolerant formation control law based on predetermined-time sliding mode control, and using a Nussbaum function to handle unknown control gains. This invention significantly improves the anti-interference capability and engineering applicability of USV systems in complex marine environments while reducing communication and computing resource consumption.

Description

Technical Field

[0001] This invention relates to the field of heterogeneous unmanned system formation control technology, and in particular to a heterogeneous multi-USV predetermined time fault-tolerant fuzzy formation control method based on dynamic event triggering. Background Technology

[0002] With the rapid development of maritime power strategies and intelligent equipment technologies, unmanned surface vehicles (USVs) have become an important research direction for multi-mission coordination at sea. USVs possess flexible maneuverability, strong mission payload capacity, and broad application prospects. However, due to significant differences in dynamic characteristics, structural parameters, and operating environments among different USVs, numerous technical challenges remain in terms of coordinated operation and control accuracy.

[0003] To overcome these challenges, particularly the limitations of fixed-time and finite-time schemes, researchers have developed predetermined-time control strategies to ensure system convergence within user-specified deadlines. In the USV domain, this strategy has been extended to critical tasks such as trajectory tracking and formation keeping, which require execution under strict time constraints. For example, predetermined-time control laws have been tailored to address input amplitude and rate limitations in underactuated passive USVs, where the inherent passivity and actuation constraints of USVs present significant challenges. Similarly, robust predetermined-time formation controllers have been designed to handle random interference and intermittent communication topologies in distributed multi-USV fleets, significantly improving their practical applicability in bandwidth- and interference-constrained marine environments.

[0004] Despite advancements in these control strategies, multiplicative faults, additive biases, or jamming inevitably occur in actuators or sensors during multi-USV collaboration. These faults can affect control accuracy and task completion quality, and even lead to system instability. Existing research has proposed fault-tolerant control methods for partial actuator and sensor failures, power outages, or jamming; however, most rely on acquiring complete dynamic parameters, which is often difficult to achieve in practical tasks, especially in environments with communication interruptions, information transmission delays, and bandwidth limitations, making the acquisition of complete and accurate information extremely challenging.

[0005] To further improve system reliability and resource utilization efficiency, event-triggered control methods have been widely proposed and applied. This method, by only transmitting data and updating control when triggering conditions are met, can significantly reduce communication resource consumption and lower energy consumption caused by frequent actuator movements. However, traditional static event-triggered strategies cannot adjust triggering conditions in real time according to changes in system operating status, easily leading to either excessively frequent or excessively sparse triggering, thus affecting control performance.

[0006] In recent years, adaptive dynamic event-triggered control strategies have become a research hotspot. This strategy, by introducing an adjustable trigger threshold, achieves dynamic optimization of the triggering frequency, effectively reducing unnecessary updates while maintaining system performance stability. However, existing research often lacks unified modeling methods and compensation mechanisms when facing comprehensive nonlinear uncertainties such as intermittent actuator failures, quantization errors, and external disturbances, making it difficult to balance fault tolerance and communication resource optimization. Furthermore, in terms of control input, input hysteresis quantization further exacerbates system uncertainty. Input hysteresis quantization refers to the nonlinear hysteresis effect introduced by the quantizer during the transmission and execution of control signals, causing the input signal to fail to accurately match the expected value, resulting in 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. Simultaneously, intermittent topology switching is also a key challenge. This phenomenon stems from intermittent interruptions or dynamic changes in communication links in marine environments, leading to frequent switching of the connection topology between USVs, thus affecting the continuity of information exchange and the coordination of formation control. Existing methods often cannot adapt to such topology switching in real time, easily causing slow or inconsistent system responses. 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 failures, input hysteresis quantization, and intermittent topology switching. Summary of the Invention

[0007] The purpose of this invention is to provide a pre-time fault-tolerant fuzzy formation control method for heterogeneous multi-USV systems based on dynamic event triggering. Addressing the formation control problem in multi-USV systems experiencing intermittent failures and exhibiting comprehensive nonlinear uncertainties such as input hysteresis quantization, external disturbances, and intermittent topology switching, this invention proposes a collaborative control strategy that can reduce communication and control resource consumption while ensuring system stability and tracking accuracy.

