A predefined time formation control method based on fuzzy neural network

Abstract

This invention relates to the field of formation control technology for heterogeneous air-sea swarm systems, and discloses a predefined-time formation control method based on fuzzy neural networks. The method includes: establishing kinematic and dynamic models of a six-DOF quadrotor UAV and a three-DOF unmanned surface vessel; establishing the formation tracking error and velocity tracking error of the heterogeneous air-sea swarm system; constructing a preset performance function and determining an error transformation function; determining a predefined-time virtual control law; establishing a predefined-time fuzzy neural network and combining it with the predefined-time virtual control law to determine a distributed predefined-time formation controller for the heterogeneous air-sea swarm system; and performing distributed predefined-time error-constrained formation control on the heterogeneous air-sea swarm system based on the distributed predefined-time formation controller. This invention improves the robustness of heterogeneous air-sea swarms, enabling the system to converge within a settable predefined time and independent of initial system values.

Description

Technical Field

[0001] This invention relates to the field of formation control technology for heterogeneous air-sea cluster systems, specifically to a predefined time formation control method based on fuzzy neural networks. Background Technology

[0002] Oceans cover more than 70% of the Earth's surface and are rich in mineral and marine biological resources. In the 21st century, with the increasing importance of marine resources and the growing demand for their development, the efficient and safe exploration and monitoring of marine resources has become a global focus. Air-sea heterogeneous swarm systems, especially the formation tracking and control methods of quadcopter UAVs and unmanned surface vessels (USVs), offer innovative solutions in this field. Quadcopter UAVs are highly maneuverable and flexible in deployment, enabling them to quickly reach target areas for aerial reconnaissance and data collection. USVs, on the other hand, can cruise on the water for extended periods, conducting underwater exploration and environmental monitoring. Through formation tracking and control technology, UAVs and USVs work collaboratively according to pre-set paths and mission requirements to achieve comprehensive monitoring of marine resources. This system enables coordinated aerial and surface operations, significantly improving the coverage of marine resource exploration and the accuracy of data acquisition. In marine resource development, the formation tracking and control methods of air-sea heterogeneous swarm systems are particularly important. This approach not only improves the efficiency of resource exploration and reduces human and material costs, but also provides a safer and more environmentally friendly operating method in complex marine environments, such as in harsh weather or sensitive ecological areas. Therefore, researching and developing formation tracking and control methods for air-sea heterogeneous swarm systems is of significant strategic importance for promoting the sustainable development of marine resources.

[0003] However, research on formation tracking control methods for quadrotor UAVs and unmanned surface vessels (USVs) faces a series of technical challenges. The dynamic and unpredictable nature of the marine environment places high demands on the stability of unmanned systems. Factors such as ocean currents, wind speed, and weather changes can affect the navigation trajectory of USVs, while UAVs in the air need to cope with changes in wind force and airflow. Formation control algorithms must have a certain degree of adaptability to adapt to these external disturbances. Meanwhile, in many application scenarios such as marine resource exploration, environmental monitoring, or emergency rescue, rapid response and timely execution of the system are crucial to completing marine missions. A configurable, stable time control algorithm can ensure the system's immediacy and time determinism. Therefore, designing a reasonable formation controller to ensure that the heterogeneous air-sea system of quadrotor UAVs and USVs can perform trajectory tracking tasks smoothly and reliably in complex marine environments has significant research value and importance.

[0004] In the field of multi-agent control systems, techniques such as PID control, sliding mode control, and adaptive control have been widely adopted. PID control is renowned for its low requirements on the system model and reliable performance in various application scenarios. However, its limitations in anti-interference and fast response cannot be ignored, and the parameter tuning process is often cumbersome. Sliding mode control is highly regarded for its excellent fast response and robustness to system parameter fluctuations and external disturbances. However, chattering near the sliding surface can adversely affect the stability and performance of the system. Adaptive control strategies update control parameters in real time to adapt to dynamic changes in the system and external disturbances, but this method requires excessive parameter updates, thus increasing computational complexity. In recent years, for the control problems caused by the uncertainty and complexity of the marine environment faced by marine unmanned systems, common methods usually involve designing state observers or using various neural networks to approximate the system, and then designing control laws to enable the system to achieve trajectory tracking control and ensure global convergence of errors. However, the observation effect of the observer depends on the observation gain; the computational complexity of neural networks and the limited online computing speed lead to some unavoidable problems, such as a large number of parameter updates, a heavy system computational burden that may cause computational explosion, and the inability to guarantee that the system converges within a finite time.

[0005] Currently, in the field of multi-agent tracking control, various types of obstacle functions and preset performance functions are often combined with backstepping methods to design asymptotically convergent, finite-time convergent, and fixed-time convergent controllers to limit system errors and achieve better control accuracy. However, asymptotically convergent controllers have slow convergence speeds, and finite-time convergent controllers are affected by the initial state of the system. It is worth mentioning that predefined-time convergence control techniques have begun to be used in recent years, effectively addressing the aforementioned problems. In the field of formation control, the application of error constraints brings significant advantages to the system. Error constraints allow formation control algorithms to consider the dynamic characteristics of each agent, thereby designing control strategies with specified performance. These constraints include, but are not limited to, position and velocity errors, ensuring that formation members maintain their formation while not exceeding their performance boundaries, thus guaranteeing system stability. Although there has been much research on error-constrained control, no corresponding research results have been obtained for error-constrained formation control of heterogeneous air-sea systems such as quadrotor UAVs and unmanned surface vessels. Furthermore, related research on error-constrained formation control has not addressed the predefined-time stability problem, which limits its control performance.

