A collaborative control method for heterogeneous multi-agent systems under state and control constraints

Abstract

The present invention discloses a method for cooperative control of heterogeneous multi-agent systems under state and control constraints, the method comprising: calculating a compensation system matrix and a motion state, a compensation state and a compensation state feedback matrix of each agent in the heterogeneous multi-agent system according to a system matrix and a control matrix of each agent in the heterogeneous multi-agent system; using the motion state, the compensation state and the compensation state feedback matrix of each agent to design a cooperative control law for it, so that the state error between the motion state and the compensation state of each agent converges to zero; each agent searches for the best coupling coefficient through the compensation state constraint and the consistency constraint to construct a distributed control law for each agent; according to the cooperative control law and the distributed control law corresponding to each agent, the motion state and the compensation state of the corresponding agent at the next moment are obtained to realize motion control of the agent. The present invention can process control and state constraints at the same time, and has low calculation cost and high real-time performance.

Description

Technical Field

[0001] The present invention relates to the cross-technical field of distributed control, optimal control and multi-constraint optimization, and in particular to a collaborative control method for a heterogeneous multi-agent system under state and control constraints. Background Art

[0002] Multiple AGVs (Automated Guided Vehicles, AGVs) work together to carry large structural parts, and the AGVs and structural parts are connected into a whole. Since the overall size and movement ability are limited by the space of the workshop, it is necessary to arrange a formation suitable for the channel type and size, and the spatial constraints between different AGVs are coupled. At the same time, the AGV body also has its specific execution capability boundaries, such as: driving torque limit, running speed limit, steering angle limit, etc. These restrictions can usually be attributed to the control and state constraints of the intelligent body. Through the collaborative transportation of large cylindrical objects by heterogeneous AGVs with multiple different drive modes (such as steering wheel drive, differential drive, Mecanum wheel, etc.), a leader-follower formation strategy can be designed, and the stability of the transportation process and the strong formation maintenance ability can be guaranteed, thereby improving the space utilization of the workshop channel. The leader runs along the established path, and the follower AGV follows the leader, running along the established route while maintaining the distance between the neighboring AGVs.

[0003] The problem of collaborative handling of heterogeneous AGV clusters is a typical problem of collaborative control of heterogeneous multi-agent systems under control and state constraints. In the study of distributed control of multi-agent systems with constraints, some studies have used "low-gain" local state feedback control to avoid the saturation of actuators, and achieved semi-global consistency control by finding feedback matrices and exponential convergence rates that do not trigger control constraints; other studies have considered distributed control problems with state constraints. Unlike low-gain feedback control, its control signal will continue to reach saturation for a period of time.

[0004] Existing methods can only handle situations with a single constraint, while for situations with multiple constraints, distributed model predictive control methods and distributed optimization methods are usually used, which are computationally intensive and have poor real-time performance. Some studies use distributed methods to solve constraint optimization problems, minimize joint posture errors and end-effector displacement errors, and avoid collisions with multiple obstacles. Some studies have explored fully distributed model predictive control methods and their recursive feasibility, achieving constraint consistency while meeting scalability.

[0005] Therefore, in response to the above problems, there is an urgent need for a collaborative control method for heterogeneous multi-agent systems that can simultaneously handle control and state constraints. Summary of the invention

[0006] The purpose of the present invention is to provide a method for cooperative control of heterogeneous multi-agent systems under state and control constraints in view of the deficiencies of the prior art. The present invention can process control and state constraints simultaneously, and has low computational cost and high real-time performance.

[0007] The objective of the present invention is achieved through the following technical solutions: In a first aspect, an embodiment of the present invention provides a method for collaborative control of a heterogeneous multi-agent system under state and control constraints, comprising the following steps:

[0008] (1) Calculate the compensation system matrix and the motion state, compensation state, and compensation state feedback matrix of each agent in the heterogeneous multi-agent system based on the system matrix and control matrix of each agent;

[0009] (2) Using the motion state, compensation state, and compensation state feedback matrix of each agent, a coordinated control law is designed for it so that the state error between the motion state and compensation state of each agent converges to zero;

[0010] (3) Each agent searches for the optimal coupling coefficient by compensating for state constraints and consistency constraints to construct a distributed control law for each agent;

[0011] (4) According to the collaborative control law and distributed control law corresponding to each intelligent agent, the motion state and compensation state of the corresponding intelligent agent at the next moment are obtained to realize the motion control of the intelligent agent.