[0008] To achieve the above objectives, this invention introduces a fractional-order predetermined-time sliding mode control method, combined with a minimum-learning-parameter fuzzy logic system to compensate for system nonlinear uncertainties. An adaptive dynamic event-triggered mechanism adjusts the timing of communication and control updates, reducing invalid communication and control updates, thereby significantly reducing network load and energy consumption. During formation, this invention utilizes a predetermined-time mechanism to pre-calculate control inputs and combines this with dynamic threshold conditions to trigger controller updates, effectively addressing the combined effects of intermittent actuator failures, input hysteresis quantization, external disturbances, and intermittent topology switching.

[0009] To achieve the aforementioned objectives, the present invention employs the following technical solution: a multi-unmanned surface vessel dynamic event triggering predetermined time fault-tolerant fuzzy formation control method, comprising the following steps:

[0010] Step 1: Establish a heterogeneous multi-USV kinematic and dynamic model considering 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 rigorously defined.

[0011] Step 2: Construct an intermittent fault model of the actuator and an input hysteresis quantizer, and model the additional fault terms, quantization errors and external disturbances into a unified nonlinear uncertainty term, providing a theoretical basis for subsequent robust control design.

[0012] Step 3: Design FLS based on MLP strategy to achieve high-precision approximation of comprehensive nonlinear uncertainty term; update weight parameters online through predetermined time adaptive law to significantly reduce computational complexity while ensuring approximation accuracy.

[0013] Step 4: Propose a predetermined time-based robust adaptive dynamic event triggering strategy, which combines an input hysteresis quantizer to compress control signal transmission and dynamically adjust the communication and controller update frequencies. This mechanism effectively reduces bandwidth consumption while ensuring system stability.

[0014] Step 5: Construct a fault-tolerant formation control law based on predetermined time sliding mode control, and use the Nussbaum function to handle the unknown control gain. Rigorous proof through Lyapunov stability analysis demonstrates that, under conditions of intermittent communication, actuator failure, and input hysteresis quantization, the formation error can converge to the zero neighborhood within a predetermined time without the Zeno phenomenon.

[0015] 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:

[0016]

[0017] 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.

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

[0019]

[0020] in, It is a constant. Taking the second derivative of the above auxiliary position vector and combining it with the dynamic equation, we can obtain:

[0021]

[0022] 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;

[0023] Here is the transformation matrix:

[0024]

[0025] as well as For the system's nonlinear terms:

[0026]

[0027] in,

[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] S i Differentiate (t) and write it in scalar form S ij (t), then the corresponding dynamic sliding surface equation is:

[0057]

[0058] in

[0059] MLP-FLS approximation is used for the unknown nonlinear uncertainty 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] Among them Ψ i (Z i (t))=‖ξ i (Z i (t))‖,μ i =‖W i ‖,σ i =‖e i ‖.

[0062] To reduce computational complexity, a pre-defined time-weighted 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 is a positive number.

[0065] Step four proposes a predetermined-time robust adaptive dynamic event triggering strategy, which, combined with an input hysteresis quantizer to compress control signal transmission, dynamically adjusts the communication and controller update frequencies. This mechanism effectively reduces bandwidth consumption while ensuring system stability.

[0066] First, design an adaptive, pre-set time dynamic event triggering mechanism.

[0067]

[0068] 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. Furthermore, let Γ i >0(Γ=[Γ1,Γ2,...,Γ) N ] T Let θ1 denote the scalar control gain. Two more fixed positive scalars, θ1∈(0,1) and ε>0, are defined and will be used for the construction and stability analysis of the robust triggering mechanism.

[0069] To prevent Zeno behavior, a minimum trigger interval T is introduced. 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 error is greater than 0, the control input is immediately updated and sent to the actuator via the communication network. This event-triggered mechanism remains silent when the error is small, and only triggers when the error increases to a certain level. This significantly reduces the communication and computational load while ensuring the system's convergence performance within the predetermined time, and maintains robustness to faults and quantization uncertainties.

[0070] In step five, the Lyapunov and Nussbaum functions are used to rigorously prove that the designed control law can converge the formation error to the zero neighborhood within a predetermined time and without Zeno phenomenon under conditions of intermittent communication, actuator failure and input hysteresis quantization.

[0071] Before proceeding with the theoretical proof, let's introduce the following lemma:

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

[0073]

[0074] Among them, λ>0, β>0, 0<p<1, Therefore, the system is stable at a predetermined time, and the convergence time satisfies...