[0006] In dealing with disturbances in the marine environment, fuzzy neural networks (NNNs) have demonstrated a series of advantages over traditional neural networks, making them an ideal choice for solving such problems. By integrating fuzzy logic, NNNs can handle the uncertainties and ambiguities in formation control. In the marine environment, unmanned surface vessels (USVs) may be affected by unpredictable currents and waves, while drones may encounter unpredictable winds. NNNs can process fuzzy data and map it into the network, transforming these fuzzy environmental variables into precise control commands, thereby improving the stability and adaptability of the formation. Furthermore, the generalization ability of NNNs is significant. In practical applications, formations may encounter new situations not encountered during the training phase. NNNs can leverage their generalization ability to learn and infer effective control strategies from existing data, maintaining formation coordination in unknown situations. In terms of computational efficiency, NNNs typically have lower model complexity, making them more advantageous in resource-constrained unmanned systems. Compared to traditional neural networks, NNNs require fewer computational resources, which is crucial for reducing the computational burden on drones and USVs. However, such networks typically lack precise control over convergence time, which can be a significant disadvantage in applications requiring rapid response. If a fuzzy neural network cannot guarantee reaching a stable state within a specific timeframe, it may degrade system performance and security. In the complex and ever-changing marine environment, this uncertainty can lead to delays in critical missions, increasing the overall risk to the system. Therefore, exploring a technique that allows for precise control over the convergence time of fuzzy neural networks is of paramount importance. Summary of the Invention

[0007] To address the aforementioned shortcomings in existing technologies, this invention provides a predefined time formation control method based on fuzzy neural networks. This method ensures that the system's tracking error converges within a predefined time and is unaffected by the system's initial state. The combination of fuzzy neural networks improves the system's stability and robustness in complex marine environments, thereby solving the problems of limited control accuracy, external environmental disturbances, and time-stability in current control methods for heterogeneous air-sea swarm systems of UAVs and unmanned surface vessels.

[0008] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0009] A predefined time-based formation control method based on fuzzy neural networks includes the following steps:

[0010] Establish kinematic and dynamic models of a six-DOF quadrotor UAV and a three-DOF unmanned surface vessel;

[0011] Based on the kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel, the formation tracking error and velocity tracking error of an air-sea heterogeneous swarm system are established.

[0012] Construct a preset performance function and determine an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0013] Based on the formation tracking error, speed tracking error, and error transformation function, a predefined time virtual control law is determined;

[0014] A predefined time fuzzy neural network is established, and a distributed predefined time formation controller for an air-sea heterogeneous cluster system is determined by combining it with a predefined time virtual control law.

[0015] Distributed predefined time error constraint formation control is performed on the air-sea heterogeneous cluster system based on the distributed predefined time formation controller of the air-sea heterogeneous cluster system.

[0016] As a preferred embodiment, the kinematic and dynamic model of the six-DOF quadrotor UAV is as follows:

[0017]

[0018] Where, χ ph =[x ph ,y ph ,z ph ] T χ represents the location information in the global coordinate system. ah =[φ ah ,θ ah ,ψ ah ] T Indicates roll angle, pitch angle, and yaw angle; d xph ,d yph ,d zph ,d φah ,d θah ,d ψah I represents a time-varying unknown ocean disturbance function; x ,I y ,I z ρ represents the moment of inertia. x ,ρ y ,ρ z ,ρ φ ,ρ θ ,ρ ψ Indicates the aerodynamic damping coefficient; m a Indicates mass and inertia parameters; u 1h ,u φh ,u θh ,u ψhΛ represents the controller to be designed; g represents gravitational acceleration; Λ represents the total remaining rotor angle; I r This represents the moment of inertia of the rotor.

[0019] As a preferred embodiment, the kinematic and dynamic model of the three-degree-of-freedom unmanned surface vessel is as follows:

[0020] χ sk，1 =R(χ) ψsk，1 )v s，k

[0021]

[0022] Where, χ sk,1 =[χ xsk,1 ,χ ysk,1 ,χ ψsk,1 ] T v represents the position and heading angle variables of the k-th unmanned surface vessel in the global coordinate system; k =[v xsk ,v ysk ,v ψsk ] T Represents the velocity and angular velocity variables of the k-th unmanned surface vessel in a fixed coordinate system; u sk =[u xsk ,u ysk ,u ψsk ] T d represents the control input quantity to be designed for the k-th unmanned surface vessel; sk (t)=[d xk ,d yk ,d ψk ] T R represents the external disturbance of the k-th unmanned surface vessel; sk It is a rotation matrix; Represents the inertia matrix; Represents the damping matrix. This represents the Coriolis matrix.

[0023] As a preferred embodiment, the formation tracking error of the air-sea heterogeneous cluster system is specifically as follows:

[0024] e i,j =Ξ i (χ i,j -β i,j )+E e,i i = ph, ah, sk;

[0025]

[0026] Among them, e i,j Indicates formation tracking error, Ξ iThe parameters represent the formation communication parameters, where ph and ah represent the position and attitude subsystems of the h-th UAV, respectively, sk represents the k-th unmanned surface vessel system, h = 1, ..., N represents the h-th UAV, N represents the number of UAVs in the heterogeneous multi-agent system, k = 1, ..., M represents the k-th unmanned surface vessel, M represents the number of unmanned surface vessels in the heterogeneous multi-agent system, N+M represents the total number of agents in the heterogeneous multi-agent system, diag represents the diagonal matrix, and a h,i b represents the communication parameters between the h-th drone and other intelligent agents. lh This represents the communication parameters between the h-th drone and the leader, a k+N,i I represents the communication parameters between the k-th unmanned surface vessel and other intelligent agents. 3×3 b represents a 3-dimensional unit vector. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. i,j β represents the state vector of the agent. i,j E represents the relative state vector that the agent needs to maintain with the leader. ei,j This indicates that an agent receives state vectors from other agents, and is defined as follows.

