Multi-target cooperative control method and device

Abstract

The invention belongs to the technical field of cooperative control, and relates to a multi-target cooperative control method and device, and the method comprises the steps: constructing a saturation pulse controller of each to-be-controlled target through a nonlinear saturation function; constructing a state-space equation of each to-be-controlled target so as to obtain a synchronous target state equation of the cooperative control system; the method comprises the following steps of: constructing an initial state solving model of a to-be-controlled target by aiming at converging an initial state variable of each to-be-controlled target to a synchronous target state under the control of a saturation pulse controller of the to-be-controlled target, thereby solving to obtain an initial state maximum value of the to-be-controlled target and a maximum gain of the saturation pulse controller; setting an initial state variable of each to-be-controlled target and a gain of each saturation pulse controller; and inputting the real-time state variables of each to-be-controlled target and the adjacent to-be-controlled target into each saturation pulse controller to control each to-be-controlled target, so that the state of each to-be-controlled target reaches a synchronous target state to realize multi-target cooperative control.

Description

Technical Field

[0001] The present invention relates to the technical field of cooperative control, and in particular to a multi-object cooperative control method and device. Background Art

[0002] Multi-object cooperative control refers to coordinating the behaviors of multiple targets in a cooperative control system to achieve synchronization under the conditions of mutual influence and restriction. This control method is widely used in fields such as robot swarms, intelligent transportation, and industrial automation. For example, when a cooperative control system composed of multiple robots performs a performance task, it is necessary to synchronously control the movements of the joints and limb parts of each robot to ensure the consistency of the actions of multiple robots; when a cooperative control system composed of multiple automatic guided vehicles performs a material handling task, it is necessary to adjust the paths of each automatic guided vehicle in real time to achieve synchronous obstacle avoidance when transporting warehouse materials; when a cooperative control system composed of a driverless vehicle fleet performs a synchronous driving task, it is necessary to cooperatively control the vehicle speeds of each driverless vehicle to keep the distance between the vehicles in the fleet constant.

[0003] Due to the advantages of fast response, strong robustness, and simple structure of pulse control signals, in the prior art, pulse control signals are often used to control the motion states such as speed, acceleration, and angular velocity of each target in a cooperative control system, so as to achieve the state synchronization of multiple targets. Specifically, the existing multi-object cooperative control method constructs a state space equation reflecting the state of each target based on the state information of each target and its adjacent targets, constructs a pulse controller for each target based on the state difference between each target and its adjacent targets, and at the same time, constructs a target synchronization state based on the states of all targets. Each pulse controller obtains the state information of each target and its adjacent targets in real time, and outputs a pulse control command to each target based on the state difference between each target and its adjacent targets to adjust the state parameters of the target, so that the states of each target converge to the target synchronization state to achieve the cooperative control of multiple targets.

[0004] However, in a cooperative control system, the states of each target are often lagged due to inertia. Moreover, there is often a proportional delay in the states of adjacent targets, that is, it takes time for the state information of adjacent targets to be transmitted, resulting in the saturation pulse controller possibly outputting a pulse control signal based on the state difference between the current state of the target and the historical state of the adjacent target. As a result, the state of each target at the current moment is affected by the historical state of the adjacent target. Additionally, in actual application scenarios, there is also a distributed delay in the states of adjacent targets, that is, the transmission time of the state information of adjacent targets may fluctuate within a time period, leading to the state of each target at the current moment being affected by the states within the historical period of the adjacent target. However, the existing cooperative control methods only consider the state information of the target and its adjacent targets at the current moment when constructing the state space equation of the target, ignoring the effects of state time delay, proportional delay, and distributed delay on the target state, thus being unable to accurately reflect the actual states of each target, causing the pulse controller to be unable to output an accurate pulse control signal, and further affecting the synchronization of multiple targets. At the same time, when constructing the pulse controller, the existing cooperative control methods ignore the matching problem between the output characteristics of the pulse controller and the input characteristics of the target, that is, the pulse control signal output by the pulse controller may exceed the physical limit that the target can execute, resulting in the target being unable to effectively execute the control instruction, and thus unable to achieve multi-target synchronization. In addition, when the initial state differences of multiple targets are too large, it will exceed the adjustment range of the pulse controller, resulting in the states of multiple targets being unable to be adjusted to the target synchronization state, thereby causing the failure of multi-target cooperative control.

[0005] In summary, the existing multi-target cooperative control methods cannot effectively perform cooperative control on multiple targets, thus enabling multiple targets to achieve synchronization. As a result, when applying this multi-target control method to the cooperative control systems in various fields, the cooperative task objectives cannot be accurately achieved. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the fact that the existing multi-target cooperative control methods cannot effectively perform cooperative control on multiple targets, thus enabling multiple targets to achieve synchronization. As a result, when applying this multi-target control method to the cooperative control systems in various fields, the cooperative task objectives cannot be accurately achieved.

[0007] To solve the above technical problem, the present invention provides a multi-target cooperative control method, including: Constructing a saturation pulse controller for each target to be controlled by using a non-linear saturation function based on the state variable difference between each target to be controlled in the cooperative control system and its adjacent target to be controlled; Based on the state variables of each target to be controlled, the state variable non-linear terms without time-delay effect, the state variable non-linear terms with time-delay effect, the state variables of its adjacent targets to be controlled under the influence of proportional delay and distributed delay, and the saturated pulse controller, construct the state space equations of each target to be controlled; Sum the state variables of each target to be controlled with weights to obtain the synchronous target state equation of the cooperative control system; with the goal that the initial state variables of each target to be controlled converge to the synchronous target state under the control of its saturated pulse controller, construct the initial state solution model of the target to be controlled; Solve the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller, so that the initial state variables of each target to be controlled are less than or equal to the maximum value of the initial state, and the gains of each saturated pulse controller are less than or equal to the maximum gain; The saturated pulse controllers of each target to be controlled output pulse control signals based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, so as to control each target to be controlled, so that the states of each target to be controlled reach the synchronous target state.

[0008] Preferably, the saturated pulse controller of each target to be controlled is expressed as: , where represents the saturated pulse controller of the th target to be controlled; represents the non-linear saturation function; , represents the gain of the saturated pulse controller, represents the th target to be controlled and the coupling weight between the th adjacent target to be controlled; represents the state variable of the th target to be controlled at time t, represents the state variable of the th target to be controlled at time t, represents the difference in the state variables between the th target to be controlled and its adjacent targets at time t, represents the number of adjacent targets to the th target to be controlled; represents the Dirac pulse function, represents the th moment in the pulse control signal, represents the th moment in the pulse control signal.

