Multi-objective collaborative control method and device

Abstract

The present invention belongs to the technical field of collaborative control and relates to a multi-objective collaborative control method and device, which utilizes a nonlinear saturation function to construct a saturated pulse controller for each target to be controlled; constructs a state space equation for each target to be controlled, thereby obtaining a synchronous target state equation of the collaborative control system; takes the initial state variables of each target to be controlled to converge to the synchronous target state under the control of its saturated pulse controller as the goal, constructs an initial state solution model for the target to be controlled, thereby solving and obtaining the initial state maximum value of the target to be controlled and the maximum gain of the saturated pulse controller, and sets the initial state variables of each target to be controlled and the gain of each saturated pulse controller; inputs the real-time state variables of each target to be controlled and adjacent targets to be controlled into each saturated pulse controller, thereby controlling each target to be controlled so that the state of each target to be controlled reaches the synchronous target state, thereby realizing multi-objective collaborative control.

Description

Technical Field

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

[0002] Multi-objective collaborative control refers to the process of coordinating the behaviors of multiple targets within a collaborative control system to synchronize them under mutual influence and constraints. This control method is widely used in fields such as robotic swarms, intelligent transportation, and industrial automation. For example, when a collaborative control system composed of multiple robots performs a performance task, it is necessary to synchronize the movements of the joints and limbs of the multiple robots to ensure the consistency of their movements. When a collaborative control system composed of multiple automated guided vehicles performs a material handling task, it is necessary to adjust the paths of each automated guided vehicle in real time to achieve synchronized obstacle avoidance when moving warehouse materials. When a collaborative control system composed of a fleet of unmanned vehicles performs a synchronized driving task, it is necessary to coordinate the speeds of each unmanned vehicle to maintain a constant distance between the fleets.

[0003] Since pulse control signals have advantages such as fast response, strong robustness, and simple structure, pulse control signals are often used in the prior art to control the speed, acceleration, angular velocity, and other motion states of each target in a collaborative control system, thereby achieving state synchronization of multiple targets. Specifically, the existing multi-target collaborative 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 simultaneously 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 instruction 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 state of each target converges to the target synchronization state, thereby achieving collaborative control of multiple targets.

[0004] However, in a collaborative control system, the state of each target is often affected by inertia and there is often a lag in the state of adjacent targets, that is, it takes time to transmit the state information of adjacent targets, which causes the saturated pulse controller to output a pulse control signal based on the difference between the state of the target at the current moment and the state of the adjacent targets at the historical moment, thereby causing the state of each target at the current moment to be affected by the historical state of the adjacent targets. In addition, in actual application scenarios, there is also a distributed delay in the state of adjacent targets, that is, the transmission time of the state information of adjacent targets may fluctuate within a time period, causing the state of each target at the current moment to be affected by the state of the adjacent targets in the historical time period. The existing collaborative control method only considers the state of the target and the adjacent targets at the current time when constructing the state space equation of the target. The state information of each target is obtained by ignoring the influence of state lag, proportional delay and distribution delay on the target state, thus failing to accurately reflect the actual state of each target, making it impossible for the pulse controller to output accurate pulse control signals, thereby affecting the synchronization of multiple targets. At the same time, the existing collaborative control method ignores the matching problem between the output characteristics of the pulse controller and the input characteristics of the target when constructing the pulse controller, 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 failing to achieve multi-target synchronization. In addition, when the initial states of multiple targets differ too much, it will exceed the adjustment range of the pulse controller, resulting in the inability to adjust the states of multiple targets to the target synchronization state, thus causing the failure of multi-target collaborative control.

[0005] In summary, the existing multi-objective collaborative control methods are unable to effectively coordinate and control multiple objectives, thereby achieving synchronization of multiple objectives. As a result, when this multi-objective control method is applied to collaborative control systems in various fields, it is impossible to accurately achieve the collaborative task goals. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problem that the multi-objective collaborative control method in the prior art is unable to effectively collaboratively control multiple objectives, so as to synchronize multiple objectives, which in turn leads to the inability to accurately achieve the collaborative task goals when this multi-objective control method is applied to collaborative control systems in various fields.

[0007] To solve the above technical problems, the present invention provides a multi-objective collaborative control method, comprising:

[0008] A saturation pulse controller for each target to be controlled is constructed using a nonlinear saturation function based on the state variable difference between each target to be controlled and its adjacent targets in the cooperative control system.

[0009] Based on the state variables of each target to be controlled, the nonlinear terms of the state variables without time lag effects, the nonlinear terms of the state variables with time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and the saturated pulse controller, the state space equations of each target to be controlled are constructed;

[0010] The state variables of each target to be controlled are weighted and summed to obtain the synchronization target state equation of the cooperative control system. With the goal of ensuring that the initial state variables of each target to be controlled converge to the synchronization target state under the control of its saturated pulse controller, an initial state solution model for the target to be controlled is constructed.

[0011] Solving the initial state solution model to obtain the maximum initial state value of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variable of each target to be controlled is less than or equal to the maximum initial state value, and the gain of each saturation pulse controller is less than or equal to the maximum gain;

[0012] The saturation pulse controller of each target to be controlled outputs a pulse control signal to control each target to be controlled based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

[0013] Preferably, the saturation pulse controller of each target to be controlled is expressed as:

[0014] ,

[0015] in, Indicates the A saturation pulse controller for a target to be controlled; represents a nonlinear saturation function; , represents the gain of the saturation pulse controller, Indicates the The target to be controlled and its adjacent The coupling weights between the controlled targets are: Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variable difference between a target to be controlled and its adjacent target to be controlled is: Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the Dirac impulse function, Indicates the first A moment, Indicates the first A moment.

[0016] Preferably, the state space equation of each target to be controlled is expressed as:

[0017] ,

[0018] in, Indicates the time t The state variables of the target to be controlled; express The first derivative of ; represents the attenuation matrix of the target to be controlled, Indicates the The state variables of the target to be controlled at time t under the influence of the attenuation matrix; represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the nonlinear term of the state variable at time t without the time lag effect; represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the nonlinear term of the state variable at time t including the time lag effect, express the time lag of moments; represents the proportional delay coupling strength between adjacent controlled targets, Indicates the The target to be controlled and its adjacent The first coupling matrix between the targets to be controlled, represents the proportional delay inline coupling matrix, Indicates The adjacent target to be controlled The state variable of the target to be controlled at time t under the influence of proportional delay, represents the proportional delay factor, Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the distributed delay coupling strength between adjacent controlled targets, represents the distributed delay inline coupling matrix, Indicates the The target to be controlled and its adjacent The second coupling matrix between the targets to be controlled, express The distribution delay of time, Indicates The adjacent target to be controlled The state variables of the target to be controlled at time t under the influence of distributed delay; represents the external interference at time t; Indicates the A saturation pulse controller for a target to be controlled.