[0027]

[0028]

[0029] Where, χ pi,j Let β represent the position and state vector of the h-th UAV. ψai,j Let β represent the relative heading angle state vector that the h-th drone needs to maintain with respect to the leader. xpi,j ,β yai,j E represents the relative position state vector that the h-th drone needs to maintain with respect to the leader. eph,j E represents the angle error vector received by the UAV from other intelligent agents. esk,j E represents the error vector received by the unmanned surface vessel from other intelligent agents. eph,j E represents the position error vector received by the UAV from other intelligent agents. eah,j This represents the attitude error vector received by the UAV from other intelligent agents, a. k+N,i and a k+N,i+N Let b represent the communication parameters between the k-th unmanned surface vessel and other intelligent agents. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. xL,j ,χ yL,j ,χ zL,j ,χ ψL,j χ represents the leader's state vector. φd,hj and χ θd,hj Let β represent the expected roll and pitch angles of the h-th UAV, respectively. pi,jχ represents the relative position vector that the h-th drone needs to maintain with respect to the leader. xpi,j ,χ ypi,j Let χ represent the position and state vector of the h-th UAV. ψai,j χ represents the heading angle of the h-th UAV. xsi,j ,χ ysi,j ,χ ψsi,j Let β represent the state vector of k unmanned surface vessels. xsi,j ,β ysi,j ,β ψsi,j Let represent the relative state vector that k unmanned surface vessels need to maintain with the leader.

[0030] Preferably, the formation tracking error and velocity tracking error of the air-sea heterogeneous cluster system are as follows:

[0031]

[0032] Among them, e gph,j and e gsk,j e represents the state error of the UAV and the unmanned surface vessel in the two-dimensional plane, respectively. ψah,j and e ψsk,j e represents the state error of the heading angle of the UAV and the unmanned surface vessel, respectively. zh,j Indicates altitude error, e φah,j and e θah,j χ represents the roll angle and pitch angle errors, respectively. xL,j ,χ yL,j ,χ ψL,j ,χ zL,j Represents the trajectory information of the virtual leader, β gph,j ,β gpi,j and β gsk,j ,β gsi,j β represents the relative positional state of the drone and unmanned surface vessel relative to the leader, respectively. ψah,j ,β ψai,j and β ψsk,j ,β ψsi,j β represents the relative heading angle state vector that the drone and unmanned surface vessel need to maintain with respect to the leader, respectively. zph,j ,β zpi,j a represents the state vector representing the relative altitude that the drone needs to maintain with respect to the leader. h,i and a h,i+N Let a represent the communication parameters between the h-th drone and other intelligent agents. k+N,i and a k+N,i+N Let b represent the communication parameters between the k-th unmanned surface vessel and other intelligent agents. lh b represents the communication parameters between the h-th drone and the leader. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. gph,j ,χ gpi,jand χ gsk,j ,χ gsi,j χ represents the position status of the drone and the unmanned surface vessel, respectively. ψah,j ,χ ψai,j and χ ψsk,j ,χ ψsi,j Let χ represent the heading angle state vectors of the UAV and the unmanned surface vessel, respectively. zph,j ,χ zpi,j Indicates the altitude status of the drone, χ φah,j and χ θah,j χ represents the roll and pitch state vectors of the h-th unmanned surface vessel, respectively. φd,hj and χ θd,hj Let a represent the expected roll and pitch angles of the h-th unmanned surface vessel, respectively. ph and a ah Let a represent the virtual control law vector of the UAV. sk χ represents the virtual control law vector of the unmanned surface vessel. ph,2 and χ ah,2 χ represents the velocity state vector of the UAV. sk,2 E represents the velocity state vector of the unmanned surface vessel. ph and E ah E represents the error vector between the UAV's speed and the virtual control law. sk E represents the error vector between the unmanned surface vessel's speed and the virtual control law. xph E yph E yph E represents the error between the UAV's velocity in the XYZ directions and the virtual control law. φah E θah E ψah E represents the error in the virtual control law relating the angular velocity and angle of the UAV. xsk E ysk E ψsk This represents the error between the unmanned surface vessel's speed and the virtual control law.

[0033] Preferably, the error transformation function is as follows:

[0034]

[0035] Among them, Z ph,1 Z ah,1 and Z ph,2 Z ah,2 Z represents the formation error transformation function vector of the UAVs. sk,1 and Z sk,2 Q represents the formation error transformation function vector of the unmanned surface vessel. ph Q ah Q sk e represents the performance function index of the formation error of UAVs and unmanned surface vessels. xph,1 ,eyph,1 ,e zph,1 e represents the formation error of the UAV in the XYZ directions. φah,1 ,e θah,1 ,e ψah,1 e represents the formation error of the drone's attitude system. xsk,1 ,e ysk,1 ,e ψsk,1 E represents the formation error of unmanned surface vessels. xph E yph E yph E represents the error between the UAV's velocity in the XYZ directions and the virtual control law. φah E θah E ψah E represents the error in the virtual control law relating the angular velocity and angle of the UAV. xsk E ysk E ψsk This represents the error between the speed of the unmanned surface vessel and the virtual control law.

[0036] Preferably, the predefined time virtual control law is as follows:

[0037]

[0038] Among them, a ph and a ah Describes the virtual control law of the drone, a sk T represents the virtual control law of the unmanned surface vessel, η represents the exponential parameter, and T represents the virtual control law of the unmanned surface vessel. c The time parameter is represented by π, and Z represents the mathematical constant pi. ph,1 Z ah,1 Z represents the formation error transformation function vector of the UAVs. sk,1 Ξ represents the formation error transformation function vector of the unmanned surface vessel. ph ,Ξ ah ,Ξ sk E represents the system's communication parameters. eph,2 E eah,2 E represents the state vector received by the drone from other intelligent agents. esk,2 This indicates that the unmanned surface vessel receives the state vector from other intelligent agents. γ represents the bias of the error transformation function. ph,1 ,γ ah,1 ,γ sk,1 β represents the time-varying coefficient of the error transformation function. ph,2 ,β ah,2 β represents the relative state vector that the drone needs to maintain with respect to the leader. sk,2 This represents the relative state vector that the unmanned surface vessel needs to maintain with respect to the leader.