[0075] Lemma 2. Assume V(·) and ζ i(·) is a specified smoothing function on [0,∞), and V(t)≥0. K(·) is a Nussbaum function. i (t) is a parameter that varies 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 It is bounded in t∈[0,∞).

[0078] By synthesizing the relevant content in steps one, two, three, and four above, the following adaptive predetermined time fault-tolerant control law was designed:

[0079]

[0080] Where i∈{1,2,...,N}, j∈{1,2}, and and These are the estimated values ​​of μ and σ, respectively.

[0081] Choose the following Lyapunov functions

[0082]

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

[0084] 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 can obtain:

[0085]

[0086] in Let m be a positive constant, and m = min{β2,θ1,θ2,θ3}.

[0087] Combining Lemma 2, we can further obtain

[0088]

[0089] In the formula,

[0090] Using Lemma 1 and the above theoretical derivation and analysis, it is proved that the controlled multi-unmanned USV system achieves predetermined time stability under a fixed communication topology.

[0091] The following analysis needs to examine the boundedness of dwell time in the case of intermittent topology switching.

[0092] Based on the scaling relationship of Young's inequality and the structure of Lyapunov functions, the following conclusions can be drawn:

[0093]

[0094] The positive constant χ > 0 is defined as... and

[0095] By recursively applying the method, for the o-th switching time t o ,get

[0096]

[0097] In the formula, the minimum dwell time condition is satisfied.

[0098] 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.

[0099] First, define the Lyapunov function as follows:

[0100]

[0101] Then, taking the derivative with respect to V2(t), we get...

[0102]

[0103] In the formula, there exists a positive constant ζ > 0, satisfying

[0104] Therefore, we can further conclude that...

[0105]

[0106] In the formula,

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

[0108]

[0109] The scheduled time is T. S .

[0110] Similarly, we can also conclude that ψ(t) is predefined as time-stable, and its corresponding compact set is as follows:

[0111]

[0112] The scheduled time is T. ψ .

[0113] Ultimately, the total scheduled time is T = T S +T ψ .

[0114] Therefore, under the designed controller and event triggering mechanism, all closed-loop signals are bounded and converge within a predetermined time, and 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, thereby achieving stable formation control of the system and providing robust fault tolerance to intermittent actuator failures, hysteresis quantization, and external disturbances.

[0115] Eliminating the Zeno phenomenon:

[0116] The control law updates only under certain conditions; otherwise, it retains the value from the previous triggering time. Under all assumptions, there exists a minimum event triggering interval:

[0117]

[0118] Where ε>0, Both θ > 0 are designed positive constants. This positive duration between adjacent triggers avoids the Zeno phenomenon. The relevant theoretical proof is as follows:

[0119]

[0120] Due to vectors Since it is bounded, 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 By integration, we can obtain

[0121]

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

[0123]

[0124] This invention proposes a pre-time fault-tolerant fuzzy formation control method for heterogeneous multi-USVs based on dynamic event triggering. It reduces communication resource waste by using an adaptive dynamic event triggering mechanism; it saves computational resources by using the MLP-FLS strategy to estimate the comprehensive uncertain dynamics; and it improves the anti-interference capability of multi-USV systems in formation tasks.

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

[0126] 1. High-efficiency resource management and performance assurance: This invention addresses the key challenges commonly encountered in multi-USV formation control, such as nonlinearity, dynamic uncertainty, and limited communication resources. It innovatively proposes a cooperative control method that integrates a predetermined-time adaptive dynamic event triggering mechanism. This method ensures stable convergence and maintains excellent performance within a predetermined time window while significantly reducing the update frequency of redundant communication and control commands. This greatly optimizes the overall resource utilization efficiency of the system, demonstrating significant engineering application potential and practical benefits.

[0127] 2. Advantages of the Adaptive Triggering Mechanism: The adaptive dynamic event triggering strategy designed in this invention has the ability to make conditional judgments based on the real-time state error of the system and dynamically adjusted triggering thresholds. 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 rate of communication bandwidth and computing resources.

[0128] 3. Robust Collaboration in Complex Environments: This invention facilitates efficient information collaboration and distributed collaborative control in resource-constrained communication environments by constructing a multi-agent collaborative information interaction architecture. This ensures that the multi-USV system maintains excellent formation stability and high-precision trajectory tracking capabilities even when facing numerous complex challenges such as external environmental disturbances, intermittent actuator failures, input hysteresis quantization, and intermittent communication topology switching.

