An inexact target tracking controller for power systems with fractional order and its design method

Abstract

The application discloses a kind of heterogeneous fractional order power system without accurate target tracking controller and its design method, the controller includes without accurate tracking target trajectory reconstruction module, radial basis neural network approximation module, command filtering and compensation signal module and controller and adaptive law module.Reconstruction module is reconstructed by Fourier series and radial basis neural network to the tracking target trajectory that cannot be accurately obtained for estimation;Approximation module approximates unknown nonlinear function in system;Filtering and compensation module filters virtual control law and compensates initial error;Adaptive law module generates virtual control law, actual control law and fractional order parameter update law.Each module is connected according to set signal flow direction, and interacts through distributed communication network.The application can realize the consistency tracking of multiple followers when the target trajectory cannot be accurately obtained, adapt to the heterogeneous dynamic characteristics of each power generation unit, avoid the complexity explosion of backstepping method, and ensure that all signals of closed-loop system are uniformly ultimately bounded.

Description

Technical Field

[0001] This invention belongs to the field of power system tracking control technology, and relates to a non-precise target tracking controller for a fractional-order power system and its design method. Background Technology

[0002] The power system is a core infrastructure supporting the normal operation of modern society. Its safe, stable, and reliable operation directly affects national economic development and the protection of people's livelihoods. With the large-scale integration of renewable energy, the widespread application of distributed generation, and the deepening of power market reforms, the operation architecture and control requirements of the power grid have undergone significant changes. The drawbacks of the traditional centralized control mode have gradually become apparent. It not only causes excessive load on communication links but also poses a high risk of single-point failures, making it difficult to adapt to the current operation and management needs of the power grid. Against this backdrop, multi-agent consensus control technology has been widely applied. This technology features decentralization, flexible architecture, and strong scalability, effectively improving the robustness and dynamic adaptability of the power grid. Energy storage components, excitation systems, and dynamic loads in the power system all exhibit complex memory and genetic characteristics. Conventional integer-order models are insufficient to accurately describe these characteristics, while fractional-order calculus can better characterize these nonlinear dynamic features. At the same time, heterogeneous fractional-order power systems can adapt to the different physical characteristics of different generation units (such as synchronous generators, wind turbines, and photovoltaic inverters), thus possessing significant research value and broad application prospects in the field of smart grid consensus tracking control.

[0003] However, existing tracking control methods for power systems still have the following problems:

[0004] First, most existing power system control methods assume that the trajectory of the target being tracked (such as the desired power angle, frequency, or voltage) is precisely known. However, in real-world operating scenarios, due to measurement noise, communication delays, network attacks, or the local agnostic nature of dispatch instructions, the trajectory of the target being tracked often cannot be accurately obtained by the follower agent, making traditional tracking control methods with precisely known target trajectories difficult to apply. Furthermore, the memory characteristics of fractional-order systems of different orders make reconstructing the trajectory of a target that cannot be accurately obtained even more complex, and existing methods lack effective handling of such uncertainties.

[0005] Second, in the field of fractional-order power system control, most existing research is based on fractional-order systems of the same order, assuming that the fractional derivative orders of all subsystems in the system are completely consistent. However, in real power systems, the dynamic characteristics of different generating equipment, controllers, and loads exhibit inherent heterogeneity, and their corresponding fractional orders often do not match (e.g., the inertial response order of a synchronous generator often does not match the control order of a wind power converter). More importantly, existing stability theories for fractional-order systems have limitations. When the equilibrium point stability of an integer-order nonlinear system can be verified through a convex Lyapunov function, the stability conclusions for its corresponding fractional-order nonlinear system of the same order can be directly applied. However, this conclusion only applies to fractional-order systems of the same order and does not hold for fractional-order systems of different orders. This means that the stability analysis of fractional-order power systems of different orders lacks mature theoretical criteria, and controller design lacks a suitable framework. Existing research has not paid sufficient attention to this scenario.