[0039] Preferably, establishing a predefined temporal fuzzy neural network includes:

[0040] A fuzzy neural network consisting of an input layer, a radial basis function layer, a normalization layer, and an output layer is established.

[0041] All uncertainties in an air-sea heterogeneous system are estimated using fuzzy neural networks, and are represented as follows:

[0042]

[0043] Among them, F i Represents all uncertain functions of the system. S represents the ideal value of the uncertain function fitted by the neural network. i The neuron function representing a neural network. This indicates that the ideal weights for estimating system uncertainty can be determined.

[0044] Preferably, the weight update law of the predefined temporal fuzzy neural network is as follows:

[0045]

[0046] Where i = ph, ah, sk represent the agent index. S represents the estimated weights of the neural network. i Z represents the neuron function of a neural network. i,2 Represents the error transformation function vector, γ i,2 The time-varying coefficients of the error transformation function are represented by η, which represents the exponential parameter, and T is the time-varying coefficient. c This represents the time parameter, and π represents the mathematical constant pi.

[0047] As a preferred embodiment, the distributed predefined time-based queuing controller of the air-sea heterogeneous cluster system is specifically:

[0048]

[0049] Among them, u ph and u ah This represents the formation control law for drones, u sk Let A, B, and f represent the formation control laws for unmanned surface vessels. ph ,f ah C represents the model parameters of the drone. sk D sk and M sk R represents the model parameters of the unmanned surface vessel. sk Represents the rotation matrix of the unmanned surface vessel. S represents the estimated weights of the neural network. ph ,S ah ,S sk The neuron function representing a neural network, Ξ ph ,Ξah ,Ξ sk Indicates the system's communication parameters. Represents a virtual control law. γ represents the bias of the error transformation function. ph,1 ,γ ah,1 ,γ sk,1 and γ ph,2 ,γ ah,2 ,γ sk,2 Z represents the time-varying coefficients of the error transformation function. ph,1 Z ah,1 Z sk,1 and Z ph,2 Z ah,2 Z sk,2 χ represents the error transformation function vector. sk,2 E represents the state vector of the unmanned surface vessel. ph E ah E sk The vector represents the error between velocity and the virtual control law, where η represents the exponential parameter, and T... c This represents the time parameter, and π represents the mathematical constant pi.

[0050] The present invention has the following beneficial effects:

[0051] 1. This invention limits the formation tracking error of a heterogeneous air-sea cluster system based on the functional characteristics of the performance function, while also constraining the speed tracking error. Compared with methods that only constrain position errors, the distributed error-constrained formation controller designed in this invention has better control performance.

[0052] 2. Based on the fuzzy neural network, this invention designs a predefined time fuzzy neural network by improving the convergence speed of the weights. While ensuring the good generalization ability of the fuzzy neural network, it improves the convergence speed of the neural network, sets and determines the stable time of the neural network, and enhances the robustness of the system.

[0053] 3. This invention addresses the heterogeneous air-sea swarm system of UAVs and unmanned surface vessels with external disturbances and model uncertainties. It establishes a distributed predefined time error constraint formation control method based on fuzzy neural networks, which improves the robustness of the heterogeneous air-sea swarm and enables the system to converge within a settable predefined time without depending on the system's initial values. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating a predefined time-based formation control method based on a fuzzy neural network.

[0055] Figure 2 A schematic diagram of a heterogeneous air-sea swarm system for drones and unmanned surface vessels;

[0056] Figure 3 A 3D tracking diagram of an air-sea heterogeneous cluster system;

[0057] Figure 4 A two-dimensional tracking diagram of an air-sea heterogeneous cluster system;

[0058] Figure 5 Error diagram of the air-sea heterogeneous cluster system;

[0059] Figure 6 This is the control input diagram for the air-sea heterogeneous cluster system.

[0060] Figure 7 The fuzzy neural network fitting diagrams for UAV 1 and UAV 2 are shown.

[0061] Figure 8 The fuzzy neural network fitting diagrams for unmanned surface vessel 1 and unmanned surface vessel 2;

[0062] Figure 9 The image shows the fuzzy neural network fitting diagrams for unmanned surface vessel 3 and unmanned surface vessel 4. Detailed Implementation

[0063] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0064] like Figure 1 As shown, an embodiment of the present invention provides a predefined time formation control method based on a fuzzy neural network, comprising the following steps S1 to S6:

[0065] S1. Establish kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel;

[0066] In an optional embodiment of the present invention, the kinematic and dynamic model of the h-th six-DOF quadrotor UAV is established as follows:

[0067]

[0068] Where, χ ph =[x ph ,y ph ,z ph ] T χ represents location information in global coordinates. ah =[φ ah ,θ ah ,ψ ah ] TIndicates roll angle, pitch angle, and yaw angle; d xph ,d yph ,d zph ,d xph ,d xph ,d xph I represents a time-varying unknown ocean disturbance function; x ,I y ,I z ρ represents the moment of inertia. x ,ρ y ,ρ z ,ρ φ ,ρ θ ,ρ ψ Indicates the aerodynamic damping coefficient; m a Indicates mass and inertia parameters; u 1h ,u φh ,u θh ,u ψh Λ represents the controller to be designed; g represents gravitational acceleration; Λ represents the total remaining rotor angle; I r This represents the moment of inertia of the rotor.