[0012] Furthermore, the step (1) includes the following sub-steps:

[0013] (1.1) Obtain the discrete time model of each agent based on the system matrix and control matrix of each agent in the heterogeneous multi-agent system, and obtain the motion state of each agent based on the discrete time model of each agent;

[0014] (1.2) Obtaining the compensation state of the corresponding intelligent agent according to the discrete time model of each intelligent agent in the compensation system;

[0015] (1.3) Obtaining the navigator model of the compensation system based on the discrete time model of the agent in the compensation system;

[0016] (1.4) Solve the optimization problem shown in formula (7) to obtain the compensation system matrix with the highest similarity to the system matrix of each intelligent agent;

[0017] (7)

[0018] (1.5) Solve the optimization problem shown in formula (8) to obtain the n×m dimensional compensation state feedback matrix of each agent:

[0019] (8)

[0020] In the formula, represents the n×m dimensional compensation state feedback matrix of the ith agent.

[0021] Furthermore, the discrete time model of the agent is expressed as:

[0022] (1)

[0023] (2)

[0024] (3)

[0025] (4)

[0026] In the formula, represents the n-dimensional motion state of the ith agent at time k+1, represents the n-dimensional motion state of the i-th agent at time k, represents the m-dimensional control input of i agents at time k, represents the n×n dimensional system matrix of the ith agent, represents the m×m dimensional control matrix of the ith agent, represents the 2-norm of a vector or matrix, represents the boundary value of the state constraint, represents the boundary value of the control constraint, and N represents the total number of agents in the heterogeneous multi-agent system.

[0027] Furthermore, the discrete time model of the agent in the compensation system is expressed as:

[0028] (5)

[0029] In the formula, represents the n-dimensional compensation state of the ith agent at time k+1, represents the n-dimensional compensation state of the ith agent at time k, represents the n-dimensional control input of the ith agent at time k, represents the n×n dimensional compensation system matrix;

[0030] The navigator model of the compensation system is expressed as:

[0031] (6)

[0032] In the formula, represents the n-dimensional compensation state of the navigator at time k+1, represents the n-dimensional compensation state of the navigator at time k, Represents the n-dimensional control input of the navigator at time k.

[0033] Furthermore, the step (2) includes the following sub-steps:

[0034] (2.1) For each agent, the motion state, compensation state and compensation state feedback matrix of the agent are used to design a cooperative control law for the agent, which can be expressed as:

[0035] (9)

[0036] In the formula, represents the m×n dimensional state error feedback matrix of the ith agent;

[0037] (2.2) The error between the actual motion state and the compensation state of each agent is defined as the state error of the agent, and the error system equation of the agent is obtained according to the state error of the agent;

[0038] (2.3) Based on the error system equation of each agent, with the state error of the agent converging to zero as the optimization goal, solve the matrix Riccati equation shown in formula (13) to obtain the unique solution of the matrix Riccati equation corresponding to the agent;

[0039] (13)

[0040] In the formula, represents the unique solution of the matrix Riccati equation corresponding to the i-th agent, the weight matrix represents the n×n dimensional semi-positive definite matrix of the ith agent, the weight matrix represents the m×m dimensional positive definite matrix of the ith agent, and the superscript T represents the transpose of a matrix or vector;

[0041] (2.4) For each agent, its state error feedback matrix is ​​obtained according to the unique solution of its corresponding matrix Riccati equation, which is expressed as:

[0042] (17)

[0043] (2.5) Substitute the state error feedback matrix of the agent obtained in step (2.4) into the cooperative control law corresponding to the agent to obtain the optimal cooperative control law in which the state error converges to zero.

[0044] Furthermore, in step (2.2), the state error of the i-th agent is expressed as:

[0045] (10)

[0046] In the formula, represents the state error of the i-th agent at time k;

[0047] The error system equation of the i-th agent is expressed as:

[0048] (12)

[0049] In the formula, Represents the state error of the ith agent at time k+1.

[0050] Furthermore, the step (3) includes the following sub-steps:

[0051] (3.1) Determine the compensation state constraints of each agent, specifically: at time k, the motion state of agent i is It is known that its control input satisfies the constraints , in order to make the motion state at time k+1 satisfy the constraint condition , then the compensation state at time k is The following compensation state constraints should be met:

[0052] (18)

[0053] (19)

[0054] (3.2) Determine the control target of the compensation system by making the compensation state of agent i consistent with the compensation state of its neighbor agent j;

[0055] (3.3) Solve the matrix Riccati equation shown in formula (21) according to the control objective of the compensation system and the compensation system matrix to obtain a unique solution of the matrix Riccati equation corresponding to the navigator;

[0056] (twenty one)

[0057] In the formula, The unique solution of the matrix Riccati equation corresponding to the navigator, the weight matrix represents the n×n dimensional semi-positive definite matrix of the navigator, the weight matrix represents the m×m dimensional positive definite matrix of the navigator;