[0006] Third, the backstepping recursive control method is currently widely used in the field of power system control. This method requires iterative differentiation of the virtual control law at each order during the design process, which can easily lead to a "complexity explosion" problem. This drawback is further amplified in fractional-order systems with different orders and complex dynamic coupling relationships, resulting in an exponential increase in the overall computational burden of the system, which seriously affects the practical application effect of the control scheme. Summary of the Invention

[0007] The purpose of this invention is to provide a non-precise target tracking controller and its design method for a multi-order fractional power system. This controller can not only achieve distributed adaptive tracking control when the trajectory of the target cannot be accurately obtained, but also adapt to the dynamic characteristics of different fractional orders of each power generation unit. Furthermore, it avoids the "complexity explosion" problem in the backstepping method through command filtering and compensation signal technology, thereby achieving stable control of the power system in uncertain network environments.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A non-precise target tracking controller for a fractional-order power system includes a non-precise target trajectory reconstruction module, a radial basis function neural network approximation module, a command filtering and compensation signal module, and a controller and adaptive law module, wherein: The output of the heterogeneous fractional-order power system is connected to the input of the trajectory reconstruction module without precise tracking target, the input of the radial basis neural network approximation module, and the input of the controller and adaptive law module, respectively. The input of the target trajectory reconstruction module without precise tracking is connected to the power system communication topology network, and its output is connected to the input of the controller and the adaptive law module and the input of the radial basis neural network approximation module, respectively. The target trajectory reconstruction module without precise tracking is used to reconstruct and estimate the target trajectory that cannot be accurately obtained by using Fourier series and radial basis neural network. The output of the radial basis function neural network approximation module is connected to the input of the controller and the adaptive law module; the radial basis function neural network approximation module is used to approximate unknown nonlinear functions in the power system. The output terminal of the virtual control law of the controller and adaptive law module is connected to the input terminal of the command filtering and compensation signal module; the output terminal of the command filtering and compensation signal module is connected to the input terminal of the controller and adaptive law module; the command filtering and compensation signal module is used to filter the virtual control law in the backstepping method and compensate for the initial filtering error. The actual control output of the controller and the adaptive law module is connected to the control input of the heterogeneous fractional-order power system.

[0010] A design method for a non-precise target tracking controller in a fractional-order power system includes the following steps: Step A: Establish a fractional-order power system model; Step B: Design a trajectory reconstruction module for targets without precise tracking; Step C: Design a radial basis function neural network approximation module; Step D: Design the command filtering and compensation signal module; Step E: Design the controller and adaptive law module.

[0011] In step A, the established fractional-order power system model is described by the following formula: (1) Among them, subscript Representative number is Follower intelligent agents; Represented as the first The system output of each subsystem; The coefficient of frictional resistance; , For Caputo fractional differential operators, These are two sets of non-identical fractions with different orders; The angular frequency of the external periodic disturbance; For system time variables; This is the adaptive control input signal for the i-th subsystem; and These represent the relative angle and angular frequency between the equivalent generators in two different regions, respectively. parameter and These are the generator's moment of inertia and damping coefficient, respectively. This is the generator's maximum power. For the unit's output power, The amplitude of the power disturbance; To meet A smooth, unknown, nonlinear function.

[0012] In step B, the input signal of the target trajectory reconstruction module without precise tracking is a known reference trajectory. The output signal is the reconstructed estimate of the tracked target. The designed target trajectory reconstruction module without precise tracking is represented as follows: (2) in, , The adaptive weight estimates of the Fourier series and radial basis function neural network are given, and their transposes are respectively... , ; The Fourier basis function vector has a dimension of , The dimension of the basis function vector for the radial basis neural network is... ; , Let be a positive definite symmetric design matrix, where is a positive integer greater than 1, representing the truncation order of the Fourier series; is a positive integer representing the number of neurons in a radial basis function neural network; , Positive design parameters; , It is a smooth bounded activation function.