[0009] Preferably, the state - space equation of each target to be controlled is expressed as: , where, represents the state variable of the th target to be controlled at time t; represents the first - order derivative of; represents the decay matrix of the target to be controlled, represents the state variable of the th target to be controlled at time t under the influence of the decay matrix; represents the weight matrix of the state - variable non - linear term without time - delay effect, represents the state - variable non - linear term at time t without time - delay effect; represents the weight matrix of the state - variable non - linear term with time - delay effect, represents the state - variable non - linear term at time t with time - delay effect, represents the time - delay at time; represents the proportional - delay coupling strength between adjacent targets to be controlled, represents the first coupling matrix between the th target to be controlled and its adjacent th target to be controlled; represents the proportional - delay inline coupling matrix, represents the state variable of the th target to be controlled adjacent to the th target to be controlled at time t under the influence of proportional - delay, represents the proportional - delay factor, represents the number of targets to be controlled adjacent to the th target to be controlled; represents the distributed - delay coupling strength between adjacent targets to be controlled, represents the distributed - delay inline coupling matrix, represents the second coupling matrix between the th target to be controlled and its adjacent th target to be controlled; represents the distributed - delay at time; represents the state variable of the th target to be controlled adjacent to the th target to be controlled at time t under the influence of distributed - delay; represents the external disturbance at time t; represents the saturation pulse controller of the th target to be controlled.

[0010] Preferably, the synchronous target state equation of the cooperative control system obtained by weighted summation based on the states of each target to be controlled includes: Construct a strongly connected digraph based on the adjacent relationships of all targets to be controlled, and obtain the generalized algebraic connectivity definition formula of the Laplacian matrix of the strongly connected digraph; Based on each eigenvalue in the left null eigenvector in the generalized algebraic connectivity definition formula, obtain the state weights of each target to be controlled; Based on the state variables and state weights of each target to be controlled, obtain the synchronous target state equation of the cooperative control system.

[0011] Preferably, the generalized algebraic connectivity definition formula is expressed as: , wherein, represents the generalized algebraic connectivity definition formula; represents the Laplacian matrix; represents the left null eigenvector, ; represents the orthogonal vector of the left null eigenmatrix; , represents the diagonal matrix; represents the transpose; ; The synchronous target state equation of the cooperative control system is expressed as: , wherein, represents the synchronous target state equation of the cooperative control system; represents the state variable of the th target to be controlled at time t; represents the th eigenvalue in the left null eigenvector in the generalized algebraic connectivity definition formula; represents the number of targets to be controlled in the cooperative control system.

[0012] Preferably, aiming at the initial states of each target to be controlled converging to the synchronous target state under the control of its saturation pulse controller, the initial state solution model of the target to be controlled is constructed, including: Based on the convex set approximation theory, approximate the range of the initial state variables of the target to be controlled as a polyhedron, and approximate the pulse control signal output by the saturation pulse controller as a scaling factor; With the maximization of the scaling factor as the goal, construct the objective function; with the polyhedron being contained within the ellipsoid under the scaling of the scaling factor as the constraint condition, construct the first constraint function; with the pulse control signal being a saturated non-linear signal as the constraint condition, construct the second constraint function; with the gain stability of the saturated pulse controller as the constraint condition, construct the third constraint function; with the state variables of the target to be controlled being stable under the influence of delay as the constraint condition, construct the fourth constraint function; with the weight of the distributed delay influence of adjacent targets to be controlled as the constraint condition, construct the fifth constraint function; with the weight of the proportional delay influence of adjacent targets to be controlled as the constraint condition, construct the sixth constraint function; with the cooperative control system being stable under the maximum distributed delay influence as the constraint condition, construct the seventh constraint function; Based on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function, obtain the initial state solution model of the target to be controlled.

[0013] Preferably, the objective function is expressed as: , where, represents the objective function; represents the scaling factor; The first constraint function is expressed as: ,

[0014] where, represents the polyhedron; represents the ellipsoid; The second constraint function is expressed as: , where, represents the pulse reduction factor of the pulse control signal; represents the Laplacian matrix; represents the non-linear matrix; represents the number of targets to be controlled within the cooperative control system; , represents the dimension of the state variables of the target to be controlled; represents the state variable weight matrix of the target to be controlled; represents the parameter of the Lyapunov function; represents the Kronecker product; The third constraint function is expressed as: , where, represents the constraint on the difference in state variables of the target to be controlled before and after being controlled by the pulse control signal, , Represents the definition formula of the generalized algebraic connectivity, Represents the saturated convex hull decomposition matrix, Represents the gain of the saturated pulse controller, Represents the non - linear convex hull decomposition matrix; ; The fourth constraint function is expressed as: , where, , Represents the normalized Laplacian matrix, Represents the first positive definite diagonal matrix, Represents the first positive scalar parameter, Represents the weight matrix of the state - variable non - linear term without time - delay effect, Represents the weight matrix of the state - variable non - linear term with time - delay effect, Represents the decay matrix of the target to be controlled, Represents the second positive definite diagonal matrix, Represents the proportional - delay coupling strength between adjacent targets to be controlled, Represents the communication topology matrix of the cooperative control system, Represents the proportional - delay inline coupling matrix, Represents the distributed - delay coupling strength between adjacent targets to be controlled, Represents the distributed - delay inline coupling matrix, Represents the first constraint of the delay - coupling strength, Represents the second constraint of the delay - coupling strength, Represents the distributed - delay coupling term, Represents the N - order identity matrix; The fifth constraint function is expressed as: , where, Represents the topology matrix of the strongly - connected digraph; Represents the second positive scalar parameter; Represents the positive definite matrix; The sixth constraint function is expressed as: , where, Represents the proportional - delay influence weight factor; The seventh constraint function is expressed as: , where, Represents the third positive scalar parameter; Represents the maximum value of the distributed delay.

[0015] Preferably, solving the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturation pulse controller includes: Performing convexification transformation on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function in the initial state solution model, and obtaining the target initial state solution model based on the transformed objective function and constraint functions; Solving the target initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturation pulse controller.

[0016] Preferably, the transformed objective function is expressed as: , wherein, represents the transformed objective function; ; The transformed first constraint function is expressed as: , wherein, represents the member vector of the auxiliary polyhedron; ; represents the number of member vectors; The transformed second constraint function is expressed as: , wherein, ; The transformed third constraint function is expressed as: , wherein, ; The transformed fourth constraint function is expressed as: , wherein, ; , ; , ; , ; , ; , represents the proportional delay inner coupling diagonal matrix; , represents the distributed delay inner coupling diagonal matrix; The transformed fifth constraint function is expressed as: , wherein, ; The converted sixth constraint function is expressed as: , The converted seventh constraint function is expressed as: .