[0019] Preferably, based on the weighted sum of the states of the various targets to be controlled, the synchronization target state equation of the collaborative control system is obtained, which includes:

[0020] A strongly connected directed graph is constructed based on the neighboring relationships of all the targets to be controlled, and the generalized algebraic connectivity definition of the Laplacian matrix of the strongly connected directed graph is obtained;

[0021] Based on the eigenvalues ​​of the left zero eigenvector in the definition of generalized algebraic connectivity, the state weights of the targets to be controlled are obtained.

[0022] Based on the state variables and state weights of each target to be controlled, the synchronization target state equation of the cooperative control system is obtained.

[0023] Preferably, the definition of generalized algebraic connectivity is expressed as:

[0024] ,

[0025] in, represents the definition of generalized algebraic connectivity; represents the Laplace matrix; represents the left zero eigenvector, ; represents the orthogonal vector of the left zero eigenmatrix; , represents a diagonal matrix; represents transpose; ;

[0026] The synchronization target state equation of the cooperative control system is expressed as:

[0027] ,

[0028] in, Represents the synchronization target state equation of the cooperative control system; Indicates the time t The state variables of the target to be controlled; represents the first left zero eigenvector in the definition of generalized algebraic connectivity. eigenvalues; Indicates the number of targets to be controlled in the collaborative control system.

[0029] Preferably, with the goal of allowing the initial state of each target to be controlled to converge 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:

[0030] Based on the convex set approximation theory, the initial state variable range of the target to be controlled is approximated as a polyhedron, and the pulse control signal output by the saturated pulse controller is approximated as a scaling factor;

[0031] With the maximization of the scaling factor as the goal, an objective function is constructed; with the polyhedron being contained in the ellipsoid under the scaling of the scaling factor as the constraint condition, a first constraint function is constructed; with the pulse control signal being a saturated nonlinear signal as the constraint condition, a second constraint function is constructed; with the gain stability of the saturated pulse controller as the constraint condition, a third constraint function is constructed; with the state variable of the target to be controlled being stable under the influence of delay as the constraint condition, a fourth constraint function is constructed; with the distributed delay influence weight of adjacent targets to be controlled as the constraint condition, a fifth constraint function is constructed; with the proportional delay influence weight of adjacent targets to be controlled as the constraint condition, a sixth constraint function is constructed; with the stability of the cooperative control system under the influence of the maximum distributed delay as the constraint condition, a seventh constraint function is constructed;

[0032] 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, an initial state solution model of the target to be controlled is obtained.

[0033] Preferably, the objective function is expressed as:

[0034] ,

[0035] in, represents the objective function; represents the scaling factor;

[0036] The first constraint function is expressed as:

[0037] ,

[0038] in, Represents a polyhedron; represents an ellipsoid;

[0039] The second constraint function is expressed as:

[0040] ,

[0041] in, represents the pulse reduction factor of the pulse control signal; represents the Laplace matrix; represents a nonlinear matrix; Indicates the number of targets to be controlled in the collaborative control system; , The dimension of the state variable representing the target to be controlled; The state variable weight matrix representing the target to be controlled; represents the parameters of the Lyapunov function; represents the Kronecker product;

[0042] The third constraint function is expressed as:

[0043] ,

[0044] in, It represents the state variable difference constraint of the target to be controlled before and after the pulse control signal is controlled. , represents the definition of generalized algebraic connectivity, represents the saturated convex hull decomposition matrix, represents the gain of the saturation pulse controller, represents the nonlinear convex hull decomposition matrix; ;

[0045] The fourth constraint function is expressed as:

[0046] ,

[0047] in, , represents the normalized Laplacian matrix, represents the first positive definite diagonal matrix, represents the first positive scalar parameter, represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the attenuation matrix of the target to be controlled, represents the second positive definite diagonal matrix, represents the proportional delay coupling strength between adjacent controlled targets, represents the communication topology matrix of the collaborative control system, represents the proportional delay inline coupling matrix, represents the distributed delay coupling strength between adjacent controlled targets, represents the distributed delay inline coupling matrix, The first constraint representing the delay coupling strength, The second constraint representing the delay coupling strength, represents the distributed delay coupling term, represents the N-order identity matrix;

[0048] The fifth constraint function is expressed as:

[0049] ,

[0050] in, A topological matrix representing a strongly connected directed graph; represents the second positive scalar parameter; represents a positive definite matrix;

[0051] The sixth constraint function is expressed as:

[0052] ,

[0053] in, represents the proportional delay impact weight factor;

[0054] The seventh constraint function is expressed as:

[0055] ,

[0056] in, represents the third positive scalar parameter; Indicates the maximum value of the distribution delay.

[0057] Preferably, solving the initial state solution model to obtain the initial state maximum value of the target to be controlled and the maximum gain of the saturation pulse controller includes:

[0058] Performing convex 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 function;

[0059] The target initial state solution model is solved to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller.

[0060] Preferably, the converted objective function is expressed as:

[0061] ,

[0062] in, represents the objective function after transformation; ;

[0063] The converted first constraint function is expressed as:

[0064] ,

[0065] in, represents the membership vector of the auxiliary polyhedron; ; represents the number of member vectors;

[0066] The converted second constraint function is expressed as:

[0067] ,

[0068] in, ;

[0069] The converted third constraint function is expressed as:

[0070] ,

[0071] in, ;

[0072] The converted fourth constraint function is expressed as:

[0073] ,

[0074] in, ; , ; , ; , ; , ; , represents the scaled delay internal coupling diagonal matrix; , represents the distributed delay internal coupling diagonal matrix;

[0075] The converted fifth constraint function is expressed as:

[0076] ,

[0077] in, ;

[0078] The converted sixth constraint function is expressed as:

[0079] ,

[0080] The converted seventh constraint function is expressed as:

[0081] .