[0013] In step C, the input signal of the radial basis function neural network approximation module is the output of the target trajectory reconstruction module without precise tracking and the state interaction information between various power systems; the output signal is the ideal weight vector of the radial basis function neural network. Radial neural network basis function vectors With bounded approximation error ; The designed radial basis function neural network approximation module is represented as follows: (3) in, The module input state vector is defined on a compact set. A continuous bounded vector on; The unknown continuous nonlinear function to be approximated; ; ; In the formula For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements; To track the target connectivity coefficients; The reconstructed tracking target; For the first The relative angles of the agents; For the first angular frequency of each agent; Output for command filter; This is the output of the radial basis function neural network that approximates the unknown function. , The ideal weight vector of the radial neural network and its adaptive estimate; is the radial neural network basis function vector, which is a continuous and smooth radial basis function; The inherent approximation error of the radial neural network is unknown but bounded. Here, is a pre-defined upper bound constant for the approximation error, and is a design parameter; State vector The compact set to which it belongs serves as the domain constraint for approximation validity.

[0014] In step D, the input of the command filter module is the first step in the backstep design. Virtual control law The output signal is a filtered virtual control signal. ; The input of the compensation signal module is for information exchange between various power systems, and the output of the command filter module is... In the backstep design Virtual control law ; The designed command filter is established as follows: (4) Initial conditions:

[0015] for Caputo fractional differential operator; in, To design the order for backstepping, ; These are the design parameters for the command filter; Output for command filter; Input to the command filter; To eliminate the impact of the initial error generated by the command filter on tracking performance, the following fractional-order compensation signal is designed. , : (5) (6) in, , , For design parameters; For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements To track the target connectivity coefficients.

[0016] In step E, the input terminals of the controller and the adaptive law module are the compensated error. Regressor quantity of radial basis function neural network and compensation signals consensus error The controller and adaptive law module includes a virtual controller computation unit, an actual controller computation unit, and a fractional-order parameter adaptive law unit, where the adaptive law unit outputs an estimate of the neural network weight norm. and estimation of approximation error bound ; definition Design a virtual controller and controller as follows (7) (8) Among them, auxiliary variables .

[0017] In step E, to ensure the boundedness of the neural network estimation, the following fractional-order parameter update law is designed: (9) (10) in, For learning rate, For correction factors; correction terms and This is used to avoid parameter drift and ensure that the estimated values ​​are bounded. Beneficial effects

[0018] Compared with the prior art, the present invention has the following beneficial effects: First, this invention combines Fourier series with radial basis function neural networks to design a trajectory reconstruction module for imprecise tracking targets in multi-order fractional power systems. This module can reconstruct the trajectory and guarantee its boundedness when the target trajectory is difficult to obtain accurately. This solves the engineering problem that dispatching instructions or reference signals cannot be obtained globally in actual power systems and improves the system's adaptability to unknown environments.

[0019] Secondly, this invention addresses the inherent characteristic of different dynamic orders among power generation units in heterogeneous fractional-order power systems by proposing a control method adapted to such systems, thus overcoming the theoretical limitations of existing homogeneous fractional-order control methods. It ensures that all signals in the closed-loop system are consistent and ultimately bounded, even when the fractional-order derivatives of each subsystem are not entirely identical. This provides theoretical support for the control of heterogeneous equipment such as synchronous generators, wind power converters, and photovoltaic inverters in practical power systems.

[0020] Third, this invention introduces fractional-order command filtering technology and a compensation signal mechanism into the backstepping recursive design. This avoids the "complexity explosion" problem caused by repeated differentiation of the virtual control law in the traditional backstepping method, significantly reducing the online computation load of the controller. At the same time, the designed fractional-order compensation signal can independently offset the impact of the initial filtering error on the tracking performance, so that the compensated tracking error does not explicitly contain the filtering error term in the dynamics, ensuring the steady-state tracking accuracy of the system without increasing the computational burden. Attached Figure Description

[0021] Figure 1This is a schematic diagram of a fractional-order power system.