[0017] The present invention also provides a multi-object collaborative control device, including: A saturation pulse controller construction module, configured to construct a saturation pulse controller for each target to be controlled based on the state variable difference between each target to be controlled and its adjacent target to be controlled in the collaborative control system by using a non-linear saturation function; A state space equation construction module, configured to construct a state space equation for each target to be controlled based on the state variables of each target to be controlled, the non-linear terms of the state variables without time-delay effect, the non-linear terms of the state variables with time-delay effect, the state variables of its adjacent target to be controlled under the influence of proportional delay and distributed delay, and the saturation pulse controller; A synchronization target construction module, configured to perform weighted summation on the state variables of each target to be controlled to obtain a synchronization target state equation of the collaborative control system; and construct an initial state solution model for the target to be controlled with the goal that the initial state variables of each target to be controlled converge to the synchronization target state under the control of its saturation pulse controller; A parameter acquisition module, configured to solve the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variables of each target to be controlled are less than or equal to the maximum value of the initial state, and the gains of each saturation pulse controller are less than or equal to the maximum gain; A collaborative control module, configured to output a pulse control signal based on the real-time state variables of each target to be controlled and its adjacent target to be controlled by the saturation pulse controller of each target to be controlled to control each target to be controlled, so that the states of each target to be controlled reach the synchronization target state.

[0018] The multi-object collaborative control method provided by the present application has the following beneficial effects: First, the present application constructs a saturated pulse controller based on the state variable difference between the target to be controlled and its adjacent target to be controlled by using a non-linear saturation function. The non-linear saturation function is used to limit the upper amplitude limit of the pulse control signal, thereby restricting the pulse control signal within the execution domain of the target to be controlled and avoiding the problem that the target to be controlled cannot effectively execute the control instruction. When constructing the state space equation of the target to be controlled, in addition to considering its state variables at the current moment, non-linear terms including its state variables at historical moments, state variable terms of its adjacent targets to be controlled under proportional delay, and state variable terms of its adjacent targets to be controlled under distributed delay are introduced, so as to comprehensively consider the effects of time delay, proportional delay, and distributed delay on the state variables of the target to be controlled, better simulate the communication delay phenomenon in the cooperative control system, and more accurately reflect the dependence of the target to be controlled on historical states and the states of adjacent targets to be controlled. Further, after constructing the synchronous target state equation based on the state variables of all targets to be controlled, an initial state solution model of the target to be controlled is constructed with the goal that the initial state variables of each target to be controlled converge to the synchronous target state under the control of its saturated pulse controller, so that the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller can be solved. Before synchronous control, by adjusting the initial states of each target to be controlled within the maximum value range and setting the gain of each saturated pulse controller to be less than the maximum gain, the initial state differences of multiple targets are matched to the adjustment range of the pulse controller. By constructing a saturated pulse controller whose output characteristics match the input characteristics of the target to be controlled, and combining the communication delay phenomenon in the actual application scenario, a state space equation that can accurately reflect the true state of the target to be controlled is constructed, and the maximum value of the initial state and the maximum gain of the saturated pulse controller that can make the states of multiple targets to be controlled effectively converge to the synchronous target state are obtained, so that each target to be controlled in the cooperative control system can reach the synchronous target state under the control of its saturated pulse controller, effectively realizing multi-target cooperative control, and further enabling the cooperative control systems in various fields to accurately achieve the cooperative task goals under this cooperative control method. Description of the Drawings

[0019] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention and in combination with the drawings, where: Figure 1 It is a flowchart of the multi-target cooperative control method provided by the present application; Figure 2 It is a state trajectory diagram of each target to be controlled when not controlled by the cooperative control method provided by the present application; Figure 3 It is a state error trajectory diagram of each target to be controlled when not controlled by the cooperative control method provided by the present application; Figure 4 The state trajectory diagram of each target to be controlled under the method provided by this application; Figure 5 The state error trajectory diagram of each target to be controlled under the method provided by this application; Figure 6 The schematic diagram of the saturation pulse control signal output by the saturation pulse controller provided by this application; Figure 7 The schematic diagram of the structure of the multi-target cooperative control device provided by this application. Detailed implementation manners

[0020] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0021] Please refer to Figure 1 , Figure 1 The flowchart of the multi-target cooperative control method provided by this application is shown as follows. The method specifically includes: S10: Based on the difference in state variables between each target to be controlled and its adjacent target to be controlled in the cooperative control system, construct a saturation pulse controller for each target to be controlled by using a non-linear saturation function.

[0022] Specifically, the cooperative control system contains multiple targets to be controlled, and each target to be controlled is a mechanical system with a PLC controller or a dedicated controller (such as UR's PolyScope). For example, in a cooperative control system composed of multiple cooperative robots, the target to be controlled is a cooperative robot with a dedicated controller; in a cooperative control system composed of multiple small assembly robotic arms, the target to be controlled is a small assembly robotic arm with a PLC controller.

[0023] S20: Based on the state variables of each target to be controlled, the non-linear terms of the state variables without time-delay effect, the non-linear terms of the state variables with time-delay effect, the state variables of its adjacent target to be controlled under the influence of proportional delay and distributed delay, and the saturation pulse controller, construct the state space equation of each target to be controlled.

[0024] Specifically, in the cooperative control system, the time-delay effect refers to the transmission delay of the pulse control signal to the target to be controlled or the system dependence of the target to be controlled. For example, the joint movement of a biped robot will have a lag due to mechanical inertia. Therefore, when constructing the state space equation of the target to be controlled, in addition to considering the state variables at the current moment, the state variables at its historical moments also need to be considered.

[0025] Meanwhile, since the saturation pulse controller for each target to be controlled needs to output a pulse control signal based on the corresponding target to be controlled and the state variables of adjacent targets to be controlled, and the transmission of the state variables of adjacent targets to be controlled takes time, that is, the current saturation pulse controller may output a pulse control signal based on the current state variables of the corresponding target to be controlled and the historical state variables of adjacent targets to be controlled. Therefore, the proportional delay refers to the delay time for the state variables of the target to be controlled to be transmitted to adjacent targets to be controlled. When constructing the state space equation of the target to be controlled, the influence of the state variables of adjacent targets to be controlled under the proportional delay is also considered; In addition, the proportional delay usually represents a fixed delay time for signal transmission. However, in actual application scenarios, the information transmission delay between adjacent targets to be controlled may fluctuate within a time period. Therefore, the distributed delay refers to the delay time interval for information transmission. In this application, in addition to considering the state variables of adjacent targets to be controlled under the proportional delay, the influence of the state variables of adjacent targets to be controlled under the distributed delay is also considered.