[0082] The present invention also provides a multi-objective collaborative control device, comprising:

[0083] A saturation pulse controller construction module is used 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 targets to be controlled in the cooperative control system using a nonlinear saturation function;

[0084] A state-space equation construction module is used to construct the state-space equation of each target to be controlled based on the state variables of each target to be controlled, the nonlinear terms of the state variables without time lag effects, the nonlinear terms of the state variables with time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and a saturated pulse controller;

[0085] The synchronization target construction module is used to perform weighted summation of the state variables of each target to be controlled to obtain the synchronization target state equation of the coordinated control system; with the goal of ensuring that the initial state variables of each target to be controlled converge to the synchronization target state under the control of its saturated pulse controller, an initial state solution model for the target to be controlled is constructed;

[0086] 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 variable of each target to be controlled is less than or equal to the maximum value of the initial state, and the gain of each saturation pulse controller is less than or equal to the maximum gain;

[0087] The collaborative control module is used for the saturation pulse controller of each target to be controlled. Based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, the controller outputs a pulse control signal to control each target to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

[0088] The multi-objective collaborative control method provided in this application has the following beneficial effects:

[0089] First, the present application utilizes a nonlinear saturation function to construct a saturated pulse controller based on the state variable difference between the target to be controlled and its adjacent targets to be controlled, and utilizes the nonlinear saturation function to limit the upper limit of the amplitude of the pulse control signal, thereby limiting the pulse control signal to 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, it also introduces nonlinear terms containing its state variables at historical moments, state variable terms of its adjacent targets to be controlled under delay proportions, and state variable terms of its adjacent targets to be controlled under distributed delays, thereby comprehensively considering the influence of time lag effects, proportional delays and distributed delays on the state variables of the target to be controlled, so as to better simulate the coordination The communication delay phenomenon in the same control system more accurately reflects the dependence of the target to be controlled on the historical state and the state of the adjacent targets to be controlled; further, after constructing the synchronous target state equation based on the state variables of all targets to be controlled, the application takes the initial state variables of each target to be controlled to converge to the synchronous target state under the control of its saturated pulse controller as the goal, and constructs an initial state solution model for the target to be controlled, 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 performing synchronous control, the initial state of each target to be controlled is adjusted to the maximum value range, and the gain of each saturated pulse controller is set to be less than the maximum gain, so that the initial state differences of multiple targets match 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 actual application scenarios, a state-space equation that can accurately reflect the true state of the target to be controlled is constructed, and the initial state maximum value 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. As a result, each target to be controlled in the collaborative control system can reach the synchronous target state under the control of its saturated pulse controller, effectively realizing multi-target collaborative control, and thus enabling collaborative control systems in various fields to accurately achieve collaborative task goals under this collaborative control method. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0091] Figure 1 Flowchart of the multi-objective collaborative control method provided for this application;

[0092] Figure 2 A state trajectory diagram of each target to be controlled when the collaborative control method provided by this application is not used;

[0093] Figure 3A state error trajectory diagram of each target to be controlled when the coordinated control method provided by the present application is not used;

[0094] Figure 4 A state trajectory diagram of each target to be controlled under the control of the method provided in this application;

[0095] Figure 5 A state error trajectory diagram of each target to be controlled under the control of the method provided in this application;

[0096] Figure 6 Schematic diagram of the saturation pulse control signal output by the saturation pulse controller provided in this application;

[0097] Figure 7 Schematic diagram of the structure of the multi-objective collaborative control device provided in this application. DETAILED DESCRIPTION

[0098] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0099] See also Figure 1 , Figure 1 The figure shows a flow chart of the multi-objective collaborative control method provided by this application, which specifically includes:

[0100] S10: constructing 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 targets to be controlled in the cooperative control system using a nonlinear saturation function.

[0101] Specifically, a collaborative control system includes multiple targets to be controlled, each of which is a mechanical system equipped with a PLC controller or a dedicated controller (such as UR's PolyScope). For example, in a collaborative control system consisting of multiple collaborative robots, the targets to be controlled are collaborative robots equipped with dedicated controllers; in a collaborative control system consisting of multiple small assembly manipulators, the targets to be controlled are small assembly manipulators equipped with PLC controllers.

[0102] S20: Construct the state space equations of each target to be controlled based on the state variables of each target to be controlled, the nonlinear terms of the state variables without time lag effects, the nonlinear terms of the state variables with time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and the saturated pulse controller.

[0103] Specifically, in collaborative control systems, the time lag 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 bipedal robot will cause lag due to mechanical inertia. Therefore, when constructing the state space equation of the target to be controlled, in addition to considering its state variables at the current moment, its state variables at historical moments must also be considered.

[0104] At the same time, since the saturation pulse controller of each target to be controlled needs to output a pulse control signal based on the state variables of its corresponding target to be controlled and the adjacent targets to be controlled, and the transmission of the state variables of the 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 its corresponding target to be controlled and the historical state variables of the adjacent targets to be controlled, the proportional delay refers to the delay time for the state variables of the target to be controlled to be transmitted to the adjacent targets to be controlled. When constructing the state space equation of the target to be controlled, the influence of the state variables of its adjacent targets to be controlled under the delay ratio is also considered;

[0105] In addition, proportional delay usually refers to 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, distributed delay refers to the delay time interval for information transmission. In addition to considering the state variables of adjacent targets to be controlled under proportional delay, this application also considers the influence of the state variables of adjacent targets to be controlled under distributed delay.

[0106] By introducing the influence of time lag 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 collaborative control system, adjust the dependence of the target to be controlled on the historical state and the state of adjacent targets to be controlled, and thus more accurately realize multi-target collaborative control.

[0107] Specifically, the state variable of each target to be controlled may be a single state variable, such as velocity, angular velocity, etc., or a vector composed of multiple state variables, such as a vector including velocity, acceleration and angular velocity.

[0108] S30: performing weighted summation of the state variables of each target to be controlled to obtain the synchronous target state equation of the cooperative control system; constructing an initial state solution model for the target to be controlled with the goal of ensuring 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.

[0109] S40: Solve the initial state solution model to obtain the initial state maximum value of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variable of each target to be controlled is less than or equal to the initial state maximum value, and the gain of each saturation pulse controller is less than or equal to the maximum gain.