[0022] Figure 2 This is a reconstruction effect diagram of the trajectory reconstruction module without precise tracking proposed in this invention.

[0023] Figure 3 This is an adaptive weight estimation map of the target trajectory reconstruction module without precise tracking.

[0024] Figure 4 This is a diagram showing the effect of distributed trajectory tracking.

[0025] Figure 5 It is a distributed trajectory tracking error map.

[0026] Figure 6 It consists of three follower intelligent agents controlling the input. Line graph.

[0027] Figure 7 It is the control state of the three follower agents. The rendered image.

[0028] Figure 8 It is an estimation of the weight norm of a neural network. picture.

[0029] Figure 9 It is an estimate that approximates the error bound. picture. Detailed Implementation

[0030] The invention will now be further described with reference to the accompanying drawings.

[0031] The present invention provides a design for a fractional-order power system without a precisely tracking target, as follows: Figure 1 As shown, this invention will be further illustrated using a non-precisely identifiable target and three followers in a fractional-order power system. In this embodiment, the system includes a non-precisely identifiable target node (node ​​0) and three follower nodes (nodes 1-3). The non-precisely identifiable target node 0 can directly send reference information to follower nodes 1 and 3; follower node 1 can transmit its own state information to nodes 2 and 3, and follower node 3 can transmit its own state information to node 2, forming a distributed communication network. The control objective of this embodiment is to achieve tracking control of the non-precisely identifiable target by the follower agent using the non-precisely identifiable distributed adaptive controller for non-precisely identifiable power systems proposed in this invention. Simultaneously, it utilizes radial basis function neural networks to approximate unknown nonlinear terms of the system and solves the computational complexity explosion problem of traditional backstepping methods through fractional-order command filtering and compensation mechanisms, ensuring that all signals in the closed-loop system are consistent and ultimately bounded, thus achieving tracking control of the power system.

[0032] To address the aforementioned problems, this embodiment provides a non-precise target tracking controller for a fractional-order power system, including a non-precise target trajectory reconstruction module, a radial basis function neural network approximation module, a command filtering and compensation signal module, and a controller and adaptive law module, wherein:

[0033] The output of the heterogeneous fractional-order power system is connected to the input of the trajectory reconstruction module without precise tracking target, the input of the radial basis neural network approximation module, and the input of the controller and adaptive law module, respectively.

[0034] The input of the target trajectory reconstruction module without precise tracking is connected to the power system communication topology network, and its output is connected to the input of the controller and adaptive law module and the input of the radial basis neural network approximation module, respectively. The target trajectory reconstruction module without precise tracking is used to reconstruct and estimate the target trajectory that cannot be accurately obtained by using Fourier series and radial basis neural network.

[0035] The output of the radial basis function neural network approximation module is connected to the input of the controller and the adaptive law module; the radial basis function neural network approximation module is used to approximate unknown nonlinear functions in power systems.

[0036] The output of the virtual control law of the controller and adaptive law module is connected to the input of the command filtering and compensation signal module; the output of the command filtering and compensation signal module is connected to the input of the controller and adaptive law module; the command filtering and compensation signal module is used to filter the virtual control law in the backstepping method and compensate for the initial filtering error.

[0037] The actual control output of the controller and adaptive law module is connected to the control input of the fractional-order power system.

[0038] The design method for a non-precise target tracking controller in a fractional-order power system according to this embodiment includes the following steps:

[0039] Step A: Establish a fractional-order power system model;

[0040] The established model of the heterogeneous fractional-order power system is described by the following formula:

[0041] (1)

[0042] Among them, subscript Representative number is Follower intelligent agents;

[0043] Represented as the first The system output of each subsystem;

[0044] The coefficient of frictional resistance;

[0045] , For Caputo fractional differential operators, , ;

[0046] The angular frequency of the external periodic disturbance;

[0047] For system time variables;

[0048] This is the adaptive control input signal for the i-th subsystem;

[0049] and These represent the relative angle and angular frequency between the equivalent generators in two different regions, respectively.