[0058] (3.4) The feedback matrix of the compensation system is obtained according to the unique solution of the matrix Riccati equation corresponding to the navigator, which is expressed as:

[0059] (twenty two)

[0060] In the formula, represents the feedback matrix of the compensation system;

[0061] (3.5) The coupling coefficient between agent i and agent j satisfies the consistency constraint and is expressed as:

[0062] (twenty three)

[0063] In the formula, is the coupling coefficient between agent i and agent j at time k, for The optimal coupling coefficient is obtained by obtaining the optimal adjustable parameters that satisfy the compensation state constraint and the consistency constraint;

[0064] (3.6) The distributed control law is constructed using the optimal coupling coefficient, the feedback matrix of the compensation system, the compensation state of each agent, and the compensation state of the leader, which is expressed as:

[0065] (25)

[0066] In the formula, Is the identifier of whether agent j sends information to agent i. If agent j sends information to agent i, then ,otherwise ; represents the compensation state of agent i at time k, represents the compensation state of agent j at time k, represents the compensation state of the navigator at time k.

[0067] Furthermore, the control target of the compensation system is expressed as:

[0068] (20)

[0069] Where J represents the control target of the compensation system, and T is the optimization step size.

[0070] Furthermore, the method obtains the best adjustable parameters that satisfy the compensation state constraint and the consistency constraint. Obtain the best coupling coefficient, including:

[0071] Solve the following optimization problem to obtain the best adjustable parameters that satisfy the compensation state constraints and consistency constraints: :

[0072] (twenty four)

[0073] In the formula, represents the adjustable parameter at time k, represents the adjustable parameters at time k-1; according to the optimal adjustable parameters at time t And the optimal coupling coefficient at time t-1 obtains the optimal coupling coefficient at the current time t.

[0074] A second aspect of an embodiment of the present invention provides a collaborative control device for implementing the above-mentioned method for collaborative control of heterogeneous multi-agent systems under state and control constraints, comprising:

[0075] A compensation system model component is used to calculate the compensation system matrix and the motion state, compensation state and compensation state feedback matrix of each agent according to the system matrix and control matrix of each agent in the heterogeneous multi-agent system;

[0076] The intelligent agent cooperative control module is used to design a cooperative control law for each intelligent agent by using the motion state, compensation state and compensation state feedback matrix of each intelligent agent so that the state error between the motion state and compensation state of each intelligent agent converges to zero;

[0077] A coupling coefficient optimization component is used to find the optimal coupling coefficient by compensating state constraints and consistency constraints to construct distributed control laws for each agent; and

[0078] The motion control module is used to obtain the motion state and compensation state of the corresponding intelligent body at the next moment according to the collaborative control law and distributed control law corresponding to each intelligent body, so as to realize the motion control of the intelligent body.

[0079] The beneficial effect of the present invention is that, for a heterogeneous multi-agent system, the present invention converts the control input and motion state constraints of the agent into the compensation state constraints of the compensation system, and solves the time-varying coupling coefficient of the compensation system to achieve consistency; the present invention can process control and state constraints at the same time, and has low computational cost and high real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of a method for cooperative control of heterogeneous multi-agent systems under state and control constraints of the present invention;

[0081] Figure 2 It is a schematic diagram of the structure of the heterogeneous multi-agent system cooperative control device under the state and control constraints of the present invention;

[0082] Figure 3 It is a schematic diagram of the structure of the heterogeneous multi-agent system of the present invention;

[0083] Figure 4 is a compensation state 1 trajectory diagram of each agent in the compensation system of the present invention;

[0084] Figure 5 is a compensation state 2 trajectory diagram of each agent in the compensation system of the present invention;

[0085] Figure 6It is a compensation state 3 trajectory diagram of each agent in the compensation system of the present invention;

[0086] Figure 7 It is a motion state 1 trajectory diagram of each agent in the heterogeneous multi-agent system of the present invention;

[0087] Figure 8 It is a motion state 2 trajectory diagram of each agent in the heterogeneous multi-agent system of the present invention;

[0088] Fig. 9 It is a motion state 3 trajectory diagram of each agent in the heterogeneous multi-agent system of the present invention. DETAILED DESCRIPTION

[0089] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0090] The terms used in the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the" and "the" used in the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0091] It should be understood that although the terms first, second, third, etc. may be used in the present invention to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present invention, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0092] The present invention is described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the features of the following embodiments and implementations can be combined with each other.

[0093] See also Figure 1 The method for cooperative control of heterogeneous multi-agent systems under state and control constraints of the present invention specifically comprises the following steps:

[0094] (1) Based on the system matrix and control matrix of each agent in the heterogeneous multi-agent system, the compensation system matrix as well as the motion state, compensation state and compensation state feedback matrix of each agent are calculated.