[0069] To prevent the drone from exhibiting unusual phenomena during operation, the rolling φ ah and pitch θ ah The following inequalities should be satisfied:

[0070] -π / 2<φ ah <π / 2;

[0071] -π / 2<θ ah <π / 2;

[0072] The six-DOF model of the h-th UAV can be divided into a position subsystem and an attitude subsystem, which includes model uncertainties and external disturbances:

[0073] Location subsystem:

[0074]

[0075] Attitude subsystem:

[0076]

[0077] Here, the three-dimensional position state vector χ is defined. ph，1 =[χ xph，1 , χ yph，1 , χ zph，1 ] T =χ ph and Define the attitude angle state vector χ ah，1 =[χ φah，1 , χ θah，1, χ ψah，1 ] T =χ ah and ;u ph (t)=R h u 1h =[u xph (t), u yph (t), u zph (t)] T ∈R 3 ;u ah (t)=[u φh (t), u θh (t), u ψh (t)] T ∈R 3 ;u xph ,u yph and u zph These represent the virtual control inputs for the longitudinal, lateral, and height channels, respectively. The control thrust can be calculated using the formula... Calculated; u φh ,u θh and u ψh These represent the ideal control inputs for roll, pitch, and yaw directions, respectively; F ph (·)=Δ ph f ph (χ ph，2 )+d ph (t)+AΔu ph and F ah (·)=Δ ah f ah (χ ah,2 )+d ah (t) represents the bounded uncertainty of the h-th UAV; d ph (·)=[d xph ,d yph ,d zph ] T ∈R 3 and Δ ph f ph (·)=Δ ph [f xph ,f yph ,f zph ] T ∈R 3 d represents the external disturbance and model uncertainty of the h-th UAV position subsystem, respectively; ah (.)=[d φah ,d θah ,d ψah ] T ∈R 3 and Δ ah fah (·)=Δ ah [f φah ,f θah ,f ψah ] T ∈R 3 and represent the external disturbance and model uncertainty of the h-th UAV attitude subsystem, respectively.

[0078]

[0079]

[0080] Based on the position control input of the UAV, the desired roll angle χ can be obtained. φd,h1 and pitch angle χ θd,h1 Therefore, based on the UAV's position control input and sin 2 (.)+cos 2 (.)=1;χ φd,h1 and χ θd,h1 It can be obtained from the following formula:

[0081]

[0082] This embodiment establishes the kinematic and dynamic model of the k-th three-degree-of-freedom unmanned surface vessel:

[0083] χ sk,1 =R(χ) ψsk,1 )v s,k

[0084]

[0085] Where, χ sk,1 =[χ xsk,1 ,χ ysk,1 ,χ ψsk,1 ] T Represents the position and heading angle variables of the k-th unmanned surface vessel in a fixed global coordinate system; v k =[v xsk ,v ysk ,v ψsk ] T Represents the velocity and angular velocity variables of the k-th unmanned surface vessel in a fixed coordinate system; u sk =[u xsk ,u ysk ,u ψsk ] T d represents the control input to be designed for the k-th unmanned surface vessel; k (t)=[d xk ,d yk ,d ψk ] TR represents the external disturbance of the k-th unmanned surface vessel; sk It is a rotation matrix and satisfies Represents the inertia matrix; Represents the damping matrix. Let R represent the Coriolis matrix and the centripetal matrix. sk , and The definition is as follows:

[0086]

[0087] Therefore, the mathematical model of the three-degree-of-freedom composite dynamics of the k-th USV can be obtained, which includes model uncertainties and external disturbances, as shown in the following formula:

[0088]

[0089] in, Let M represent the model uncertainty of the k-th USV, and M s,k C s,k D s,k It can be described as follows:

[0090]

[0091] The composite dynamics model of the k-th USV is obtained by the following formula:

[0092]

[0093] in, The total uncertainty of the k-th USV is defined by the velocity state information χ. sk,2 =[χ xsk,2 ,χ ysk,2 ,χ ψsk,2 ] T , k=1,...,M.

[0094] S2. Based on the kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel, establish the formation tracking error and velocity tracking error of the air-sea heterogeneous swarm system.

[0095] In an optional embodiment of the present invention, this embodiment first uses graph theory to represent the communication situation of the air-sea heterogeneous cluster system; the communication transmission lines between N heterogeneous intelligent agents can be represented by an undirected graph. It is represented as Γ={v1,v2,…,v N} represents all intelligent agents. Representing a communication line, A = [a ij ]∈R N ×NLet a represent a non-negative adjacency matrix. ij This indicates the directed information transmission between agents i and j, if Then a ij >0 indicates that agent i can receive information transmission from agent j; otherwise, a kj =0. Define L = DA as the Laplace matrix L, where D = diag{d v1 ,…,d vN} represents a weighted diagonal matrix, and the elements of matrix D are represented as The augmented matrix corresponding to the leader is defined as B, with diagonal terms as b. i (i = 1, ..., N), when the agent can obtain leader information, then b i =1, otherwise b i =0.

[0096] This embodiment will next establish the formation tracking position and velocity error in three-dimensional space:

[0097]

[0098] Where r = 1, ..., N+M, j = 1, 2, e gph,j and e gsk,j e represents the state error of the UAV and the unmanned surface vessel in the two-dimensional plane, respectively. zh,j Indicates altitude error, e φah,j and e θah,j χ represents the roll angle and pitch angle errors, respectively. xL,j ,χ yL,j ,χ ψL,j ,χ zL,j Represents the trajectory information of the virtual leader, β gsi,j This indicates the relative position to the virtual leader. Integrating formation errors, the following formula can be obtained:

[0099] e i,j =Ξ i (χ i,j -β i,j )+E e,i i = ph, ah, sk

[0100]

[0101]

[0102] Among them, Ξ i E represents the formation error parameter. ei,j This indicates that agent i has received information from other agents.

[0103] S3. Construct a preset performance function and determine an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system;

[0104] In an optional embodiment of the present invention, this embodiment establishes a speed tracking error:

[0105] E i =χ i,2 -a i i = ph, ah, sk;

[0106] Among them, a i This represents the virtual control law that needs to be designed.