[0050] parameter and These are the generator's moment of inertia and damping coefficient, respectively.

[0051] This is the generator's maximum power. For the unit's output power, The amplitude of the power disturbance;

[0052] , , , ;

[0053] , ;

[0054] Step B: Design a trajectory reconstruction module for targets without precise tracking;

[0055] The input signal for the target trajectory reconstruction module without precise tracking is a known baseline trajectory. The output signal is the reconstructed estimate of the tracked target. The designed target trajectory reconstruction module without precise tracking is represented as follows:

[0056] (2)

[0057] in, , The adaptive weight estimates of the Fourier series and radial basis function neural network are given, and their transposes are respectively... , ;

[0058] The Fourier basis function vector has a dimension of , The dimension of the basis function vector for the radial basis neural network is... ;

[0059] , Let be a positive definite symmetric design matrix, where is a positive integer greater than 1, representing the truncation order of the Fourier series; is a positive integer representing the number of neurons in a radial basis function neural network;

[0060] , Positive design parameters;

[0061] , It is a smooth bounded activation function.

[0062] Step C: Design a radial basis function neural network approximation module;

[0063] The input signals of the radial basis function neural network approximation module are the output of the target trajectory reconstruction module without precise tracking and the state interaction information between various power systems; the output signal is the ideal weight vector of the radial basis function neural network. Radial neural network basis function vectors With bounded approximation error ;

[0064] The designed radial basis function neural network approximation module is represented as follows:

[0065] (3)

[0066] in, The module input state vector is defined on a compact set. A continuous bounded vector on;

[0067] The unknown continuous nonlinear function to be approximated;

[0068] ;

[0069] ;

[0070] In the formula For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements;

[0071] To track the target connectivity coefficients;

[0072] The reconstructed tracking target;

[0073] For the first The relative angles of the agents;

[0074] For the first angular frequency of each agent;

[0075] Output for command filter;

[0076] This is the output of the radial basis function neural network that approximates the unknown function.

[0077] , The ideal weight vector of the radial neural network and its adaptive estimate;

[0078] is the radial neural network basis function vector, which is a continuous and smooth radial basis function;

[0079] The inherent approximation error of the radial neural network is unknown but bounded.

[0080] Here, is a pre-defined upper bound constant for the approximation error, and is a design parameter;

[0081] State vector The compact set to which it belongs serves as the domain constraint for approximation validity.

[0082] Step D: Design the command filtering and compensation signal module;

[0083] The input of the command filter module is the first step in the backstep design. Virtual control law The output signal is a filtered virtual control signal. ;

[0084] The input of the compensation signal module is for information exchange between various power systems, and the output of the command filter module is... In the backstep design Virtual control law ;

[0085] The designed command filter is established as follows:

[0086] (4)

[0087] Initial conditions:

[0088] for Caputo fractional differential operator;

[0089] in, To design the order for backstepping, ;

[0090] These are the design parameters for the command filter;

[0091] Output for command filter;

[0092] Input to the command filter;

[0093] To eliminate the impact of the initial error generated by the command filter on tracking performance, the following fractional-order compensation signal is designed. , :

[0094] (5)

[0095] (6)

[0096] in, , , For design parameters;

[0097] For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements;

[0098] To track the target connectivity coefficients.

[0099] Step E: Design the controller and adaptive law module;

[0100] The input terminals of the controller and the adaptive law module are the compensated error. Regressor quantity of radial basis function neural network and compensation signals consensus error The controller and adaptive law module includes a virtual controller computation unit, an actual controller computation unit, and a fractional-order parameter adaptive law unit, where the adaptive law unit outputs an estimate of the neural network weight norm. and estimation of approximation error bound ;

[0101] definition Design a virtual controller and controller as follows

[0102] (7)

[0103] (8)

[0104] Among them, auxiliary variables .