[0095] (1.1) The discrete-time model of each agent is obtained based on the system matrix and control matrix of each agent in the heterogeneous multi-agent system, and the motion state of each agent is obtained based on the discrete-time model of each agent.

[0096] Furthermore, the discrete-time model of the agent is expressed as:

[0097] (1)

[0098] (2)

[0099] (3)

[0100] (4)

[0101] In the formula, represents the n-dimensional motion state of the ith agent at time k+1, represents the n-dimensional motion state of the i-th agent at time k, represents the m-dimensional control input of i agents at time k, represents the n×n dimensional system matrix of the ith agent, represents the m×m dimensional control matrix of the ith agent, represents the 2-norm of a vector or matrix, represents the boundary value of the state constraint, represents the boundary value of the control constraint, and N represents the total number of agents in the heterogeneous multi-agent system.

[0102] (1.2) Obtain the compensation state of the corresponding agent according to the discrete time model of each agent in the compensation system.

[0103] Furthermore, the discrete-time model of the agent in the compensation system is expressed as:

[0104] (5)

[0105] In the formula, represents the n-dimensional compensation state of the ith agent at time k+1, represents the n-dimensional compensation state of the ith agent at time k, represents the n-dimensional control input of the ith agent at time k, represents the n×n dimensional compensation system matrix.

[0106] (1.3) Obtain the navigator model of the compensation system based on the discrete-time model of the agent in the compensation system.

[0107] Furthermore, the navigator model of the compensation system is expressed as:

[0108] (6)

[0109] In the formula, represents the n-dimensional compensation state of the navigator at time k+1, represents the n-dimensional compensation state of the navigator at time k, represents the n-dimensional control input of the navigator at time k. The navigator is designed Sets the reference signal for the compensation system.

[0110] (1.4) Solve the optimization problem shown in formula (7) to obtain the compensation system matrix with the highest similarity to the system matrix of each intelligent agent.

[0111] (7)

[0112] (1.5) Solve the optimization problem shown in formula (8) to obtain the n×m dimensional compensation state feedback matrix of each agent, so that the system matrix of the heterogeneous multi-agent system can be transformed into the compensation system matrix.

[0113] (8)

[0114] In the formula, represents the n×m dimensional compensation state feedback matrix of the ith agent.

[0115] (2) The motion state, compensation state and compensation state feedback matrix of each intelligent agent are used to design a collaborative control law for it so that the state error between the motion state and compensation state of each intelligent agent converges to zero.

[0116] (2.1) For each agent, the motion state, compensation state and compensation state feedback matrix of the agent are used to design a cooperative control law for the agent, which can be expressed as:

[0117] (9)

[0118] In the formula, represents the m×n dimensional state error feedback matrix of the ith agent.

[0119] (2.2) The error between the actual motion state and the compensation state of each agent is defined as the state error of the agent, and the error system equation of the agent is obtained according to the state error of the agent.

[0120] Furthermore, the state error of the i-th agent is expressed as:

[0121] (10)

[0122] In the formula, Represents the state error of the ith agent at time k.

[0123] Furthermore, a series of deformation calculations are performed according to formula (1), formula (5), formula (8), formula (9) and formula (10), and the process is shown in formula (11):

[0124] (11)

[0125] From the above formula (11), we can finally get the error system equation of the agent, which is expressed as:

[0126] (12)

[0127] In the formula, Represents the state error of the ith agent at time k+1.

[0128] (2.3) Based on the error system equation of each agent, with the optimization goal of converging the state error of the agent to zero, solve the matrix Riccati equation shown in formula (13) to obtain the unique solution of the matrix Riccati equation corresponding to the agent.

[0129] (13)

[0130] In the formula, represents the unique solution of the matrix Riccati equation corresponding to the i-th agent, the weight matrix represents the n×n dimensional semi-positive definite matrix of the ith agent, the weight matrix represents the m×m dimensional positive definite matrix of the ith agent. The superscript T represents the transpose of a matrix or vector.

[0131] Furthermore, based on the error system equation of each agent, the optimization goal is to converge the state error of the agent to zero, which specifically includes:

[0132] ① The compensation system achieves consistency, namely:

[0133] (14)

[0134] In the formula, represents the compensation state of the ith agent at time k, represents the compensation state of the j-th agent at time k.

[0135] ②The state error eventually converges to zero, that is , which is equivalent to:

[0136] (15)

[0137] ③ The multi-agent system achieves the consistency of its motion state, that is:

[0138] (16)

[0139] In the formula, represents the motion state of the ith agent at time k, Represents the motion state of the j-th agent at time k.