[0129] 4. Enhanced Robustness and Fault Tolerance: This invention cleverly integrates nonlinear dynamic compensation and a forward-looking robust control paradigm in the control law design. This design significantly enhances the system's adaptability and resilience in dealing with complex operating conditions such as model uncertainties, external disturbances, and intermittent faults, thereby significantly improving the reliability and resistance to external disturbances of the multi-USV system. Attached image description:

[0130] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0131] Figure 1This is a control block diagram for fault-tolerant fuzzy formation control under the predetermined time dynamic event triggering mechanism of the heterogeneous multi-USV system in this invention.

[0132] Figure 2 This is a schematic diagram of the communication switching topology of the heterogeneous multi-USV system in this invention.

[0133] Figure 3 Schematic diagram of the formation trajectory of multiple USVs in time-varying pentagonal formation in this invention Figure 1

[0134] Figure 4 This is a schematic diagram of the formation trajectory of multiple USVs in a time-varying pentagonal formation in this invention. Figure 2 .

[0135] Figure 5 This is a schematic diagram illustrating the two-dimensional trajectory changes of multiple USVs at different times in a time-varying pentagonal formation task in this invention.

[0136] Figure 6 This diagram illustrates the lateral and longitudinal formation errors of multiple USVs in a time-varying pentagonal formation task according to the present invention. Figure 1 .

[0137] Figure 7 This diagram illustrates the lateral and longitudinal formation errors of multiple USVs in a time-varying pentagonal formation task according to the present invention. Figure 2 .

[0138] Figure 8 This is a schematic diagram of the event triggering time interval for the first USV in a time-varying pentagonal formation mission in this invention. Figure 1 .

[0139] Figure 9 This is a schematic diagram of the event triggering time interval for the second USV in a time-varying pentagonal formation mission in this invention. Figure 2 .

[0140] Figure 10 This is a schematic diagram of the event triggering time interval for the third USV in the time-varying pentagonal formation mission of this invention. Figure 3 .

[0141] Figure 11 This is a schematic diagram of the event triggering time interval for the fourth USV in the time-varying pentagonal formation mission of this invention. Figure 4 .

[0142] Figure 12 This is a schematic diagram of the event triggering time interval of the fifth USV in the time-varying pentagonal formation mission of this invention. Figure 5 .

[0143] Figure 13This is a schematic diagram comparing the control input and hysteresis quantization control input of the first USV in this invention. Figure 1 .

[0144] Figure 14 This is a schematic diagram comparing the control input of the second USV and the hysteresis quantization control input in this invention. Figure 2 .

[0145] Figure 15 This is a schematic diagram comparing the control input of the third USV and the hysteresis quantization control input in this invention. Figure 3 .

[0146] Figure 16 This is a schematic diagram comparing the control input and hysteresis quantization control input of the fourth USV in this invention. Figure 4 .

[0147] Figure 17 This is a schematic diagram comparing the control input and hysteresis quantization control input of the fifth USV in this invention. Figure 5 .

[0148] Figure 18 This is a bar chart comparing the total number of triggers for each USV under different triggering strategies in this invention. Detailed implementation method:

[0149] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0150] Example 1

[0151] This example presents a technical solution for a heterogeneous multi-USV predetermined-time fault-tolerant fuzzy formation control method based on dynamic event triggering. To better illustrate the invention, MATLAB numerical simulation is used to verify the proposed controller, and the results are as follows. Figures 3 to 10 As shown, the specific steps are as follows:

[0152] Step 1: Establish a multi-USV model and transform it into a full-drive system using coordinate transformation; furthermore, unify actuator fault and hysteresis quantization to obtain the actual input applied to the USV:

[0153]

[0154] Step 2: To save communication resources, design an adaptive, pre-set time dynamic event triggering mechanism:

[0155] First, design an adaptive, pre-set time dynamic event triggering mechanism.

[0156]

[0157] 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. Furthermore, let Γ i >0(Γ=[Γ1,Γ2,...,Γ) N ] T Let θ1 denote the scalar control gain. Two more fixed positive scalars, θ1∈(0,1) and ε>0, are defined and will be used for the construction and stability analysis of the robust triggering mechanism.

[0158] To prevent Zeno behavior, a minimum trigger interval T is introduced. 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 error is greater than 0, the control input is immediately updated and sent to the actuator via the communication network. This event-triggered mechanism remains silent when the error is small, and only triggers when the error increases to a certain level. This significantly reduces the communication and computational load while ensuring the system's convergence performance within the predetermined time, and maintains robustness to faults and quantization uncertainties.