[0026] By introducing the influence of time-delay effect, proportional delay, and distributed delay on the state variables of the target to be controlled, this application can better simulate the communication delay phenomenon in the cooperative control system, adjust the dependence of the target to be controlled on the historical state and the states of adjacent targets to be controlled, and thus more accurately achieve multi-target cooperative control.

[0027] Specifically, the state variables of each target to be controlled can be a single state variable, such as speed, angular velocity, etc., or a vector composed of multiple state variables, such as a vector including speed, acceleration, and angular velocity.

[0028] S30: Weight and sum the state variables of each target to be controlled to obtain the synchronous target state equation of the cooperative control system; aiming at the initial state variables of each target to be controlled converging to the synchronous target state under the control of its saturation pulse controller, construct the initial state solution model of the target to be controlled.

[0029] S40: Solve the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variables of each target to be controlled are less than or equal to the maximum value of the initial state, and the gains of each saturation pulse controller are less than or equal to the maximum gain.

[0030] S50: The saturation pulse controllers of each target to be controlled output pulse control signals based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled to control each target to be controlled, so that the states of each target to be controlled reach the synchronous target state.

[0031] The multi-objective cooperative control method provided by this application uses a non-linear saturation function to construct a saturated pulse controller based on the state variable difference between the target to be controlled and its adjacent target to be controlled. The non-linear saturation function is used to limit the upper amplitude limit of the pulse control signal, thereby restricting the pulse control signal within the execution domain of the target to be controlled, avoiding the problem that the target to be controlled cannot effectively execute the control instruction. When constructing the state space equation of the target to be controlled, in addition to considering its state variables at the current moment, non-linear terms including its state variables at historical moments, state variable terms of its adjacent targets to be controlled under proportional delay, and state variable terms of its adjacent targets to be controlled under distributed delay are introduced, so as to comprehensively consider the influence of time delay effect, proportional delay and distributed delay on the state variables of the target to be controlled, in order to better simulate the communication delay phenomenon in the cooperative control system and more accurately reflect the dependence of the target to be controlled on historical states and the states of adjacent targets to be controlled. Further, after constructing the synchronous target state equation based on the state variables of all targets to be controlled, with the goal that the initial state variables of each target to be controlled converge to the synchronous target state under the control of its saturated pulse controller, an initial state solution model of the target to be controlled is constructed, so that the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller can be solved. Before synchronous control, by adjusting the initial states of each target to be controlled within the maximum value range and setting the gain of each saturated pulse controller to be less than the maximum gain, the initial state differences of multiple targets are matched with the adjustment range of the pulse controller. By constructing a saturated pulse controller whose output characteristics match the input characteristics of the target to be controlled, and combining the communication delay phenomenon in the actual application scenario, a state space equation that can accurately reflect the true state of the target to be controlled is constructed, and the maximum value of the initial state and the maximum gain of the saturated pulse controller that can make the states of multiple targets to be controlled effectively converge to the synchronous target state are obtained, so that each target to be controlled in the cooperative control system can reach the synchronous target state under the control of its saturated pulse controller, effectively realizing multi-objective cooperative control, and further enabling the cooperative control systems in various fields to accurately achieve the cooperative task goals under this cooperative control method.

[0032] Further, in some embodiments of this application, the saturated pulse controller of each target to be controlled is expressed as: , where represents the saturated pulse controller of the th target to be controlled; represents the non-linear saturation function; , represents the gain of the saturated pulse controller, represents the th target to be controlled and its The coupling weight between the targets to be controlled, denotes the state variable of the th target to be controlled at time t, denotes the state variable of the th target to be controlled at time t, denotes the difference in state variables between the th target to be controlled and its adjacent targets to be controlled at time t, denotes the number of adjacent targets to be controlled of the th target to be controlled; denotes the Dirac impulse function, denotes the th moment in the impulse control signal, denotes the th moment in the impulse control signal.

[0033] Specifically, , and , denotes the sign function, denotes the number of targets to be controlled in the cooperative control system; meanwhile, since the state variables of the targets to be controlled may be vectors containing various state information, the impulse control signal output by the saturated impulse controller also contains signals for controlling various states, that is, denotes the non - linear saturation function term of the n - th state variable, denotes the dimension of the state variable.

[0034] Furthermore, the state - space equations of each target to be controlled are expressed as: , where, denotes the state variable of the th target to be controlled at time t; denotes 's first - order derivative; denotes the decay matrix of the target to be controlled, denotes the state variable of the th target to be controlled at time t under the influence of the decay matrix; denotes the weight matrix of the non - linear term of the state variable without time - delay effect, denotes the non - linear term of the state variable at time t without time - delay effect; denotes the weight matrix of the non - linear term of the state variable with time - delay effect, denotes the non - linear term of the state variable at time t with time - delay effect, denotes 's time - delay at time denotes the proportional delay coupling strength between adjacent targets to be controlled, Indicates the first coupling matrix between the th target to be controlled and the th adjacent target to be controlled, Indicates the proportional delay inline coupling matrix, Indicates the state variable of the th target to be controlled adjacent to the th target to be controlled at time t under the influence of proportional delay, Indicates the proportional delay factor, Indicates the number of targets to be controlled adjacent to the th target to be controlled; Indicates the distributed delay coupling strength between adjacent targets to be controlled, Indicates the distributed delay inline coupling matrix, Indicates the second coupling matrix between the th target to be controlled and the th adjacent target to be controlled, Indicates the distributed delay at time Indicates the state variable of the th target to be controlled adjacent to the th target to be controlled at time t under the influence of distributed delay; Indicates the external disturbance at time t; Indicates the saturation pulse controller of the th target to be controlled.

[0035] Specifically, , Indicates the dimension of the state variable; , Indicates the decay vector corresponding to the th state variable; And both satisfy , , Indicates the constant of the Lipschitz continuity condition, And Indicates two input parameters; , ; ; , , if there is a connection from the th target to be controlled and the th target to be controlled, then , otherwise ; In addition, the diagonal element , .

[0036] The above state - space equation is explained below through a specific example: In the cooperative application scenario of biped robots, represents the state variables of the th robot at time t, including state information such as joint angles and angular velocities; represents the mechanical damping or energy dissipation characteristics of the robot joints; represents the non - linear dynamic characteristics of the current state of the robot joints, usually related to the control input of the motor or the joint drive characteristics; represents the influence of the past state of the robot joints on the current state, corresponding to communication delay or the historical dependence of the mechanical system. For example, the lag effect of joint movement caused by mechanical inertia; represents the interaction intensity of the robot based on the state at the historical proportional moment, represents the degree of dependence of the robot on the average state of adjacent robots over a past period of time; represents the joint force fluctuation caused by, for example, ground inequality interference at time t.