[0140] (2.4) For each agent, its state error feedback matrix is ​​obtained according to the unique solution of its corresponding matrix Riccati equation, which is expressed as:

[0141] (17)

[0142] It should be understood that the state error feedback matrix calculated by formula (13) can make the state error between the motion state and the compensation state of the intelligent agent converge to zero, so substituting it into formula (8) can obtain the optimal cooperative control law in which the state error converges to zero.

[0143] (2.5) Substitute the state error feedback matrix of the agent obtained in step (2.4) into the cooperative control law corresponding to the agent, that is, formula (8), to obtain the optimal cooperative control law in which the state error converges to zero.

[0144] (3) Each intelligent agent seeks the optimal coupling coefficient by compensating for state constraints and consistency constraints to construct a distributed control law for each intelligent agent.

[0145] (3.1) Determine the compensation state constraints of each agent, specifically: at time k, the motion state of agent i is It is known that its control input satisfies the constraints , in order to make the motion state at time k+1 satisfy the constraint condition , then the compensation state at time k is The following compensation state constraints should be met:

[0146] (18)

[0147] (19)

[0148] (3.2) The control objective of the compensation system is determined by making the compensation state of agent i consistent with the compensation state of its neighbor agent j.

[0149] Furthermore, the control objective of the compensation system is expressed as:

[0150] (20)

[0151] In the formula, J represents the control target of the compensation system, T is the optimization step size, and the weight matrix represents the n×n dimensional semi-positive definite matrix of the navigator, the weight matrix represents the m×m dimensional positive definite matrix of the navigator. The superscript T represents the transpose of the matrix or vector.

[0152] (3.3) According to the control objective of the compensation system and the compensation system matrix, the matrix Riccati equation shown in formula (21) is solved to obtain the unique solution of the matrix Riccati equation corresponding to the navigator.

[0153] (twenty one)

[0154] In the formula, Represents the unique solution of the matrix Riccati equation corresponding to the navigator.

[0155] (3.4) The feedback matrix of the compensation system is obtained according to the unique solution of the matrix Riccati equation corresponding to the navigator, which is expressed as:

[0156] (twenty two)

[0157] In the formula, represents the feedback matrix of the compensation system.

[0158] (3.5) The coupling coefficient between agent i and agent j satisfies the consistency constraint and is expressed as:

[0159] (twenty three)

[0160] In the formula, is the coupling coefficient between agent i and agent j at time k, for The optimal coupling coefficient is obtained by obtaining the optimal adjustable parameters that satisfy the compensation state constraint and consistency constraint.

[0161] Furthermore, by obtaining the optimal adjustable parameters that satisfy the compensation state constraints and consistency constraints Obtaining the optimal coupling coefficient includes: solving the following optimization problem to obtain the optimal adjustable parameters that satisfy the compensation state constraints and consistency constraints :

[0162] (twenty four)

[0163] In the formula, represents the adjustable parameter at time k, represents the adjustable parameter at time k-1, that is, to solve under the constraints shown in formula (5), formula (18), formula (19) and formula (23) , we can get the optimal adjustable parameters at time t ; According to the optimal adjustable parameters at time t And the optimal coupling coefficient at time t-1 obtains the optimal coupling coefficient at the current time t.

[0164] It should be understood that the optimal adjustable parameter obtained by solving formula (24) is As in formula (23) Substitute it into the calculation and finally get the optimal coupling coefficient at time k .

[0165] (3.6) The distributed control law is constructed using the optimal coupling coefficient, the feedback matrix of the compensation system, the compensation state of each agent, and the compensation state of the leader, which is expressed as:

[0166] (25)

[0167] In the formula, Is the identifier of whether agent j sends information to agent i. If agent j sends information to agent i, then ,otherwise ; represents the compensation state of agent i at time k, represents the compensation state of agent j at time k, represents the compensation state of the navigator at time k.

[0168] (4) According to the collaborative control law and distributed control law corresponding to each intelligent agent, the motion state and compensation state of the corresponding intelligent agent at the next moment are obtained to realize the motion control of the intelligent agent.

[0169] In summary, the present invention is directed to a heterogeneous multi-agent system, which converts the control input and motion state constraints of the agent into the compensation state constraints of the compensation system, and solves the time-varying coupling coefficient of the compensation system to achieve consistency; the present invention can process control and state constraints at the same time, and has low computational cost and high real-time performance.

[0170] It is worth mentioning that an embodiment of the present invention further provides a collaborative control device for implementing the heterogeneous multi-agent system collaborative control method under the state and control constraints in the above embodiment, the device includes a compensation system distributed control module, an agent collaborative control module and a motion control module, wherein the compensation system distributed control module includes a compensation system model component and a coupling coefficient optimization component, such as Figure 2 shown.