[0105] To ensure the boundedness of the neural network estimation, the following fractional-order parameter update law is designed:

[0106] (9)

[0107] (10)

[0108] in, For learning rate, For correction factors; correction terms and This is used to avoid parameter drift and ensure that the estimated values ​​are bounded.

[0109] Simulation results are as follows Figure 2-9 Figure 2 shows the reconstruction effect of the target trajectory reconstruction module without precise tracking proposed in this invention on the target trajectory. It can be seen that the reconstructed trajectory can track the real target trajectory, providing a reliable reference signal for distributed tracking control. Figure 3 depicts the estimation curve of the adaptive weight in the target trajectory reconstruction module without precise tracking. It can be seen that the weight estimate can remain stable, verifying the effectiveness of the adaptive law of the target trajectory reconstruction module without precise tracking. Figure 4 shows the distributed trajectory tracking effect of three follower agents. It can be observed that each follower agent can achieve consistent tracking of the target trajectory that cannot be precisely obtained under the action of the controller of this invention. Figure 5 shows the distributed trajectory tracking error curve. It can be seen that the tracking error of all followers can quickly converge to a small neighborhood near zero, verifying the tracking performance of the control method. Figure 6 shows the control input of the three follower agents. The change curves show that the control input is continuous and bounded, which meets the engineering application requirements of practical power systems. Figure 7 depicts the control states of the three follower agents. The response curves show that all state variables remain stable and show no divergence, indicating that the closed-loop system has good dynamic performance. Figure 8 shows the estimation curve of the weight norm of the radial basis function neural network. The estimated value can adaptively adjust online and eventually stabilize. Figure 9 shows the estimation curve of the neural network approximation error. , It can adaptively adjust and cover the actual approximation error, further ensuring the stability and robustness of the system.

[0110] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A precision-tracking controller for a fractional-order power system, characterized in that, It includes a target trajectory reconstruction module without precise tracking, a radial basis function neural network approximation module, a command filtering and compensation signal module, and a controller and adaptive law module, wherein: The output of the fractional-order power system is connected to the input of the untracked target trajectory reconstruction module, the input of the radial basis neural network approximation module, and the input of the controller and adaptive law module, respectively. The input of the target trajectory reconstruction module without precise tracking is connected to the power system communication topology network, and its output is connected to the input of the controller and the adaptive law module and the input of the radial basis neural network approximation module, respectively. The target trajectory reconstruction module without precise tracking is used to reconstruct and estimate the target trajectory that cannot be accurately obtained by using Fourier series and radial basis neural network. The output of the radial basis function neural network approximation module is connected to the input of the controller and the adaptive law module; the radial basis function neural network approximation module is used to approximate unknown nonlinear functions in the power system. The output terminal of the virtual control law of the controller and adaptive law module is connected to the input terminal of the command filtering and compensation signal module; the output terminal of the command filtering and compensation signal module is connected to the input terminal of the controller and adaptive law module; the command filtering and compensation signal module is used to filter the virtual control law in the backstepping method and compensate for the initial filtering error. The actual control output of the controller and the adaptive law module is connected to the control input of the heterogeneous fractional-order power system.

2. A design method for a precision-tracking controller for a multi-order fractional-order power system, characterized in that, Includes the following steps: Step A: Establish a fractional-order power system model; Step B: Design a trajectory reconstruction module for targets without precise tracking; Step C: Design a radial basis function neural network approximation module; Step D: Design the command filtering and compensation signal module; Step E: Design the controller and adaptive law module.