[0037] Furthermore, based on the weighted sum of the states of each control target, the synchronous target state equation of the cooperative control system includes: Construct a strongly - connected directed graph based on the adjacent relationships of all control targets, and obtain the generalized algebraic connectivity definition formula of the Laplacian matrix of the strongly - connected directed graph; Based on each eigenvalue in the left - null eigenvector in the generalized algebraic connectivity definition formula, obtain the state weights of each control target; Based on the state variables of each control target and their state weights, obtain the synchronous target state equation of the cooperative control system.

[0038] Specifically, in the strongly - connected directed graph, nodes represent control targets and directed edges represent the information transfer direction. Therefore, the communication topology in the multi - target cooperative system can be accurately described through the strongly - connected directed graph. At the same time, strong connectivity is a necessary condition for all control targets to tend to synchronization. If there are isolated nodes, it indicates that there are control targets in the cooperative control system that cannot exchange information with adjacent control targets, which will inevitably lead to the failure of cooperative control. Therefore, this application chooses to use a strongly - connected directed graph to reflect the topological structure of the cooperative control system. Furthermore, during the implementation of multi - target cooperation, the state vectors of each control target interfere differently with global synchronization. Therefore, it is necessary to assign weights to each control target. The Laplacian matrix is the core tool for analyzing graph connectivity, and the left - null eigenvector in the Laplacian matrix is Figure 1 the consensus vector. Therefore, the elements in the left - null eigenvector can be interpreted as the relative influence of nodes in the strongly - connected directed graph in cooperation. Therefore, this application uses the left - null eigenvector to assign weights to each control target.

[0039] Specifically, the definition formula of the generalized algebraic connectivity is expressed as: , where represents the definition formula of the generalized algebraic connectivity; represents the Laplacian matrix; represents the left zero eigenvector, ; represents the orthogonal vector of the left zero eigenmatrix; , represents the diagonal matrix; represents the transpose; ; The synchronization target state equation of the cooperative control system is expressed as: , where represents the synchronization target state equation of the cooperative control system; represents the state variable of the th target to be controlled at time t; represents the th eigenvalue in the left zero eigenvector in the definition formula of the generalized algebraic connectivity; represents the number of targets to be controlled in the cooperative control system.

[0040] The above synchronization target state equation is explained below through a specific example: Still taking the application scenario of a biped robot as an example, can represent global features such as the average stride and average walking speed of the team. By controlling the states of each robot to converge to , the consistency of the robot team's actions can be ensured, and formation chaos caused by individual differences can be avoided. For example, when a biped robot team needs to maintain a unified walking rhythm to pass through a narrow passage, at this time as the average state target can directly quantify the synchronization degree of the team, which is convenient for designing cooperative control strategies. When the elements in the left zero eigenvector are used as the weights of the state variables of each robot, is the only consistency equilibrium point of the cooperative control system, that is, if the states of all robots converge to , synchronization is achieved.

[0041] Furthermore, since the initial state variables of the targets to be controlled and the gains of the saturation pulse controllers will both affect whether the state variables of each target to be controlled can converge to the synchronization target state, it is necessary to obtain the maximum value of the initial state variables of the targets to be controlled (i.e., the maximum range of the attraction domain) and the maximum gains of the saturation pulse controllers.

[0042] Specifically, since the boundary of the region of attraction is convex and closed, that is, when the initial state variables of each target to be controlled are within this region of attraction, no matter from which direction they approach the synchronous target state (i.e., the equilibrium point), they will not diverge due to different initial values and cause synchronous failure. This makes it difficult to represent the region of attraction analytically. Therefore, based on the convex set approximation theory, this application transforms complex convex set constraints into algebraic problems through geometric transformation and parameter optimization, that is, introducing a polyhedron to approximately measure the ellipsoid, aiming that the polyhedron is always included within the ellipsoid under the scaling factor scaling, obtaining the maximum value of the scaling factor and the maximum value of the polyhedron, thereby obtaining the maximum value of the pulse control signal output by the saturated pulse controller and the maximum estimation of the region of attraction, and then obtaining the maximum gain estimation based on the maximum value of the saturated pulse control signal.

[0043] Specifically, aiming at the initial states of each target to be controlled converging to the synchronous target state under the control of its saturated pulse controller, constructing the initial state solution model of the target to be controlled includes: Approximating the range of the initial state variables of the target to be controlled as a polyhedron based on the convex set approximation theory, and approximating the pulse control signal output by the saturated pulse controller as the scaling factor; Aiming at maximizing the scaling factor, constructing the objective function; aiming at the polyhedron being included within the ellipsoid under the scaling factor scaling as the constraint condition, constructing the first constraint function; aiming at the pulse control signal being a saturated non - linear signal as the constraint condition, constructing the second constraint function; aiming at the gain of the saturated pulse controller being stable as the constraint condition, constructing the third constraint function; aiming at the state variables of the target to be controlled being stable under the influence of delay as the constraint condition, constructing the fourth constraint function; aiming at the weight of the distributed delay influence of adjacent targets to be controlled as the constraint condition, constructing the fifth constraint function; aiming at the weight of the proportional delay influence of adjacent targets to be controlled as the constraint condition, constructing the sixth constraint function; aiming at the cooperative control system being stable under the maximum distributed delay influence as the constraint condition, constructing the seventh constraint function; Based on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function, obtaining the initial state solution model of the target to be controlled.

[0044] Specifically, the objective function is expressed as: , where, represents the objective function; represents the scaling factor; The first constraint function is expressed as:

[0045] where, represents the polyhedron; represents the ellipsoid; The second constraint function is expressed as: , where represents the pulse reduction factor of the pulse control signal; represents the Laplacian matrix; represents the nonlinear matrix; represents the number of control targets to be controlled in the cooperative control system; , represents the state variable dimension of the control target to be controlled; represents the state variable weight matrix of the control target to be controlled; represents the parameter of the Lyapunov function; represents the Kronecker product; The third constraint function is expressed as: , where represents the state variable difference constraint of the control target to be controlled before and after the pulse control signal is applied, , represents the definition formula of the generalized algebraic connectivity, represents the saturation convex hull decomposition matrix, represents the gain of the saturation pulse controller, represents the nonlinear convex hull decomposition matrix; ; The fourth constraint function is expressed as: , where , represents the normalized Laplacian matrix, represents the first positive definite diagonal matrix, represents the first positive scalar parameter, represents the weight matrix of the state variable nonlinear term without time-delay effect, represents the weight matrix of the state variable nonlinear term with time-delay effect, represents the attenuation matrix of the control target to be controlled, represents the second positive definite diagonal matrix, represents the proportional delay coupling strength between adjacent control targets to be controlled, represents the communication topology matrix of the cooperative control system, represents the proportional delay inline coupling matrix, represents the distributed delay coupling strength between adjacent control targets to be controlled, represents the distributed delay inline coupling matrix, represents the first constraint of the delay coupling strength, represents the second constraint of the delay coupling strength, represents the distributed delay coupling term, represents the N - order identity matrix; The fifth constraint function is expressed as: , where, represents the topological matrix of the strongly connected directed graph; represents the second positive scalar parameter, which is used to adjust the influence of the distributed delay term on the stability of the cooperative control system; represents a positive definite matrix, which is used to construct the Lyapunov function; The sixth constraint function is expressed as: , where, represents the proportional delay influence weight factor; The seventh constraint function is expressed as: , where, represents the third positive scalar parameter, which is used to adjust the weight of the distributed delay term; represents the maximum value of the distributed delay.