[0171] In this embodiment, the compensation system model component is used to calculate the compensation system matrix and the motion state, compensation state and compensation state feedback matrix of each agent based on the system matrix and control matrix of each agent in the heterogeneous multi-agent system.

[0172] In this embodiment, the intelligent agent collaborative control module is used to design a collaborative control law for each intelligent agent using the motion state, compensation state and compensation state feedback matrix so that the state error between the motion state and compensation state of each intelligent agent converges to zero.

[0173] In this embodiment, the coupling coefficient optimization component is used to find the optimal coupling coefficient by compensating the state constraint and the consistency constraint to construct a distributed control law for each intelligent agent.

[0174] In this embodiment, the motion control module is used to obtain the motion state and compensation state of the corresponding intelligent body at the next moment according to the collaborative control law and distributed control law corresponding to each intelligent body, so as to realize the motion control of the intelligent body.

[0175] The following describes in detail the method and device for collaborative control of heterogeneous multi-agent systems under state and control constraints of the present invention based on the embodiments, and the purpose and effect of the present invention will become more obvious.

[0176] In this embodiment, a multi-agent system, whose structure and communication topology are as follows Figure 3 As shown, it includes three heterogeneous agents and a leader.

[0177] Step 1. Due to , , , , weight matrix , weight matrix , weight matrix , weight matrix , the initial motion state of each agent And the initial compensation state of each agent is known, so it is initialized; and the optimization step size T is set. In this embodiment, the system matrix and control matrix of the three agents are:

[0178] , , ;

[0179] , , .

[0180] The initial motion state and initial compensation state of each agent are:

[0181] , , , .

[0182] Selection weight matrix , weight matrix , weight matrix , weight matrix is the identity matrix, ; , , .

[0183] Step 2: Based on the known , solving the optimization problem (7), that is, formula (7), we can get According to the known , And the solved , solving the optimization problem (8), that is, formula (8), we can get , According to the known , And the solved , solve formula (21), and we get According to known And the solved and , solve formula (22), and we can get According to the known , , , , solve formula (13), and we get According to known , , And the solved , solve formula (17), and we can get , According to the navigator model of the compensation system shown in formula (6), the navigator is constructed by artificial Set the reference signal of the compensation system as the reference signal of each agent, .

[0184] Step 3. Loop through the following steps:

[0185] For the i-th agent, solve the optimization problem (24), that is, formula (24), to obtain the optimal adjustable parameters ; Based on the best adjustable parameters Solve formula (23) to obtain the optimal coupling coefficient ; According to the solution And the compensation state of the intelligent agent, use formula (25) to construct the distributed control law ; Then use formula (5) to obtain the compensation state at the next moment , ;

[0186] Then use formula (9) to construct the coordinated control law , and then use formula (1) to obtain the motion state at the next moment .

[0187] Finally, we can get Figure 4-Figure 9 The trajectory result diagram is shown in Figure 1. The trajectory diagram of compensation state 1 of each intelligent agent in the compensation system is shown in Figure 2. Figure 4 As shown in the figure, the compensation state 2 trajectory diagram of each agent in the compensation system is as follows Figure 5 As shown in the figure, the compensation state 3 trajectory diagram of each agent in the compensation system is as follows Figure 6 As shown, Indicates the compensation state of the navigator 1, Indicates the compensation state 1 of agent 2. The 2 in the subscript position represents agent 2, and the 1 in the superscript position represents the compensation state 1. The motion state 1 trajectory diagram of each agent in the heterogeneous multi-agent system is shown in Figure 7 As shown in the figure, the motion state 2 trajectory diagram of each agent in the heterogeneous multi-agent system is as follows Figure 8 As shown in the figure, the motion state trajectory diagram of each agent in the heterogeneous multi-agent system is as follows Fig. 9 As shown, The subscript 3 represents the motion state 2 of agent 3, and the superscript 2 represents the motion state 2. It can be seen from the above trajectory diagram that when the consistency of the compensation system is achieved, the heterogeneous multi-agent system also quickly achieves the consistency of the motion state.