[0107] The following boundary functions are defined as preset performance functions to limit formation tracking error and velocity tracking error:

[0108] Q i (t)=(Q i,0 -Q i,∞ )exp(-λ i t)+Q i,∞ ;

[0109] Where, i = ph, ah, sk; h = 1, ..., N; k = 1, ..., M; λ i >0 represents the speed parameter of the performance function. Q i,0 >Q i,∞ >0 is the domain parameter of the performance function. Under the influence of the performance function, the formation tracking error and velocity error satisfy the following constraints:

[0110] -Q i (t)<e i,1 <Q i (t)

[0111] -Q i (t)<E i <Q i (t);

[0112] Establish error constraint error transformation function:

[0113]

[0114] S4. Determine the predefined time virtual control law based on the formation tracking error, speed tracking error, and error transformation function;

[0115] In an optional embodiment of the present invention, the derivative of the formation error transformation function can be obtained as follows:

[0116]

[0117] Where i = ph, ah, sk; h = 1, ..., N; k = 1, ..., M; and γ represents the bias of the error transformation function. i,1 The time-varying coefficients of the transformation function are defined as follows:

[0118]

[0119] Determine the virtual control laws for the h-th UAV and the k-th unmanned surface vessel:

[0120]

[0121] Where 0 < η < 1 represents the exponential parameter; T c Indicates the time parameter.

[0122] S5. Establish a predefined time fuzzy neural network and combine it with a predefined time virtual control law to determine the distributed predefined time formation controller of the air-sea heterogeneous cluster system.

[0123] In an optional embodiment of the present invention, a fuzzy neural network is defined, consisting of four layers: an input layer, a radial basis function layer, a normalization layer, and an output layer. The specific description is as follows:

[0124] Input layer: This layer contains q neurons, representing q-dimensional input variables. For the input vector L = [L1, L2, ..., L...] q ] T The output of this layer represents x = [x1, x2, ..., x]. q ] T , where x i This represents the output of the i-th neuron in the input layer. The output of this layer can be expressed as:

[0125] x i =L i ,i=1,...,q;

[0126] Radial basis function layer: This layer contains M neurons. The output of this layer is calculated using the following formula:

[0127]

[0128] in, It is the output of the j-th neuron in this layer, ξ ij This represents the membership degree of neuron j relative to the input of neuron i. A Gaussian function, μ, is used to represent the membership degree. ij σ represents the central parameter of the j-th neuron's input to the i-th neuron. ij This represents the width parameter of the input from neuron j to neuron i.

[0129] Normalization layer: This layer contains M neurons. The output of this layer is calculated using the following formula:

[0130]

[0131] Among them, S j It is the output value of the j-th neuron.

[0132] Output Layer: The output layer of a fuzzy neural network has only one neuron. The formula for calculating the network output is:

[0133]

[0134] Among them, W j It represents the weight between the j-th neuron in the normalization layer and the output layer, and represents the result part of the j-th fuzzy rule.

[0135] Using fuzzy neural networks to estimate all uncertainties in an air-sea heterogeneous system, we can obtain the following formula:

[0136]

[0137] in, This indicates the ability to estimate the ideal weights for system uncertainty, and the weight error is defined as...

[0138] Determine the update law for the weights of a predefined temporal fuzzy neural network:

[0139]

[0140] Where i = ph, ah, sk.

[0141] This embodiment defines a distributed predefined time-based queuing controller for an air-sea heterogeneous cluster system:

[0142]

[0143] S6. Perform distributed predefined time error constraint formation control on the air-sea heterogeneous cluster system based on the distributed predefined time formation controller of the air-sea heterogeneous cluster system.

[0144] To verify the effectiveness of the method of the present invention, simulation experiments were conducted, as follows:

[0145] Simulation experiments were conducted using a heterogeneous air-sea swarm system of UAVs and unmanned surface vessels to verify the effectiveness of the designed distributed predefined time error constraint formation control method based on fuzzy neural networks. System parameters are shown in Table 1, and controller parameters are shown in Table 2.

[0146] Table 1. Model Parameters of Heterogeneous Air-Sea Cluster System for UAVs and Unmanned Surface Vessels

[0147]

[0148] Table 2 Controller Parameter Table

[0149]

[0150] The relative quantity of the UAV attitude subsystem is β ah,1 =[0,0,0] T The relative position vector β of the air-sea heterogeneous swarm system of UAVs and unmanned surface vessels ph,1 and β sk,1 The following options are available:

[0151]

[0152] Simulation results are as follows Figure 2-7 As shown, the designed distributed predefined time error-constrained formation controller can complete 3D formation tracking control of a heterogeneous air-sea swarm system of UAVs and unmanned surface vessels within a predefined time. It exhibits good robustness, fast convergence speed, and independence from initial states. The designed predefined time fuzzy neural network improves the convergence speed while maintaining the good generalization ability of fuzzy neural networks.

[0153] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0154] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0155] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0156] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0157] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A predefined time formation control method based on a fuzzy neural network, characterized in that, Includes the following steps: Establish kinematic and dynamic models of a six-DOF quadrotor UAV and a three-DOF unmanned surface vessel; Based on the kinematic and dynamic models of a six-degree-of-freedom quadrotor UAV and a three-degree-of-freedom unmanned surface vessel, the formation tracking error and velocity tracking error of an air-sea heterogeneous swarm system are established. Construct a preset performance function and determine an error transformation function based on the formation tracking error and speed tracking error of the air-sea heterogeneous cluster system; Based on the formation tracking error, speed tracking error, and error transformation function, a predefined time virtual control law is determined; A predefined time fuzzy neural network is established, and a distributed predefined time formation controller for an air-sea heterogeneous cluster system is determined by combining it with a predefined time virtual control law. Distributed predefined time error constraint formation control is performed on the air-sea heterogeneous cluster system based on the distributed predefined time formation controller of the air-sea heterogeneous cluster system.