[0046] Furthermore, since the initial state solution model of the above - mentioned control target contains multiple bilinear matrix inequalities, it is necessary to convert it into an inequality based on linear matrices first before solving it.

[0047] Specifically, solving the initial state solution model to obtain the maximum value of the initial state of the control target and the maximum gain of the saturated impulse controller includes: Performing convexification transformation on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function in the initial state solution model, and obtaining the target initial state solution model based on the transformed objective function and constraint functions; Solving the target initial state solution model to obtain the maximum value of the initial state of the control target and the maximum gain of the saturated impulse controller.

[0048] The specific steps of the convexification transformation include: 1. The first constraint function is equivalent to ; 2. The second constraint function is equivalent to ; 3. Using multiplying before and after with the third constraint function to obtain: , where, ; 4. Similarly, multiply the fourth constraint function with the matrix on the left and right, and it becomes: ,

[0049] where, , , , , , , , , ; 5. From the fifth, sixth, and seventh constraint functions, it can be seen that:

[0050] Let , , , , , , , , .

[0051] Furthermore, the transformed objective function is expressed as: , where, represents the transformed objective function; ; The transformed first constraint function is expressed as: , where, represents the member vector of the auxiliary polyhedron; ; represents the number of member vectors; The transformed second constraint function is expressed as: , where, ; The transformed third constraint function is expressed as: , where, ; The transformed fourth constraint function is expressed as: , where, ; , ; , ; , ; , ; , represents the proportional delay inner-coupling diagonal matrix; , represents the distributed delay inner-coupling diagonal matrix; The transformed fifth constraint function is expressed as: , where, ; The transformed sixth constraint function is expressed as: , The transformed seventh constraint function is expressed as: .

[0052] Furthermore, in this embodiment, the sufficient conditions for the local synchronization of multiple targets to be controlled under the saturation pulse controller are also derived to verify the effectiveness of the method provided in this application: First, based on the state space equations of each target to be controlled and the synchronization target state equation, the state error of each target to be controlled at time t is calculated, so as to obtain the state error equation of the cooperative control system; Specifically, the error vector composed of the state errors of each target to be controlled can be written as , represents dimensional Euclidean space.

[0053] Let represent the set of continuous functions from to , and use to represent initial value and , then the state error of the cooperative control system can be expressed in the following compact form:

[0054] where, the non-linear function , , and satisfies ; represents the N-column vector with all elements being 1; represents the N-order identity matrix.

[0055] Since is right continuous, that is , and at the pulse moment , when, exists, where represents the set of positive integers.

[0056] Describe the window center as and the window radius as Then represents the pulse moment of the random injection pulse control signal and is the pulse time window.

[0057] Next, derive the conditions for the locally synchronized realization of the target to be controlled under the action of the saturation pulse controller according to the state error of the cooperative control system: 1. Define the solution of the state error of the cooperative control system as and ; 2. According to it can be obtained that ; 3. Construct the Lyapunov function: ; 4. Verify , always holds. If not, there exists satisfying ; 5. Construct inf It is easy to obtain and ; 6. For, assume is a pulse instant, that is, , then according to: , , it can be obtained that: , where is a positive definite matrix; Since is contradictory to the definition of , therefore, cannot be the pulse moment.

[0058] 7. Assume is the solution of the state error of the cooperative control system. By setting the initial value , it is proved that for any : ; When , When calculating the derivative of \(V(t)\) along the state error trajectory of the cooperative control system, it is: , where represents the right derivative, which is used to characterize the one-sided derivative of a piecewise continuous function at a non-smooth point; represents the left zero eigenvector; Then, according to: , , , and , , it can be obtained that: ,

[0059] 8. Further, for any a comparison system with the general solution is established:

[0060] According to the parameter variation formula, can be calculated as an integral equation: , where is the Cauchy matrix of the following linear impulsive system: ,

[0061] The Cauchy matrix can be expressed as: ; where ; represents the upper bound of the impulsive interval; Substituting the Cauchy matrix into the integral equation, we get:

[0062] where ; represents the largest eigenvalue of

[0063] 9. Since , , , it is obvious that for the following equation holds: , where Indicates the exponential convergence rate of the systematic error; And, for , the above equation is still valid, that is , Assume that the above equation is not applicable to Then there is at least one moment Satisfying: , However, due to the inequality regarding Still holds for , that is: , Define: ; Then it can be calculated that: , To prove this contradiction, define:

[0064] Among them, , , Further calculate the derivative of to obtain ; Specifically, if and only if , it can be obtained that , where it can be through: , , Among them, , , Derive: ; In addition, for , Holds, indicating that for , Is increasing, and at the same time, for Holds, indicating that for , Is increasing.

[0065] Therefore, it can be obtained that , and it can be deduced that Has .

[0066] That is, when , Holds.

[0067] 10. When and , it can be obtained that:

[0068] where: ; Since and , it can be obtained that ; Let be set as: ; According to it can be proved that ; Construct as: , Obviously, and ; Therefore, is a monotonically decreasing function. For any , holds, that is: ; Furthermore, it can be deduced that: , This contradicts the above inequality about . Therefore, the above inequality is still valid for all . Let , there is: , This further shows that: , Therefore, it can be obviously deduced that for any , there is , where represents the maximum eigenvalue in the left zero eigenvector; This contradicts . Therefore, it can be deduced that holds for all .

[0069] From the above derivation process, it can be seen that the state error of the cooperative control system converges exponentially to the origin, and the convergence speed is , that is, the local exponential synchronization of the cooperative control system can be realized under the saturation pulse controller.

[0070] The effectiveness of the method provided by this application is verified through a specific example as follows: Step 1: The parameters of the target to be controlled are given as follows:

[0071] And , , , , , .

[0072] As Figure 2 shown, the state trajectory diagrams of each target to be controlled without using the cooperative control method provided by this application; Figure 3 shown, the state error trajectory diagrams of each target to be controlled without using the cooperative control method provided by this application; It can be seen from Figure 2 and Figure 3 that without any control input, it is impossible to achieve the synchronization of multiple targets to be controlled.