[0110] S50: The saturation pulse controller of each target to be controlled outputs a pulse control signal to control each target to be controlled based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

[0111] The multi-objective collaborative control method provided in the present application utilizes a nonlinear saturation function to construct a saturated pulse controller based on the state variable difference of the target to be controlled and its adjacent targets to be controlled, and utilizes the nonlinear saturation function to limit the upper limit of the amplitude of the pulse control signal, thereby limiting the pulse control signal to 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, it also introduces nonlinear terms containing its state variables at historical moments, state variable terms of its adjacent targets to be controlled under delay proportions, and state variable terms of its adjacent targets to be controlled under distributed delays, thereby comprehensively considering the influence of time lag effects, proportional delays and distributed delays on the state variables of the target to be controlled, so as to better The invention can better simulate the communication delay phenomenon in the collaborative control system and more accurately reflect the dependence of the target to be controlled on the historical state and the state of the adjacent target to be controlled. Furthermore, after constructing the synchronization target state equation based on the state variables of all the targets to be controlled, the application takes the initial state variables of each target to be controlled to converge to the synchronization target state under the control of its saturated pulse controller as the goal, and constructs an initial state solution model for the target to be controlled, 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 performing the synchronization control, the initial state of each target to be controlled is adjusted to the maximum value range, and the gain of each saturated pulse controller is set to be less than the maximum gain, so that the initial state difference of multiple targets matches 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 actual application scenarios, a state-space equation that can accurately reflect the true state of the target to be controlled is constructed, and the initial state maximum value 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. As a result, each target to be controlled in the collaborative control system can reach the synchronous target state under the control of its saturated pulse controller, effectively realizing multi-target collaborative control, and thus enabling collaborative control systems in various fields to accurately achieve collaborative task goals under this collaborative control method.

[0112] Furthermore, in some embodiments of the present application, the saturation pulse controller of each target to be controlled is expressed as:

[0113] ,

[0114] in, Indicates the A saturation pulse controller for a target to be controlled; represents a nonlinear saturation function; , represents the gain of the saturation pulse controller, Indicates the The target to be controlled and its adjacent The coupling weights between the controlled targets are: Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variable difference between a target to be controlled and its adjacent target to be controlled is: Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the Dirac impulse function, Indicates the first A moment, Indicates the first A moment.

[0115] Specifically, ,and , represents the symbolic function, represents the number of targets to be controlled in the cooperative control system; at the same time, since the state variable of the target to be controlled may be a vector containing multiple state information, the pulse control signal output by the saturated pulse controller also contains signals for controlling various states, that is, represents the nonlinear saturation function term of the nth state variable, Represents the dimension of the state variable.

[0116] Furthermore, the state space equation of each target to be controlled is expressed as:

[0117] ,

[0118] in, Indicates the time t The state variables of the target to be controlled; express The first derivative of ; represents the attenuation matrix of the target to be controlled, Indicates the The state variables of the target to be controlled at time t under the influence of the attenuation matrix; represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the nonlinear term of the state variable at time t without the time lag effect; represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the nonlinear term of the state variable at time t including the time lag effect, express the time lag of moments; represents the proportional delay coupling strength between adjacent controlled targets, Indicates the The target to be controlled and its adjacent The first coupling matrix between the targets to be controlled, represents the proportional delay inline coupling matrix, Indicates The adjacent target to be controlled The state variable of the target to be controlled at time t under the influence of proportional delay, represents the proportional delay factor, Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the distributed delay coupling strength between adjacent controlled targets, represents the distributed delay inline coupling matrix, Indicates the The target to be controlled and its adjacent The second coupling matrix between the targets to be controlled, express The distribution delay of time, Indicates The adjacent target to be controlled The state variables of the target to be controlled at time t under the influence of distributed delay; represents the external interference at time t; Indicates the A saturation pulse controller for a target to be controlled.

[0119] Specifically, , Represents the dimension of the state variable; , Indicates the corresponding The decay vector of the state variables; and All satisfied , , A constant representing the Lipschitz continuity condition, and Represents two input parameters; , ; ; 、 , if from the The target to be controlled and If there is a connection between the target to be controlled, ,otherwise ; In addition, the diagonal elements , .

[0120] The following is an explanation of the above state space equation through a specific example:

[0121] In the application scenario of bipedal robot collaboration, Indicates the time t The state variables of each robot include the state information of each joint angle, angular velocity, etc. Represents the mechanical damping or energy dissipation characteristics of the robot joint; The nonlinear dynamic characteristics of the robot joint's current state, usually related to the motor's control input or joint drive characteristics; Represents the influence of the past state of the robot joint on the current state, corresponding to communication delay or historical dependence of the mechanical system, such as the lag effect of joint motion caused by mechanical inertia; Indicates the interaction strength of the robot based on the historical proportional moment state, Indicates the degree of dependence of the robot on the average state of the neighboring robots over the past period of time; It represents the joint force fluctuation caused by uneven ground disturbance at time t.

[0122] Furthermore, based on the weighted sum of the states of the various targets to be controlled, the synchronization target state equation of the coordinated control system is obtained, including:

[0123] A strongly connected directed graph is constructed based on the neighboring relationships of all the targets to be controlled, and the generalized algebraic connectivity definition of the Laplacian matrix of the strongly connected directed graph is obtained;

[0124] Based on the eigenvalues ​​of the left zero eigenvector in the definition of generalized algebraic connectivity, the state weights of the targets to be controlled are obtained.

[0125] Based on the state variables and state weights of each target to be controlled, the synchronization target state equation of the cooperative control system is obtained.

[0126] Specifically, a strongly connected directed graph represents the target to be controlled through nodes, and directed edges represent the direction of information transmission. Therefore, a strongly connected directed graph can accurately describe the communication topology in a multi-target collaborative system. At the same time, strong connectivity is a necessary condition for all targets to be controlled to tend to be synchronized. If there are isolated nodes, it means that there are targets to be controlled in the collaborative control system that cannot exchange information with adjacent targets to be controlled, which will inevitably lead to the failure of collaborative control. Therefore, this application chooses to use a strongly connected directed graph to reflect the topological structure of the collaborative control system. Furthermore, in the process of realizing multi-target collaboration, the state vectors of each target to be controlled have different interferences on global synchronization, so it is necessary to assign weights to each target to be controlled. The Laplace matrix is ​​the core tool for analyzing graph connectivity. The left zero eigenvector in the Laplace matrix is Figure 1 Consistency vector, so the elements in the left zero eigenvector can be interpreted as the relative influence of the nodes in the strongly connected directed graph in the collaboration. Therefore, this application uses the left zero eigenvector to assign weights to each target to be controlled.

[0127] Specifically, the definition of generalized algebraic connectivity is expressed as:

[0128] ,

[0129] in, represents the definition of generalized algebraic connectivity; represents the Laplace matrix; represents the left zero eigenvector, ; represents the orthogonal vector of the left zero eigenmatrix; , represents a diagonal matrix; represents transpose; ;

[0130] The synchronization target state equation of the cooperative control system is expressed as:

[0131] ,

[0132] in, Represents the synchronization target state equation of the cooperative control system; Indicates the time t The state variables of the target to be controlled; represents the first left zero eigenvector in the definition of generalized algebraic connectivity. eigenvalues; Indicates the number of targets to be controlled in the collaborative control system.