2. The predefined time formation control method based on a fuzzy neural network according to claim 1, characterized in that, The kinematic and dynamic model of the six-DOF quadcopter UAV is as follows: Where, χ ph =[x ph ,y ph ,z ph ] T χ represents the location information in the global coordinate system. ah =[φ ah ,θ ah ,ψ ah ] T Indicates roll angle, pitch angle, and yaw angle; d xph ,d yph ,d zph ,d φah ,d θah ,d ψah I represents a time-varying unknown ocean disturbance function; x ,I y ,I z ρ represents the moment of inertia. x ,ρ y ,ρ z ,ρ φ ,ρ θ ,ρ ψ Indicates the aerodynamic damping coefficient; m a Indicates mass and inertia parameters; u 1h ,u φh ,u θh ,u ψh Λ represents the controller to be designed; g represents gravitational acceleration; Λ represents the total remaining rotor angle; I r This represents the moment of inertia of the rotor.

3. The predefined time formation control method based on a fuzzy neural network according to claim 2, characterized in that, The kinematic and dynamic model of the three-degree-of-freedom unmanned surface vessel is as follows: x sk,1 =R(x ψsk,1 )v s，k Where, χ sk,1 =[χ xsk,1 ,χ ysk,1 ,χ ψsk,1 ] T v represents the position and heading angle variables of the k-th unmanned surface vessel in the global coordinate system; k =[v xsk ,v ysk ,v ψsk ] T Represents the velocity and angular velocity variables of the k-th unmanned surface vessel in a fixed coordinate system; u sk =[u xsk ,u ysk ,u ψsk ] T d represents the control input quantity to be designed for the k-th unmanned surface vessel; sk (t)=[d xk ,d yk ,d ψk ] T R represents the external disturbance of the k-th unmanned surface vessel; sk It is a rotation matrix; Represents the inertia matrix; Represents the damping matrix. This represents the Coriolis matrix.

4. The predefined time formation control method based on a fuzzy neural network according to claim 3, characterized in that, The specific formation tracking error of the air-sea heterogeneous cluster system is as follows: And i,j =Ξ i (χ i,j -β i,j )+E ei,j ,i=ph,ah,sk Among them, e i,j Indicates formation tracking error, Ξ i The parameters represent the formation communication parameters, where ph and ah represent the position and attitude subsystems of the h-th UAV, respectively, sk represents the k-th unmanned surface vessel system, h = 1, ..., N represents the h-th UAV, N represents the number of UAVs in the heterogeneous multi-agent system, k = 1, ..., M represents the k-th unmanned surface vessel, M represents the number of unmanned surface vessels in the heterogeneous multi-agent system, N+M represents the total number of agents in the heterogeneous multi-agent system, diag represents the diagonal matrix, and a h,i b represents the communication parameters between the h-th drone and other intelligent agents. lh This represents the communication parameters between the h-th drone and the leader, a k+N,i I represents the communication parameters between the k-th unmanned surface vessel and other intelligent agents. 3×3 b represents a 3-dimensional unit vector. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. i,j β represents the state vector of the agent. i,j E represents the relative state vector that the agent needs to maintain with the leader. ei,j This indicates that an agent receives state vectors from other agents, defined as follows: Where, χ pi,j Let β represent the position and state vector of the h-th UAV. ψai,j Let β represent the relative heading angle state vector that the h-th drone needs to maintain with respect to the leader. xpi,j ,β yai,j E represents the relative position state vector that the h-th drone needs to maintain with respect to the leader. eph,j E represents the angle error vector received by the UAV from other intelligent agents. esk,j E represents the error vector received by the unmanned surface vessel from other intelligent agents. eph,j E represents the position error vector received by the UAV from other intelligent agents. eah,j This represents the attitude error vector received by the UAV from other intelligent agents, a. k+N,i and a k+N,i+N Let b represent the communication parameters between the k-th unmanned surface vessel and other intelligent agents. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. xL,j ,χ yL,j ,χ zL,j ,χ ψL,j χ represents the leader's state vector. φd,hj and χ θd,hj Let β represent the expected roll and pitch angles of the h-th UAV, respectively. pi,j χ represents the relative position vector that the h-th drone needs to maintain with respect to the leader. xpi,j ,χ ypi,j Let χ represent the position and state vector of the h-th UAV. ψai,j χ represents the heading angle of the h-th UAV. xsi,j ,χ ysi,j ,χ ψsi,j Let β represent the state vector of k unmanned surface vessels. xsi,j ,β ysi,j ,β ψsi,j Let represent the relative state vector that k unmanned surface vessels need to maintain with the leader.

5. The predefined time formation control method based on a fuzzy neural network according to claim 4, characterized in that, The formation tracking error and velocity tracking error of the air-sea heterogeneous cluster system are as follows: e φah，j =x φah，j -x φd，hj ,e θah，j =x θah，j -x θd，hj Among them, e gph,j and e gsk,j e represents the state error of the UAV and the unmanned surface vessel in the two-dimensional plane, respectively. ψah,j and e ψsk,j e represents the state error of the heading angle of the UAV and the unmanned surface vessel, respectively. zh,j Indicates altitude error, e φah,j and e θah,j χ represents the roll angle and pitch angle errors, respectively. xL,j ,χ yL,j ,χ ψL,j ,χ zL,j Represents the trajectory information of the virtual leader, β gph,j ,β gpi,j and β gsk,j ,β gsi,j β represents the relative positional state of the drone and unmanned surface vessel relative to the leader, respectively. ψah,j ,β ψai,j and β ψsk,j ,β ψsi,j β represents the relative heading angle state vector that the drone and unmanned surface vessel need to maintain with respect to the leader, respectively. zph,j ,β zpi,j a represents the state vector representing the relative altitude that the drone needs to maintain with respect to the leader. h,i and a h,i+N Let a represent the communication parameters between the h-th drone and other intelligent agents. k+N,i and a k+N,i+N Let b represent the communication parameters between the k-th unmanned surface vessel and other intelligent agents. lh b represents the communication parameters between the h-th drone and the leader. l(k+N) χ represents the communication parameters between the k-th unmanned surface vessel and its leader. gph,j ,χ gpi,j and χ gsk,j ,χ gsi,j χ represents the position status of the drone and the unmanned surface vessel, respectively. ψah,j ,χ ψai,j and χ ψsk,j ,χ ψsi,j Let χ represent the heading angle state vectors of the UAV and the unmanned surface vessel, respectively. zph,j ,χ zpi,j Indicates the altitude status of the drone, χ φah,j and χ θah,j χ represents the roll and pitch state vectors of the h-th unmanned surface vessel, respectively. φd,hj and χ θd,hj Let a represent the expected roll and pitch angles of the h-th unmanned surface vessel, respectively. ph and a ah Let a represent the virtual control law vector of the UAV. sk χ represents the virtual control law vector of the unmanned surface vessel. ph,2 and χ ah,2 χ represents the velocity state vector of the UAV. sk,2 E represents the velocity state vector of the unmanned surface vessel. ph and E ah E represents the error vector between the UAV's speed and the virtual control law. sk E represents the error vector between the unmanned surface vessel's speed and the virtual control law. xph E yph E yph E represents the error between the UAV's velocity in the XYZ directions and the virtual control law. φah E θah E ψah E represents the error in the virtual control law relating the angular velocity and angle of the UAV. xsk E ysk E ψsk This represents the error between the unmanned surface vessel's speed and the virtual control law.