[0188] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A method for cooperative control of heterogeneous multi-agent systems under state and control constraints, characterized in that: The following steps are involved: (1) Calculate the compensation system matrix and the motion state, compensation state, and compensation state feedback matrix of each agent in the heterogeneous multi-agent system based on the system matrix and control matrix of each agent; (2) Using the motion state, compensation state, and compensation state feedback matrix of each agent, a coordinated control law is designed for it so that the state error between the motion state and compensation state of each agent converges to zero; The step (2) comprises the following sub-steps: (2.1) For each agent, the coordinated control law is designed for the agent using the motion state, compensation state and compensation state feedback matrix of the agent, which can be expressed as: In the formula, K i represents the m×n dimensional state error feedback matrix of the ith agent, u i (k) represents the m-dimensional control input of the i-agent at time k, x i (k) represents the n-dimensional motion state of the i-th agent at time k, represents the n-dimensional compensation state of the ith agent at time k, L i represents the n×m-dimensional compensation state feedback matrix of the ith agent; (2.2) The error between the actual motion state and the compensation state of each agent is defined as the state error of the agent, and the error system equation of the agent is obtained according to the state error of the agent; (2.3) Based on the error system equation of each agent, with the state error of the agent converging to zero as the optimization goal, solve the matrix Riccati equation shown in formula (13) to obtain the unique solution of the matrix Riccati equation corresponding to the agent; Where P i represents the unique solution of the matrix Riccati equation corresponding to the i-th agent, the weight matrix Q i represents the n×n dimensional semi-positive definite matrix of the ith agent, the weight matrix R i represents the m×m dimensional positive definite matrix of the ith agent, the superscript T represents the transpose of the matrix or vector, A i represents the n×n dimensional system matrix of the ith agent, B i represents the m×m dimensional control matrix of the ith agent; (2.4) For each agent, its state error feedback matrix is ​​obtained according to the unique solution of its corresponding matrix Riccati equation, which is expressed as: (2.5) Substitute the state error feedback matrix of the agent obtained in step (2.4) into the cooperative control law corresponding to the agent to obtain the optimal cooperative control law in which the state error converges to zero; (3) Each agent seeks the optimal coupling coefficient by compensating for state constraints and consistency constraints to construct a distributed control law for each agent; The step (3) comprises the following sub-steps: (3.1) Determine the compensation state constraints of each agent, specifically: At time k, the motion state x of agent i is i (k) It is known that its control input satisfies the constraint condition ||u i (k)||≤β i , in order to make the motion state at time k+1 satisfy the constraint condition ||x i (k)||≤α i , then the compensation state at time k is The following compensation state constraints should be met: Among them, α i represents the boundary value of the state constraint, β i represents the boundary value of the control constraint; (3.2) Determine the control target of the compensation system by making the compensation state of agent i consistent with the compensation state of its neighbor agent j; (3.3) Solve the matrix Riccati equation shown in formula (21) according to the control target of the compensation system and the compensation system matrix to obtain the unique solution of the matrix Riccati equation corresponding to the navigator; Where P0 represents the unique solution of the matrix Riccati equation corresponding to the navigator, the weight matrix Q0 represents the n×n dimensional semi-positive definite matrix of the navigator, the weight matrix R0 represents the m×m dimensional positive definite matrix of the navigator, and A0 represents the n×n dimensional compensation system matrix; (3.4) The feedback matrix of the compensation system is obtained according to the unique solution of the matrix Riccati equation corresponding to the navigator, which is expressed as: K0=-(R0+P0) -1 P0A0 (22) Where K0 represents the feedback matrix of the compensation system; (3.5) The coupling coefficient between agent i and agent j satisfies the consistency constraint condition and is expressed as: In the formula, c ij (k)>0 is the coupling coefficient between agent i and agent j at time k, λ ij (k-1)>0 is c ij (k) is an adjustable parameter of the growth rate; and the optimal coupling coefficient is obtained by obtaining the optimal adjustable parameter that satisfies the compensation state constraint and the consistency constraint; By obtaining the optimal adjustable parameter λ that satisfies the compensation state constraint and the consistency constraint ij (k) Obtaining the optimal coupling coefficient, specifically including: Solve the following optimization problem to obtain the optimal adjustable parameter λ that satisfies the compensation state constraint and consistency constraint: ij (k): In the formula, λ ij (k) represents the adjustable parameter at time k, λ ij (k-1) represents the adjustable parameter at time k-1, st(5),(18),(19),(23) represent the solution of min|λ ij (k)-λ ij The constraints of (k-1)| are formula (5), formula (18), formula (19) and formula (23); according to the optimal adjustable parameter λ at time t ij (k) and the optimal coupling coefficient at time t-1 to obtain the optimal coupling coefficient at the current time t; Formula (5) is the discrete time model of the agent in the compensation system, and its expression is: In the formula, represents the n-dimensional compensation state of the ith agent at time k+1, represents the n-dimensional compensation state of the ith agent at time k, ν i (k) represents the n-dimensional control input of the ith agent at time k, and A0 represents the n×n-dimensional compensation system matrix; (3.6) The distributed control law is constructed using the optimal coupling coefficient, the feedback matrix of the compensation system, the compensation state of each agent, and the compensation state of the navigator, which is expressed as: In the formula, a ij is the identifier of whether agent j sends information to agent i. If agent j sends information to agent i, then a ij =1, otherwise a ij =0; represents the compensation state of agent i at time k, represents the compensation state of agent j at time k, represents the compensation state of the navigator at time k; ν i (k) represents the n-dimensional control input of the ith agent at time k, and N represents the total number of agents in the heterogeneous multi-agent system; (4) According to the collaborative control law and distributed control law corresponding to each intelligent agent, the motion state and compensation state of the corresponding intelligent agent at the next moment are obtained to realize the motion control of the intelligent agent.