[0133] The following is an explanation of the above synchronization target state equation through a specific example:

[0134] Still taking the bipedal robot application scenario as an example, It can express the team's average stride, average walking speed and other global characteristics, and control the status of each robot to Convergence ensures that the robot team moves in unison and avoids formation confusion caused by individual differences. For example, a bipedal robot team needs to maintain a unified walking rhythm to pass through a narrow passage. As the average state target, it can directly quantify the degree of synchronization of the team and facilitate the design of collaborative control strategies. When the elements in the left zero eigenvector are used as the weights of the state variables of each robot, This is the only consistent equilibrium point of the collaborative control system, that is, if the states of all robots converge to , synchronization is achieved.

[0135] Furthermore, since the initial state variables of the target to be controlled and the gain of the saturation pulse controller will 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 target to be controlled (that is, the maximum range of the attraction domain) and the maximum gain of the saturation pulse controller.

[0136] Specifically, since the boundary of the attraction domain is convex and closed, that is, when the initial state variables of each target to be controlled are within the attraction domain, no matter from which direction they approach the synchronization target state (that is, the equilibrium point), they will not diverge due to different initial values, resulting in synchronization failure. This makes it difficult to express the attraction domain analytically. Therefore, based on the convex set approximation theory, this application transforms the complex convex set constraints into an algebraic problem through geometric transformation and parameter optimization, that is, introducing a polyhedron to approximate the measurement ellipsoid, with the goal of always containing the polyhedron within the ellipsoid under scaling by the scaling factor, 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 estimate of the attraction domain, and thus obtaining the maximum gain estimate based on the maximum value of the saturated pulse control signal.

[0137] Specifically, with the goal of making the initial state of each target to be controlled converge to the synchronous target state under the control of its saturated pulse controller, the initial state solution model of the target to be controlled is constructed, including:

[0138] Based on the convex set approximation theory, the initial state variable range of the target to be controlled is approximated as a polyhedron, and the pulse control signal output by the saturated pulse controller is approximated as a scaling factor;

[0139] With the maximization of the scaling factor as the goal, an objective function is constructed; with the polyhedron being contained in the ellipsoid under the scaling of the scaling factor as the constraint condition, a first constraint function is constructed; with the pulse control signal being a saturated nonlinear signal as the constraint condition, a second constraint function is constructed; with the gain stability of the saturated pulse controller as the constraint condition, a third constraint function is constructed; with the state variable of the target to be controlled being stable under the influence of delay as the constraint condition, a fourth constraint function is constructed; with the distributed delay influence weight of adjacent targets to be controlled as the constraint condition, a fifth constraint function is constructed; with the proportional delay influence weight of adjacent targets to be controlled as the constraint condition, a sixth constraint function is constructed; with the stability of the cooperative control system under the influence of the maximum distributed delay as the constraint condition, a seventh constraint function is constructed;

[0140] 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, an initial state solution model of the target to be controlled is obtained.

[0141] Specifically, the objective function is expressed as:

[0142] ,

[0143] in, represents the objective function; represents the scaling factor;

[0144] The first constraint function is expressed as:

[0145]

[0146] in, Represents a polyhedron; represents an ellipsoid;

[0147] The second constraint function is expressed as:

[0148] ,

[0149] in, represents the pulse reduction factor of the pulse control signal; represents the Laplace matrix; represents a nonlinear matrix; Indicates the number of targets to be controlled in the collaborative control system; , The dimension of the state variable representing the target to be controlled; The state variable weight matrix representing the target to be controlled; represents the parameters of the Lyapunov function; represents the Kronecker product;

[0150] The third constraint function is expressed as:

[0151] ,

[0152] in, It represents the state variable difference constraint of the target to be controlled before and after the pulse control signal is controlled. , represents the definition of generalized algebraic connectivity, represents the saturated convex hull decomposition matrix, represents the gain of the saturation pulse controller, represents the nonlinear convex hull decomposition matrix; ;

[0153] The fourth constraint function is expressed as:

[0154] ,

[0155] in, , represents the normalized Laplacian matrix, represents the first positive definite diagonal matrix, represents the first positive scalar parameter, represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the attenuation matrix of the target to be controlled, represents the second positive definite diagonal matrix, represents the proportional delay coupling strength between adjacent controlled targets, represents the communication topology matrix of the collaborative control system, represents the proportional delay inline coupling matrix, represents the distributed delay coupling strength between adjacent controlled targets, represents the distributed delay inline coupling matrix, The first constraint representing the delay coupling strength, The second constraint representing the delay coupling strength, represents the distributed delay coupling term, represents the N-order identity matrix;

[0156] The fifth constraint function is expressed as:

[0157] ,

[0158] in, A topological matrix representing a 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, used to construct the Lyapunov function;

[0159] The sixth constraint function is expressed as:

[0160] ,

[0161] in, represents the proportional delay impact weight factor;

[0162] The seventh constraint function is expressed as:

[0163] ,

[0164] in, represents the third positive scalar parameter, which is used to adjust the weight of the distribution delay term; Indicates the maximum value of the distribution delay.

[0165] Furthermore, since the initial state solution model of the target to be controlled contains multiple bilinear matrix inequalities, it is necessary to first convert them into inequalities based on linear matrices before solving them.

[0166] Specifically, solving the initial state solution model to obtain the maximum initial state of the target to be controlled and the maximum gain of the saturation pulse controller include:

[0167] Performing convex 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 function;

[0168] The target initial state solution model is solved to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller.

[0169] The specific steps of convex transformation include:

[0170] 1. The first constraint function is equivalent to ;

[0171] 2. The second constraint function is equivalent to ;

[0172] 3. Utilize Multiplying it with the third constraint function before and after gives:

[0173] ,

[0174] in, ;

[0175] 4. Similarly, combine the fourth constraint function with the matrix Multiplying left and right, it becomes:

[0176] ,

[0177] in, , , , , , , , , ;

[0178] 5. From the fifth, sixth and seventh constraint functions, we can know that:

[0179]

[0180] make , , , , , , , , .