[0159] Step 3: A robust adaptive dynamic event triggering strategy with predetermined time is proposed. This strategy, combined with an input hysteresis quantizer to compress control signal transmission, dynamically adjusts the communication and controller update frequencies. This mechanism effectively reduces bandwidth consumption while ensuring system stability.

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

[0161]

[0162] Then, based on the fractional-order formation error Θ(ψ) i (t) Construct a sliding surface S with a predetermined time. i (t)

[0163] S i (t)=ψ i (t)+Θ(ψ i (t)),

[0164] Where α1≥1, T ψ >0.

[0165] To further ensure that the sliding surface reaches zero within the predetermined time, the following predetermined time sliding function is selected:

[0166]

[0167] Where α2≥1, T S >0.

[0168] S i Differentiate (t) and write it in scalar form S ij (t), then the corresponding dynamic sliding surface equation is:

[0169]

[0170] in

[0171] Step 4: Design an FLS based on the MLP strategy to achieve high-precision approximation of the comprehensive nonlinear uncertainty term; update the weight parameters online through a predetermined time adaptive law to significantly reduce computational complexity while ensuring approximation accuracy; and by comprehensively utilizing the content of Steps 1, 2, 3, and 4 above, design the following adaptive law for weight coefficients and a predetermined time fault-tolerant control law:

[0172] To reduce computational complexity, a pre-defined time-weighted adaptive law is used to adaptively adjust the weight coefficients:

[0173]

[0174] Where μ = [μ1, μ2, ..., μ N ] T , And T μ ,T σ >0 is a positive number.

[0175] To achieve scheduled formation control, the following scheduled fault-tolerant control law is used:

[0176]

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

[0178] Step 5: Stability analysis, selecting the Lyapunov function:

[0179] Choose the following Lyapunov functions

[0180]

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

[0182] 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 can obtain:

[0183]

[0184] in Let m be a positive constant, and m = min{β2,θ1,θ2,θ3}.

[0185] Combining Lemma 2, we can further obtain

[0186]

[0187] In the formula,

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

[0189] Then, define the Lyapunov function as follows:

[0190]

[0191] Then, taking the derivative with respect to V2(t), we get...

[0192]

[0193] In the formula, there exists a positive constant ζ > 0, satisfying

[0194] Therefore, we can further conclude that...

[0195]

[0196] In the formula,

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

[0198]

[0199] The scheduled time is T. S .

[0200] Similarly, we can also conclude that ψ(t) is predefined as time-stable, and its corresponding compact set is as follows:

[0201]

[0202] The scheduled time is T. ψ .

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

[0204] The model parameters of a heterogeneous multi-USV system consisting of a virtual leader i=0 and four follower unmanned surface vessels (USVs) (i=1,2,3,4,5) are as follows:

[0205]

[0206] The relevant parameter selections for MLP-FLS are as follows:

[0207]

[0208] The relevant 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 velocity of the multi-USV system is zero. The following time-varying pentagonal desired formation function is selected:

[0214]

[0215] Results show that, under the defined time-varying pentagonal expected formation scenario, Figure 1 A block diagram of a heterogeneous multi-USV pre-time fault-tolerant fuzzy grouping control based on dynamic event triggering is presented. Figure 2 The communication switching topology of a heterogeneous multi-USV system is shown. Figure 3 and Figure 4The formation postures of the system at different times are described respectively. Figure 5 This intuitively depicts the formation trajectory of a heterogeneous multi-USV system in two-dimensional space. Furthermore, Figure 6 and Figure 7 This demonstrates that the proposed control strategy can effectively suppress formation errors and achieve convergence. Meanwhile, Figures 8 to 12 The designed pre-set time adaptive dynamic event triggering mechanism was verified to flexibly and efficiently reduce the communication triggering frequency while ensuring control performance, significantly saving communication resources and improving communication efficiency. More importantly, from Figures 13 to 17 It is evident that even under adverse conditions such as input lag and quantization effects, the proposed method can still achieve the desired formation objective, demonstrating strong robustness and engineering applicability.

[0216] Example 2

[0217] The parameters for the heterogeneous multi-USV system and related controllers are the same as in Example 1. In implementation step three, the adaptive predetermined-time dynamic event triggering mechanism is replaced with a traditional static event triggering mechanism and a time-triggered mechanism.