6. The predefined time formation control method based on a fuzzy neural network according to claim 5, characterized in that, The error transformation function is as follows: Among them, Z ph,1 Z ah,1 and Z ph,2 Z ah,2 Z represents the formation error transformation function vector of the UAVs. sk,1 and Z sk,2 Q represents the formation error transformation function vector of the unmanned surface vessel. ph Q ah Q sk e represents the performance function index of the formation error of UAVs and unmanned surface vessels. xph,1 ,e yph,1 ,e zph,1 e represents the formation error of the UAV in the XYZ directions. φah,1 ,e θah,1 ,e ψah,1 e represents the formation error of the drone's attitude system. xsk,1 ,e ysk,1 ,e ψsk,1 E represents the formation error of unmanned surface vessels. xph E yph E yph E represents the error between the UAV's velocity in the XYZ directions and the virtual control law. φah E θah E ψah E represents the error in the virtual control law relating the angular velocity and angle of the UAV. xsk E ysk E ψsk This represents the error between the unmanned surface vessel's speed and the virtual control law.

7. The predefined time formation control method based on a fuzzy neural network according to claim 6, characterized in that, The predefined time-based virtual control law is as follows: Among them, a ph and a ah Let a represent the virtual control law vector of the UAV. sk Let η represent the virtual control law vector of the unmanned surface vessel, and T represent the exponential parameter. c The time parameter is represented by π, and Z represents the mathematical constant pi. ph,1 Z ah,1 Z represents the formation error transformation function vector of the UAVs. sk,1 Ξ represents the formation error transformation function vector of the unmanned surface vessel. ph ,Ξ ah ,Ξ sk E represents the system's communication parameters. eph,2 E eah,2 E represents the state vector received by the drone from other intelligent agents. esk,2 This indicates that the unmanned surface vessel receives the state vector from other intelligent agents. γ represents the bias of the error transformation function. ph,1 ,γ ah,1 ,γ sk,1 β represents the time-varying coefficient of the error transformation function. ph,2 ,β ah,2 β represents the relative state vector that the drone needs to maintain with respect to the leader. sk,2 This represents the relative state vector that the unmanned surface vessel needs to maintain with respect to the leader.

8. The predefined time formation control method based on a fuzzy neural network according to claim 7, characterized in that, Establishing a predefined temporal fuzzy neural network includes: A fuzzy neural network consisting of an input layer, a radial basis function layer, a normalization layer, and an output layer is established. All uncertainties in the air-sea heterogeneous system are estimated using a fuzzy neural network, expressed as follows: F i =f i * =W i * S i ,i=ph.ah,sk; Among them, F i f represents all uncertain functions of the system. i * S represents the ideal value of the uncertain function fitted by the neural network. i W represents the neuron function of a neural network. i * This indicates that the ideal weights for estimating system uncertainty can be determined.

9. The predefined time formation control method based on a fuzzy neural network according to claim 8, characterized in that, The weight update law of the predefined temporal fuzzy neural network is as follows: Where i = ph, ah, sk represent intelligent agents. S represents the estimated weights of the neural network. i Z represents the neuron function of a neural network. i,2 Represents the error transformation function vector, γ i,2 The time-varying coefficients of the error transformation function are represented by η, which represents the exponential parameter, and T is the time-varying coefficient. c This represents the time parameter, and π represents the mathematical constant pi.

10. A predefined time formation control method based on a fuzzy neural network according to claim 9, characterized in that, The distributed predefined time-based queuing controller for the air-sea heterogeneous cluster system is as follows: Among them, u ph and u ah This represents the formation control law for drones, u sk Let A, B, and f represent the formation control laws for unmanned surface vessels. ph ,f ah C represents the model parameters of the drone. sk D sk and M sk R represents the model parameters of the unmanned surface vessel. sk Represents the rotation matrix of the unmanned surface vessel. S represents the estimated weights of the neural network. ph ,S ah ,S sk The neuron function representing a neural network, Ξ ph ,Ξ ah ,Ξ sk Indicates the system's communication parameters. Represents a virtual control law. γ represents the bias of the error transformation function. ph,1 ,γ ah,1 ,γ sk,1 and γ ph,2 ,γ ah,2 ,γ sk,2 Z represents the time-varying coefficients of the error transformation function. ph,1 Z ah,1 Z sk,1 and Z ph,2 Z ah,2 Z sk,2 χ represents the error transformation function vector. sk,2 E represents the state vector of the unmanned surface vessel. ph E ah E sk The vector represents the error between velocity and the virtual control law, where η represents the exponential parameter, and T... c This represents the time parameter, and π represents the mathematical constant pi.

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