[0181] Furthermore, the converted objective function is expressed as:

[0182] ,

[0183] in, represents the objective function after transformation; ;

[0184] The converted first constraint function is expressed as:

[0185] ,

[0186] in, represents the membership vector of the auxiliary polyhedron; ; represents the number of member vectors;

[0187] The converted second constraint function is expressed as:

[0188] ,

[0189] in, ;

[0190] The converted third constraint function is expressed as:

[0191] ,

[0192] in, ;

[0193] The converted fourth constraint function is expressed as:

[0194] ,

[0195] in, ; , ; , ; , ; , ; , represents the scaled delay internal coupling diagonal matrix; , represents the distributed delay internal coupling diagonal matrix;

[0196] The converted fifth constraint function is expressed as:

[0197] ,

[0198] in, ;

[0199] The converted sixth constraint function is expressed as:

[0200] ,

[0201] The converted seventh constraint function is expressed as:

[0202] .

[0203] Furthermore, this embodiment also derives sufficient conditions for local synchronization of multiple controlled targets under the control of a saturated pulse controller, thereby verifying the effectiveness of the method provided by this application:

[0204] First, based on the state space equation of each target to be controlled and the state equation of the synchronization target, the state error of each target to be controlled at time t is calculated, thereby obtaining the state error equation of the cooperative control system;

[0205] Specifically, the error vector composed of the state errors of each target to be controlled can be written as , express Euclidean space.

[0206] make Indicates from arrive The continuous function set of express The initial value of , then the state error of the cooperative control system can be expressed in the following compact form:

[0207]

[0208] Among them, the nonlinear function , ,and satisfy ; N is a column vector with all elements set to 1; Represents the N-th order identity matrix.

[0209] because is right continuous, i.e. , and at the pulse moment , hour, Existence, among them, Represents the set of positive integers.

[0210] Describe the window center as , the window radius is described as ,but Indicates the random injection pulse control signal Pulse moment Pulse time window.

[0211] Next, based on the state error of the cooperative control system, the conditions for the controlled target to achieve local synchronization under the action of the saturated pulse controller are derived:

[0212] 1. Define the solution of the state error of the cooperative control system as and ;

[0213] 2. According to Available ;

[0214] 3. Construct Lyapunov function: ;

[0215] 4. Verification , If it is not established, then it exists satisfy ;

[0216] 5. Construction inf , easy to get and ;

[0217] 6. Regarding , assuming is a pulse instant, that is , , then according to:

[0218] ,

[0219] ,

[0220] We can get:

[0221] ,

[0222] in, is a positive definite matrix;

[0223] because and The definition of is contradictory, so It cannot be a pulse moment.

[0224] 7. Assumptions is the solution of the state error of the cooperative control system, by setting the initial value , prove that for any :

[0225] ;

[0226] when , When , the derivative of V(t) along the state error trajectory of the cooperative control system is calculated as:

[0227] ,

[0228] in, Represents the right derivative, which is used to characterize the unilateral derivative of a piecewise continuous function at a non-smooth point; represents the left zero eigenvector;

[0229] According to:

[0230] ,

[0231] ,

[0232] ,

[0233] and

[0234] ,

[0235] ,

[0236] We can get:

[0237] ,

[0238] 8. Further, for any Establish a general solution Comparison system:

[0239]

[0240] According to the parameter variation formula, we can Computed as an integral equation:

[0241] ,

[0242] in, is the Cauchy matrix of the following linear impulse system:

[0243] ,

[0244] The Cauchy matrix can be expressed as:

[0245] ;

[0246] in, ; Indicates the upper bound of the pulse interval;

[0247] Substituting the Cauchy matrix into the integral equation yields:

[0248]

[0249] in, ; express The maximum eigenvalue of .

[0250] 9. Due to , , , obviously for , the following formula holds:

[0251] ,

[0252] in, Represents the exponential convergence rate of the system error;

[0253] And, for , the above formula is still valid, that is

[0254] ,

[0255] Assume that the above formula is Not applicable, then there is at least one moment satisfy:

[0256] ,

[0257] But because of the The inequality for Still holds true, that is:

[0258] ,

[0259] definition: ;

[0260] Then we can calculate:

[0261] ,

[0262] To prove this contradiction, define:

[0263]

[0264] in, , ,

[0265] Further calculation The derivative of ;

[0266] Specifically, if and only if , we can get , which can be achieved by:

[0267] ,

[0268] ,

[0269] in, , ,

[0270] It can be deduced that:

[0271] ;

[0272] In addition, for , Established, indicating that , Increasing, at the same time, for Established, indicating that , Increasing.

[0273] Therefore, we can get , and it can be deduced that have .

[0274] That is hour, Established.

[0275] 10. When and When , we can get:

[0276]

[0277] in: ;

[0278] because and , we can get ;

[0279] Will Set as: ;

[0280] according to It can be proved ;

[0281] structure for: ,

[0282] Obviously, and ;

[0283] therefore, is a monotonically decreasing function, for any , Established, that is:

[0284] ;

[0285] Then we can deduce that:

[0286] ,

[0287] This is consistent with the above Therefore, the above inequality The inequality for all Still valid, ,have:

[0288] ,

[0289] This further indicates that:

[0290] ,

[0291] Therefore, it can be clearly deduced that for any ,have

[0292] ,

[0293] in, represents the largest eigenvalue among the left zero eigenvectors;

[0294] This is similar to Therefore, it can be deduced that For all Both are established.

[0295] From the above derivation process, it can be seen that the state error index of the cooperative control system converges to the origin, and the convergence speed is , that is, the local exponential synchronization of the cooperative control system can be achieved under the saturated pulse controller.

[0296] The effectiveness of the method provided by this application is verified by a specific example below:

[0297] Step 1: Give the parameters of the target to be controlled as follows:

[0298]

[0299] and , , , , ,

[0300] .

[0301] like Figure 2 The figure shows the state trajectory diagram of each target to be controlled when the coordinated control method provided by the present application is not used; Figure 3 The figure shows the state error trajectory diagram of each target to be controlled when the coordinated control method provided by the present application is not used; Figure 2 and Figure 3 It can be seen from the figure that without any control input, it is impossible to achieve synchronization of multiple controlled targets.

[0302] Step 2: Select , , select the polyhedron , , solve the model based on the initial state of the target to be controlled, by selecting , 32, , , it can be deduced that , under this condition, other feasible solutions are as follows:

[0303] , ,

[0304] , ,

[0305] , ,

[0306] ,

[0307] like Figure 4 Shown is a state trajectory diagram of each target to be controlled under the control of the method provided by this application; Figure 5 The figure shows the state error trajectory diagram of each target to be controlled under the control of the method provided by this application; Figure 6 The figure shows a schematic diagram of the saturation pulse control signal output by the saturation pulse controller provided by the present application. Figure 4 、 Figure 5 and Figure 6 It can be seen that when the initial states of the targets to be controlled are all within the attraction domain and the gain of the saturated pulse controller is less than the maximum gain, the state variables of all targets to be controlled will eventually converge to the target state, which further shows that the multi-objective collaborative control method provided in this application can achieve multi-objective collaborative control.