[0073] Step 2: Select , , select the polyhedron , , based on the initial state of the target to be controlled to solve the model, by selecting , 32, , , it can be deduced that , under this condition, the following other feasible solutions are as follows: , , , , , , , As Figure 4 shown, the state trajectory diagrams of each target to be controlled under the control of the method provided by this application; Figure 5 shown, the state error trajectory diagrams of each target to be controlled under the control of the method provided by this application; Figure 6 shown, the schematic diagram of the saturation pulse control signal output by the saturation pulse controller provided by this application. It can be seen from Figure 4 、 Figure 5 and Figure 6It can be seen that when the initial states of the to-be-controlled targets are all within the attraction domain and the gain of the saturation pulse controller is less than the maximum gain, the state variables of all the to-be-controlled targets will eventually converge to the target state, which further indicates that the multi-objective cooperative control method provided in this application can achieve multi-objective cooperative control.

[0074] Based on the multi-objective cooperative control method provided in the above embodiments, the embodiments of this application further provide a multi-objective cooperative control device, as Figure 7 shown. The device specifically includes: A saturation pulse controller construction module 10, configured to construct a saturation pulse controller for each to-be-controlled target by using a non-linear saturation function based on the state variable differences between each to-be-controlled target and its adjacent to-be-controlled targets in the cooperative control system; A state space equation construction module 20, configured to construct a state space equation for each to-be-controlled target based on the state variables of each to-be-controlled target, the non-linear terms of the state variables without time-delay effects, the non-linear terms of the state variables with time-delay effects, the state variables of its adjacent to-be-controlled targets affected by proportional delay and distributed delay, and the saturation pulse controller; A synchronization target construction module 30, configured to perform weighted summation on the state variables of each to-be-controlled target to obtain a synchronization target state equation of the cooperative control system; and construct an initial state solution model for the to-be-controlled target with the goal that the initial state variables of each to-be-controlled target converge to the synchronization target state under the control of its saturation pulse controller; A parameter acquisition module 40, configured to solve the initial state solution model to obtain the maximum value of the initial state of the to-be-controlled target and the maximum gain of the saturation pulse controller, so that the initial state variables of each to-be-controlled target are less than or equal to the maximum value of the initial state, and the gains of each saturation pulse controller are less than or equal to the maximum gain; A cooperative control module 50, configured to output a pulse control signal based on the saturation pulse controllers of each to-be-controlled target and the real-time state variables of each to-be-controlled target and its adjacent to-be-controlled targets to control each to-be-controlled target, so that the states of each to-be-controlled target reach the synchronization target state.

[0075] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for realizing the functions specified in the flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or a device for realizing the functions specified in multiple blocks. These computer program instructions can 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 generate a manufactured article including an instruction device, and the instruction device realizes the functions specified in the flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or a device for realizing the functions specified in multiple blocks. These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in the flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or a device for realizing the functions specified in multiple blocks.

[0076] Obviously, the above embodiments are only examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A multi-objective collaborative control method, characterized in that Including: Constructing a saturation pulse controller for each target to be controlled based on the difference in state variables between each target to be controlled and its adjacent target to be controlled within a cooperative control system by using a non-linear saturation function; Constructing a state space equation for each target to be controlled based on the state variables of each target to be controlled, the non-linear terms of the state variables without time-delay effect, the non-linear terms of the state variables with time-delay effect, the state variables of its adjacent target to be controlled under the influence of proportional delay and distributed delay, and the saturation pulse controller; Weighted summing the state variables of each target to be controlled to obtain a synchronous target state equation of the cooperative control system; Constructing an initial state solution model for the target to be controlled with the goal that the initial state variables of each target to be controlled converge to the synchronous target state under the control of its saturation pulse controller; Solving the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variables of each target to be controlled are less than or equal to the maximum value of the initial state, and the gains of each saturation pulse controller are less than or equal to the maximum gain; The saturation pulse controller of each target to be controlled outputs a pulse control signal based on the real-time state variables of each target to be controlled and its adjacent target to be controlled to control each target to be controlled, so that the states of each target to be controlled reach the synchronous target state.

2. The multi-objective collaborative control method according to claim 1, characterized in that The saturation pulse controller of each target to be controlled is expressed as: ， Among them, represents the saturation pulse controller for the th target to be controlled; represents the non - linear saturation function; , represents the gain of the saturation pulse controller, represents the th target to be controlled and the coupling weight between it and the th adjacent target to be controlled, represents the state variable of the th target to be controlled at time t, represents the state variable of the th target to be controlled at time t, represents the difference in state variables between the th target to be controlled and its adjacent target to be controlled at time t, represents the number of adjacent targets to be controlled of the th target to be controlled; represents the Dirac pulse function, represents the th moment in the pulse control signal, represents the th moment in the pulse control signal.

3. The multi-objective collaborative control method according to claim 1, wherein The state space equation of each target to be controlled is expressed as: ， Among them, represents the state variable of the th target to be controlled at time t; represents the first derivative of; represents the attenuation matrix of the target to be controlled, represents the th state variable of the target to be controlled at time t under the influence of the attenuation matrix; represents the weight matrix of the state variable nonlinear term without time-delay effect, represents the state variable nonlinear term at time t without time-delay effect; represents the weight matrix of the state variable nonlinear term with time-delay effect, represents the state variable nonlinear term at time t with time-delay effect, represents the time-delay at time; represents the proportional delay coupling strength between adjacent targets to be controlled, represents the th first coupling matrix between the th target to be controlled and its adjacent th target to be controlled; represents the proportional delay inline coupling matrix, represents the th state variable of the th target to be controlled adjacent to the th target to be controlled at time t under the influence of proportional delay, represents the proportional delay factor, represents the distributed delay coupling strength between adjacent targets to be controlled, represents the distributed delay inline coupling matrix, represents the th second coupling matrix between the th target to be controlled and its adjacent represents the distributed delay at time; represents the th state variable of the th target to be controlled adjacent to the represents the external disturbance at time t; represents the th saturation pulse controller of the target to be controlled.

4. The multi-objective collaborative control method according to claim 1, characterized in that Weighted summing based on the states of each target to be controlled to obtain a synchronous target state equation of the cooperative control system including: Constructing a strongly connected digraph based on the adjacent relationships of all targets to be controlled, and obtaining a generalized algebraic connectivity definition formula of the Laplacian matrix of the strongly connected digraph; Obtaining the state weights of each target to be controlled based on the eigenvalues in the left null eigenvector in the generalized algebraic connectivity definition formula; Obtaining a synchronous target state equation of the cooperative control system based on the state variables of each target to be controlled and its state weights.