3. The design method according to claim 2, characterized in that, In step A, the established fractional-order power system model is described by the following formula: （1） Among them, subscript Representative number is Follower intelligent agents; Represented as the first The system output of each subsystem; The coefficient of frictional resistance; , For Caputo fractional differential operators, These are two sets of non-identical fractions with different orders; The angular frequency of the external periodic disturbance; For system time variables; This is the adaptive control input signal for the i-th subsystem; and These represent the relative angle and angular frequency between the equivalent generators in two different regions, respectively. parameter and These are the generator's moment of inertia and damping coefficient, respectively. This is the generator's maximum power. For the unit's output power, The amplitude of the power disturbance; To meet A smooth, unknown, nonlinear function.

4. The design method according to claim 3, characterized in that, In step B, the input signal of the target trajectory reconstruction module without precise tracking is a known reference trajectory. The output signal is the reconstructed estimate of the tracked target. The designed target trajectory reconstruction module without precise tracking is represented as follows: （2） in, , The adaptive weight estimates of the Fourier series and radial basis function neural network are given, and their transposes are respectively... , ; The Fourier basis function vector has a dimension of , The dimension of the basis function vector for the radial basis neural network is... ; , Let be a positive definite symmetric design matrix, where is a positive integer greater than 1, representing the truncation order of the Fourier series; is a positive integer representing the number of neurons in a radial basis function neural network; , Positive design parameters; , It is a smooth bounded activation function.

5. The design method according to claim 4, characterized in that, In step C, the input signal of the radial basis function neural network approximation module is the output of the target trajectory reconstruction module without precise tracking and the state interaction information between various power systems; the output signal is the ideal weight vector of the radial basis function neural network. Radial neural network basis function vectors With bounded approximation error ; The designed radial basis function neural network approximation module is represented as follows: （3） in, The module input state vector is defined on a compact set. A continuous bounded vector on; The unknown continuous nonlinear function to be approximated; ； ； In the formula For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements; To track the target connectivity coefficients; The reconstructed tracking target; For the first The relative angles of the agents; For the first angular frequency of each agent; Output for command filter; This is the output of the radial basis function neural network that approximates the unknown function. , The ideal weight vector of the radial neural network and its adaptive estimate; is the radial neural network basis function vector, which is a continuous and smooth radial basis function; The inherent approximation error of the radial neural network is unknown but bounded. Here, is a pre-defined upper bound constant for the approximation error, and is a design parameter; State vector The compact set to which it belongs serves as the domain constraint for approximation validity.

6. The design method according to claim 5, characterized in that, In step D, the input of the command filter module is the first step in the backstep design. Virtual control law ; The output signal is a filtered virtual control signal. ; The input of the compensation signal module is for information exchange between various power systems, and the output of the command filter module is... In the backstep design Virtual control law ; The designed command filter is established as follows: （4） Initial conditions: in, To design the order for backstepping, ; for Caputo fractional differential operator; These are the design parameters for the command filter; Output for command filter; Input to the command filter; To eliminate the impact of the initial error generated by the command filter on tracking performance, the following fractional-order compensation signal is designed. , : （5） （6） in, , , For design parameters; For followers to enter into enlightenment, The nth in the directed communication adjacency matrix OK Column elements To track the target connectivity coefficients.

7. The design method according to claim 6, characterized in that, In step E, the input terminals of the controller and the adaptive law module are the compensated error. Regressor quantity of radial basis function neural network and compensation signals consensus error The controller and adaptive law module includes a virtual controller computation unit, an actual controller computation unit, and a fractional-order parameter adaptive law unit, where the adaptive law unit outputs an estimate of the neural network weight norm. and estimation of approximation error bound ; definition Design a virtual controller and controller as follows （7） （8） Among them, auxiliary variables .

8. The design method according to claim 7, characterized in that, In step E, to ensure the boundedness of the neural network estimation, the following fractional-order parameter update law is designed: （9） （10） in, For learning rate, For correction factors; correction terms and This is used to avoid parameter drift and ensure that the estimated values ​​are bounded.

Images