[0308] Based on the multi-objective collaborative control method provided in the above embodiment, the embodiment of the present application also provides a multi-objective collaborative control device, such as Figure 7 As shown, the device specifically includes:

[0309] A saturation pulse controller construction module 10 is used 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 targets to be controlled in the cooperative control system using a nonlinear saturation function;

[0310] A state-space equation construction module 20 is 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 nonlinear terms of the state variables excluding time lag effects, the nonlinear terms of the state variables including time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and a saturated pulse controller.

[0311] The synchronization target construction module 30 is used to perform a weighted summation of the state variables of each target to be controlled to obtain the synchronization target state equation of the coordinated control system; with the goal of ensuring that the initial state variables of each target to be controlled converge to the synchronization target state under the control of its saturated pulse controller, an initial state solution model for the target to be controlled is constructed;

[0312] a parameter acquisition module 40 for solving the initial state solution model to obtain the initial state maximum value of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variable of each target to be controlled is less than or equal to the initial state maximum value, and the gain of each saturation pulse controller is less than or equal to the maximum gain;

[0313] The collaborative control module 50 is used for the saturation pulse controller of each target to be controlled. Based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, the controller outputs a pulse control signal to control each target to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

[0314] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may 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.) containing computer-usable program code. The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of processes and / or boxes in the flowchart and / or block diagram, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the functions described in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including the instruction device, which implements the function specified in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 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 produce a computer-implemented process, thereby providing instructions for implementing the process in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0315] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A multi-objective collaborative control method, characterized in that: include: A saturation pulse controller for each target to be controlled is constructed using a nonlinear saturation function based on the state variable difference between each target to be controlled and its adjacent targets in the cooperative control system. The saturation pulse controller of each target to be controlled is expressed as: ， in, Indicates the A saturation pulse controller for a target to be controlled; represents a nonlinear saturation function; , represents the gain of the saturation pulse controller, Indicates the The target to be controlled and its adjacent The coupling weights between the controlled targets are: Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variable difference between a target to be controlled and its adjacent target to be controlled is: Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the Dirac impulse function, Indicates the first A moment, Indicates the first a moment; Based on the state variables of each target to be controlled, the nonlinear terms of the state variables without time lag effects, the nonlinear terms of the state variables with time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and the saturated pulse controller, the state space equations of each target to be controlled are constructed; the state space equations of each target to be controlled are expressed as follows: ， in, express The first derivative of ; represents the attenuation matrix of the target to be controlled, Indicates the The state variables of the target to be controlled at time t under the influence of the attenuation matrix; represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the nonlinear term of the state variable at time t without the time lag effect; represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the nonlinear term of the state variable at time t including the time lag effect, express the time lag of moments; represents the proportional delay coupling strength between adjacent controlled targets, Indicates the The target to be controlled and its adjacent The first coupling matrix between the targets to be controlled, represents the proportional delay inline coupling matrix, Indicates The adjacent target to be controlled The state variable of the 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 controlled targets, represents the distributed delay inline coupling matrix, Indicates the The target to be controlled and its adjacent The second coupling matrix between the targets to be controlled, express The distribution delay of time, Indicates The adjacent target to be controlled The state variables of the target to be controlled at time t under the influence of distributed delay; represents the external interference at time t; The state variables of each target to be controlled are weighted and summed to obtain the synchronous target state equation of the cooperative control system. With the goal of ensuring 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 for the target to be controlled is constructed. This model specifically includes: Based on the convex set approximation theory, the initial state variable range of the target to be controlled is approximated as a polyhedron, and the pulse control signal output by the saturated pulse controller is approximated as a scaling factor; With the maximization of the scaling factor as the goal, an objective function is constructed; with the polyhedron being contained in the ellipsoid under the scaling of the scaling factor as the constraint condition, a first constraint function is constructed; with the pulse control signal being a saturated nonlinear signal as the constraint condition, a second constraint function is constructed; with the gain stability of the saturated pulse controller as the constraint condition, a third constraint function is constructed; with the state variable of the target to be controlled being stable under the influence of delay as the constraint condition, a fourth constraint function is constructed; with the distributed delay influence weight of adjacent targets to be controlled as the constraint condition, a fifth constraint function is constructed; with the proportional delay influence weight of adjacent targets to be controlled as the constraint condition, a sixth constraint function is constructed; with the stability of the cooperative control system under the influence of the maximum distributed delay as the constraint condition, a seventh constraint function is constructed; 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, an initial state solution model of the target to be controlled is obtained; Solving the initial state solution model to obtain the maximum initial state value of the target to be controlled and the maximum gain of the saturation pulse controller, so that the initial state variable of each target to be controlled is less than or equal to the maximum initial state value, and the gain of each saturation pulse controller is less than or equal to the maximum gain; The saturation pulse controller of each target to be controlled outputs a pulse control signal to control each target to be controlled based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

2. The multi-objective collaborative control method according to claim 1, characterized in that: Based on the weighted sum of the states of each target to be controlled, the synchronization target state equation of the cooperative control system is obtained, which includes: A strongly connected directed graph is constructed based on the neighboring relationships of all the targets to be controlled, and the generalized algebraic connectivity definition of the Laplacian matrix of the strongly connected directed graph is obtained; Based on the eigenvalues ​​of the left zero eigenvector in the definition of generalized algebraic connectivity, the state weights of the targets to be controlled are obtained. Based on the state variables and state weights of each target to be controlled, the synchronization target state equation of the cooperative control system is obtained.

3. The multi-objective collaborative control method according to claim 2, characterized in that: The definition of generalized algebraic connectivity is expressed as: ， in, represents the definition of generalized algebraic connectivity; represents the Laplace matrix; represents the left zero eigenvector, ; represents the orthogonal vector of the left zero eigenmatrix; , represents a diagonal matrix; represents transpose; ; The synchronization target state equation of the cooperative control system is expressed as: ， in, Represents the synchronization target state equation of the cooperative control system; Indicates the time t The state variables of the target to be controlled; represents the first left zero eigenvector in the definition of generalized algebraic connectivity. eigenvalues; Indicates the number of targets to be controlled in the collaborative control system.