5. The multi-objective collaborative control method according to claim 4, wherein The generalized algebraic connectivity definition formula is expressed as: ， Among them, represents the definition formula of the generalized algebraic connectivity; represents the Laplacian matrix; represents the left zero eigenvector, ; represents the orthogonal vector of the left zero eigenmatrix; , represents the diagonal matrix; represents the transpose; ; The synchronous target state equation of the cooperative control system is expressed as: ， Among them, represents the synchronous target state equation of the cooperative control system; represents the state variable of the th target to be controlled at time t; represents the th eigenvalue in the left zero eigenvector in the definition formula of the generalized algebraic connectivity; represents the number of targets to be controlled within the cooperative control system.

6. The multi-objective collaborative control method according to claim 1, wherein Constructing an initial state solution model for the target to be controlled with the goal that the initial state of each target to be controlled converges to the synchronous target state under the control of its saturation pulse controller including: Approximating the range of the initial state variables of the target to be controlled as a polyhedron based on the convex set approximation theory, and approximating the pulse control signal output by the saturation pulse controller as a scaling factor; Taking the maximization of the scaling factor as the goal, construct the objective function; taking the polyhedron being contained within the ellipsoid under the scaling factor scaling as the constraint condition, construct the first constraint function; taking the pulse control signal as a saturated nonlinear signal as the constraint condition, construct the second constraint function; taking the gain stability of the saturated pulse controller as the constraint condition, construct the third constraint function; taking the state variables of the target to be controlled being stable under the influence of delay as the constraint condition, construct the fourth constraint function; taking the distributed delay influence weight of adjacent targets to be controlled as the constraint condition, construct the fifth constraint function; taking the proportional delay influence weight of adjacent targets to be controlled as the constraint condition, construct the sixth constraint function; taking the cooperative control system being stable under the maximum distributed delay influence as the constraint condition, construct the seventh constraint function; Based on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function, obtain the initial state solution model of the target to be controlled.

7. The multi-objective collaborative control method according to claim 6, wherein The objective function is expressed as: ， Among them, represents the objective function; represents the scaling factor; The first constraint function is expressed as: ， Among them, represents a polyhedron; represents an ellipsoid; The second constraint function is expressed as: ， Among them, represents the pulse reduction factor of the pulse control signal; represents the Laplacian matrix; represents the nonlinear matrix; represents the number of control targets to be controlled within the cooperative control system; , represents the state variable dimension of the control target to be controlled; represents the state variable weight matrix of the control target to be controlled; represents the parameter of the Lyapunov function; represents the Kronecker product; The third constraint function is expressed as: ， Among them, represents the state variable difference constraint of the target to be controlled before and after being controlled by the pulse control signal, , represents the definition formula of the generalized algebraic connectivity, represents the saturation convex hull decomposition matrix, represents the gain of the saturation pulse controller, represents the non - linear convex hull decomposition matrix; ; The fourth constraint function is expressed as: ， Among them, , represents the normalized Laplacian matrix, represents the first positive definite diagonal matrix, represents the first positive scalar parameter, represents the weight matrix of the state variable nonlinear term without time-delay effect, represents the weight matrix of the state variable nonlinear term with time-delay effect, represents the decay matrix of the target to be controlled, represents the second positive definite diagonal matrix, represents the proportional delay coupling strength between adjacent targets to be controlled, represents the communication topology matrix of the cooperative control system, represents the proportional delay inline coupling matrix, represents the distributed delay coupling strength between adjacent targets to be controlled, represents the distributed delay inline coupling matrix, represents the first constraint of the delay coupling strength, represents the second constraint of the delay coupling strength, represents the distributed delay coupling term, represents the N-order identity matrix; The fifth constraint function is expressed as: ， Among them, represents the topological matrix of a strongly connected digraph; represents a second positive scalar parameter; represents a positive definite matrix; The sixth constraint function is expressed as: ， Among them, represents the proportional delay impact weight factor; The seventh constraint function is expressed as: ， Among them, represents the third positive scalar parameter; represents the maximum value of the distributed delay.

8. The multi-objective collaborative control method according to claim 7, wherein Solving the initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller includes: Perform convexification transformation on the objective function, the first constraint function, the second constraint function, the third constraint function, the fourth constraint function, the fifth constraint function, the sixth constraint function, and the seventh constraint function in the initial state solution model, and obtain the target initial state solution model based on the transformed objective function and constraint functions; Solve the target initial state solution model to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller.

9. The multi-objective collaborative control method according to claim 8, wherein The transformed objective function is expressed as: ， Among them, represents the objective function after conversion; ; The transformed first constraint function is expressed as: ， Among them, represents the member vector of the auxiliary polyhedron; ; represents the number of member vectors; The transformed second constraint function is expressed as: ， Among them, ; The transformed third constraint function is expressed as: ， Among them, ; The transformed fourth constraint function is expressed as: ， Among them, ; , ; , ; , ; , ; , represents the proportional delay internal coupling diagonal matrix; , represents the distributed delay internal coupling diagonal matrix; The transformed fifth constraint function is expressed as: ， Among them, ; The transformed sixth constraint function is expressed as: ， The transformed seventh constraint function is expressed as: 。 10. A multi-objective collaborative control device, characterized in that, Including: A saturated pulse controller construction module, configured to use a nonlinear saturation function to construct a saturated pulse controller for each target to be controlled based on the state variable differences between each target to be controlled in the cooperative control system and its adjacent targets to be controlled; A state space equation construction module, configured to construct a state space equation for each target to be controlled based on the state variables of each target to be controlled, the state variable nonlinear terms without time delay effects, the state variable nonlinear terms with time delay effects, the state variables of its adjacent targets to be controlled under the influence of proportional delay and distributed delay, and the saturated pulse controller; A synchronization target construction module, configured to perform weighted summation on the state variables of each target to be controlled to obtain a synchronization target state equation of the cooperative control system; taking the initial state variables of each target to be controlled converging to the synchronization target state under the control of its saturated pulse controller as the goal, construct an initial state solution model of the target to be controlled. A parameter acquisition module, which is used to solve the initial state maximum value of the to-be-controlled target and the maximum gain of the saturation pulse controller by solving the initial state solution model, so that the initial state variables of each to-be-controlled target are less than or equal to the initial state maximum value, and the gains of each saturation pulse controller are less than or equal to the maximum gain; A cooperative control module, which is used for the saturation pulse controllers of each to-be-controlled target to output pulse control signals based on the real-time state variables of each to-be-controlled target and its adjacent to-be-controlled targets to control each to-be-controlled target, so that the states of each to-be-controlled target reach the synchronous target state.

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