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

[0219] Design a 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 a timed triggering mode with a step size of 0.001s, collect data and update the input control quantity every 0.001s.

[0222] The final total number of triggers is as follows Figure 18 As shown. By comparing the traditional static event triggering mechanism, the time triggering mechanism, and the adaptive dynamic event triggering mechanism based on a predetermined time proposed in this patent, it can be clearly seen that the algorithm proposed in this invention can significantly reduce the communication frequency between individual agents while ensuring the convergence and stability of system errors. Thus, it exhibits better overall performance in terms of communication overhead and computing resource utilization, demonstrating higher resource saving efficiency and engineering application value.

[0223] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for fault-tolerant fuzzy formation control of multiple unmanned surface vessels (USVs) triggered by dynamic events 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 additional fault 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 ignoring the high degrees of freedom motion of the USV, the first... The kinematic and dynamic model of a USV in the horizontal plane is represented as follows: ； In the formula, Number the unmanned surface vessel; This represents the position and heading angle in the Earth-fixed coordinate system. The sway velocity, roll velocity, and yaw rate in the body coordinate system; The system inertia matrix includes the added mass; The matrix represents the Coriolis force and the centripetal force. The hydrodynamic damping matrix; To control the input vector, where For longitudinal thrust, For steering torque; These are unknown external disturbances caused by the external environment, such as wind, waves, and currents. This 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, For equivalent control input; 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, regarding the first The first USV Each execution channel satisfies the following relationship between the actuator output and the desired input: ； in, Indicates a multiplicative fault term. This indicates additional fault items caused by additive deviations or disturbances; including the following situations: 1) :normal; 2) : The effectiveness is partially lost; 3) Additive fault / bias; 4) Actuator stuck; Secondly, regarding control input The Each component is hysteresis quantized, and the quantized output is: ； in , dead zone width, , ; Decompose the hysteresis quantization output into equivalent gain With residual form: ； in, ； 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 of all, the Distributed formation error of USV followers Defined as: ； in, This represents the expected trajectory of the virtual leader USV, and the topology parameters satisfy... , and , No. The time-varying formation error of each follower is caused by Given, and the corresponding error vector is defined as 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 fractional-order formation error Construct a sliding surface for a predetermined time ; ； in ; To ensure that the sliding surface reaches zero within the predetermined time, the following predetermined time sliding function is selected: ； in ; Will Find the derivative and write it in scalar form. The corresponding dynamic sliding surface equation is: ； in , ; The fuzzy logic system MLP-FLS approximation for unknown nonlinear uncertainties using minimum learning parameters: ； in , , ; The weighting coefficients are adaptively adjusted using a predetermined time-weighted adaptive law. ； in, , , , and , It 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 be a set of robust parameter vectors that vary with time, where each... All satisfied ,set up Let be a set of positive design constant vectors, and for all ,have Furthermore, let's assume To represent the scalar control gain, define two fixed positive scalars. and Used for the construction and stability analysis of robust triggering mechanisms; Introducing minimum trigger interval When the triggering condition is met and the time interval between the previous trigger and the current trigger is greater than 100,000, the triggering condition is met. At that time, 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: ; in, , , and , and They are and The estimated value; Choose the following Lyapunov functions ； in Let the sliding surface vector be... , 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 A positive constant. , , ; 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: ； Where the positive constant The definition of ,and ; By applying recursion, for the first... Switching time ,get ； In the formula, the minimum dwell time condition is satisfied. , ; Regarding the boundedness established above, the sliding surface will be derived based on the same control and switching conditions. and formation error Convergence characteristics within a predetermined time period; First, define the Lyapunov function as follows: ； Then to Differentiating gives ； In the formula, there exists a positive constant. ,satisfy ; The conclusion is ； In the formula, ; By Lyapunov function and sliding surfaces Both are bounded, and The scheduled time slipform compaction is as follows: ； The scheduled time is ; get It is time-stable under a predefined definition, and its corresponding The compact set is as follows: ； The scheduled time is ; Ultimately, the total scheduled time is ; Under the designed controller and event triggering mechanism, all closed-loop signals are bounded and converge within a predetermined time, and the sliding surface... With formation error At the scheduled time 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: ； in , and All of these 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. , making , noticed and In the interval Top Integrating ； Therefore, the minimum event triggering time interval is: 。

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