4. The multi-objective collaborative control method according to claim 1, characterized in that: The objective function is expressed as: ， in, represents the objective function; represents the scaling factor; The first constraint function is expressed as: ， in, Represents a polyhedron; represents an ellipsoid; The second constraint function is expressed as: ， in, represents the pulse reduction factor of the pulse control signal; represents the Laplace matrix; represents a nonlinear matrix; Indicates the number of targets to be controlled in the collaborative control system; , The dimension of the state variable representing the target to be controlled; The state variable weight matrix representing the target to be controlled; represents the parameters of the Lyapunov function; represents the Kronecker product; The third constraint function is expressed as: ， in, It represents the state variable difference constraint of the target to be controlled before and after the pulse control signal is controlled. , represents the definition of generalized algebraic connectivity, represents the saturated 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: ， in, , represents the normalized Laplacian matrix, represents the first positive definite diagonal matrix, represents the first positive scalar parameter, represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the attenuation matrix of the target to be controlled, represents the second positive definite diagonal matrix, represents the proportional delay coupling strength between adjacent controlled targets, represents the communication topology matrix of the collaborative control system, represents the proportional delay inline coupling matrix, represents the distributed delay coupling strength between adjacent controlled targets, represents the distributed delay inline coupling matrix, The first constraint representing the delay coupling strength, The second constraint representing the delay coupling strength, represents the distributed delay coupling term, represents the N-order identity matrix; The fifth constraint function is expressed as: ， in, A topological matrix representing a strongly connected directed graph; represents the second positive scalar parameter; represents a positive definite matrix; The sixth constraint function is expressed as: ， in, represents the proportional delay impact weight factor; The seventh constraint function is expressed as: ， in, represents the third positive scalar parameter; Indicates the maximum value of the distribution delay.

5. The multi-objective coordinated control method according to claim 4, characterized in that: Solving the initial state solution model to obtain the maximum initial state of the target to be controlled and the maximum gain of the saturation pulse controller include: Performing convex 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 function; The target initial state solution model is solved to obtain the maximum value of the initial state of the target to be controlled and the maximum gain of the saturated pulse controller.

6. The multi-objective coordinated control method according to claim 5, characterized in that: The converted objective function is expressed as: ， in, represents the objective function after transformation; ; The converted first constraint function is expressed as: ， in, represents the membership vector of the auxiliary polyhedron; ; represents the number of member vectors; The converted second constraint function is expressed as: ， in, ; The converted third constraint function is expressed as: ， in, ; The converted fourth constraint function is expressed as: ， in, ; , ; , ; , ; , ; , represents the scaled delay internal coupling diagonal matrix; , represents the distributed delay internal coupling diagonal matrix; The converted fifth constraint function is expressed as: ， in, ; The converted sixth constraint function is expressed as: ， The converted seventh constraint function is expressed as: 。 7. A multi-objective collaborative control device, characterized in that: include: The saturation pulse controller construction module is used 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 targets in the coordinated control system using a nonlinear saturation function. The saturation pulse controller for each target to be controlled is expressed as: ， in, Indicates the A saturation pulse controller for a target to be controlled; represents a nonlinear saturation function; , represents the gain of the saturation pulse controller, Indicates the The target to be controlled and its adjacent The coupling weights between the controlled targets are: Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variables of the target to be controlled, Indicates the time t The state variable difference between a target to be controlled and its adjacent target to be controlled is: Indicates The number of targets to be controlled adjacent to the target to be controlled; represents the Dirac impulse function, Indicates the first A moment, Indicates the first a moment; The state-space equation construction module is used to construct the state-space equation of each target to be controlled based on the state variables of each target to be controlled, the nonlinear terms of the state variables without time lag effects, the nonlinear terms of the state variables with time lag effects, the state variables of the adjacent targets to be controlled under the influence of proportional delays and the state variables under the influence of distributed delays, and the saturated pulse controller. The state-space equation of each target to be controlled is expressed as follows: ， in, express The first derivative of ; represents the attenuation matrix of the target to be controlled, Indicates the The state variables of the target to be controlled at time t under the influence of the attenuation matrix; represents the weight matrix of the nonlinear terms of the state variables without the time lag effect, represents the nonlinear term of the state variable at time t without the time lag effect; represents the weight matrix of the nonlinear terms of the state variables including the time lag effect, represents the nonlinear term of the state variable at time t including the time lag effect, express the time lag of moments; represents the proportional delay coupling strength between adjacent controlled targets, Indicates the The target to be controlled and its adjacent The first coupling matrix between the targets to be controlled, represents the proportional delay inline coupling matrix, Indicates The adjacent target to be controlled The state variable of the 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 controlled targets, represents the distributed delay inline coupling matrix, Indicates the The target to be controlled and its adjacent The second coupling matrix between the targets to be controlled, express The distribution delay of time, Indicates The adjacent target to be controlled The state variables of the target to be controlled at time t under the influence of distributed delay; represents the external interference at time t; The synchronization target construction module is used to perform weighted summation of the state variables of each target to be controlled to obtain the synchronization target state equation of the coordinated control system; with the goal of ensuring that the initial state variables of each target to be controlled converge to the synchronization target state under the control of its saturated pulse controller, an initial state solution model for the target to be controlled is constructed; it specifically includes: Based on the convex set approximation theory, the initial state variable range of the target to be controlled is approximated as a polyhedron, and the pulse control signal output by the saturated pulse controller is approximated as a scaling factor; With the maximization of the scaling factor as the goal, an objective function is constructed; with the polyhedron being contained in the ellipsoid under the scaling of the scaling factor as the constraint condition, a first constraint function is constructed; with the pulse control signal being a saturated nonlinear signal as the constraint condition, a second constraint function is constructed; with the gain stability of the saturated pulse controller as the constraint condition, a third constraint function is constructed; with the state variable of the target to be controlled being stable under the influence of delay as the constraint condition, a fourth constraint function is constructed; with the distributed delay influence weight of adjacent targets to be controlled as the constraint condition, a fifth constraint function is constructed; with the proportional delay influence weight of adjacent targets to be controlled as the constraint condition, a sixth constraint function is constructed; with the stability of the cooperative control system under the influence of the maximum distributed delay as the constraint condition, a seventh constraint function is constructed; 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, an initial state solution model of the target to be controlled is obtained; 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 variable of each target to be controlled is less than or equal to the maximum value of the initial state, and the gain of each saturation pulse controller is less than or equal to the maximum gain; The collaborative control module is used for the saturation pulse controller of each target to be controlled. Based on the real-time state variables of each target to be controlled and its adjacent targets to be controlled, the controller outputs a pulse control signal to control each target to be controlled, so that the state of each target to be controlled reaches the synchronous target state.

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