2. The method for cooperative control of heterogeneous multi-agent systems under state and control constraints according to claim 1 is characterized in that: The step (1) comprises the following sub-steps: (1.1) Obtaining the discrete time model of each agent based on the system matrix and control matrix of each agent in the heterogeneous multi-agent system, and obtaining the motion state of each agent based on the discrete time model of each agent; (1.2) obtaining the compensation state of the corresponding intelligent agent according to the discrete time model of each intelligent agent in the compensation system; (1.3) Obtaining the navigator model of the compensation system based on the discrete time model of the agent in the compensation system; (1.4) Solve the optimization problem shown in formula (7) to obtain the compensation system matrix with the highest similarity to the system matrix of each intelligent agent; In the formula, A i represents the n×n dimensional system matrix of the i-th agent, A0 represents the n×n dimensional compensation system matrix, and N represents the total number of agents in the heterogeneous multi-agent system; (1.5) Solve the optimization problem shown in formula (8) to obtain the n×m dimensional compensation state feedback matrix of each agent: Where, L i represents the n×m-dimensional compensation state feedback matrix of the ith agent, B i represents the m×m dimensional control matrix of the ith agent.

3. The method for cooperative control of heterogeneous multi-agent systems under state and control constraints according to claim 2 is characterized in that: The discrete-time model of the agent is expressed as: x i (k+1)=A i x i (k)+B i u i (k) (1) ||x i (k)||≤α i (2) ||in i (k)||≤β i (3) 1≤i≤N (4)In the formula, x i (k+1) represents the n-dimensional motion state of the ith agent at time k+1, x i (k) represents the n-dimensional motion state of the ith agent at time k, u i (k) represents the m-dimensional control input of the i-agent at time k, A i represents the n×n dimensional system matrix of the ith agent, B i represents the m×m dimensional control matrix of the ith agent, ||·|| represents the 2-norm of a vector or matrix, α i represents the boundary value of the state constraint, β i represents the boundary value of the control constraint, and N represents the total number of agents in the heterogeneous multi-agent system.

4. The method for cooperative control of heterogeneous multi-agent systems under state and control constraints according to claim 2, characterized in that: The discrete time model of the agent in the compensation system is expressed as: In the formula, represents the n-dimensional compensation state of the ith agent at time k+1, represents the n-dimensional compensation state of the ith agent at time k, ν i (k) represents the n-dimensional control input of the ith agent at time k, and A0 represents the n×n-dimensional compensation system matrix; The navigator model of the compensation system is expressed as: In the formula, represents the n-dimensional compensation state of the navigator at time k+1, represents the n-dimensional compensation state of the navigator at time k, and ν0(k) represents the n-dimensional control input of the navigator at time k.

5. The method for cooperative control of heterogeneous multi-agent systems under state and control constraints according to claim 1, characterized in that: In step (2.2), the state error of the i-th agent is expressed as: In the formula, ε i (k) represents the state error of the i-th agent at time k; The error system equation of the i-th agent is expressed as: e i (k+1)=(A i +B i K i )e i (k)-n i (k) (12) In the formula, ε i (k+1) represents the state error of the i-th agent at time k+1.

6. The method for cooperative control of heterogeneous multi-agent systems under state and control constraints according to claim 1, characterized in that: The control objective of the compensation system is expressed as: Where J represents the control target of the compensation system, and T is the optimization step size.

7. A collaborative control device for implementing the collaborative control method of heterogeneous multi-agent systems under state and control constraints as described in any one of claims 1 to 6, characterized in that: include: A compensation system model component is used to calculate the compensation system matrix and the motion state, compensation state and compensation state feedback matrix of each agent according to the system matrix and control matrix of each agent in the heterogeneous multi-agent system; The intelligent agent cooperative control module is used to design a cooperative control law for each intelligent agent by using the motion state, compensation state and compensation state feedback matrix of each intelligent agent so that the state error between the motion state and compensation state of each intelligent agent converges to zero; The coupling coefficient optimization component is used to find the optimal coupling coefficient by compensating state constraints and consistency constraints to construct distributed control laws for each intelligent agent; and The motion control module is used to obtain the motion state and compensation state of the corresponding intelligent body at the next moment according to the collaborative control law and distributed control law corresponding to each intelligent body, so as to realize the motion control of the intelligent body.

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