Multi-agent system distributed consistency optimization method considering unbalanced directed communication graph

Abstract

The invention relates to a multi-agent system distributed consistency optimization method considering an unbalanced directed communication graph, and belongs to the field of multi-agent system coordination control. The method comprises the following steps: S1, establishing a first-order dynamic model of a multi-agent system; s2, constructing an unbalanced directed communication topology network of the multi-agent system, and describing a communication relationship between agents through an adjacent matrix; s3, defining a global optimization target to minimize the sum of local cost functions of all agents; s4, constructing a distance-based adaptive precise penalty function, and converting a set constraint optimization problem into a set-free constraint optimization problem; s5, designing an adaptive coupling gain to solve a distributed optimization problem, and designing an auxiliary variable to estimate a left eigenvector corresponding to a zero eigenvalue of the Laplacian matrix; and then updating the state variable and the auxiliary variable of the intelligent agent according to the estimated value, and solving the problem of consistency optimization of the multi-intelligent-agent system of which the cost function cannot be differentiated.

Description

Technical Field

[0001] The present invention belongs to the field of coordinated control of multi-agent systems, and relates to a distributed consensus optimization method for multi-agent systems considering unbalanced directed communication graphs. Background Art

[0002] With the rapid development of energy Internet and intelligent Internet of Things technologies, distributed multi-agent systems have shown important application values in key fields such as electric power energy and intelligent transportation. In the battery energy storage system of the smart grid, the coordinated control of the output power of multiple battery packs requires achieving the optimal distribution of the total discharge power while ensuring the consistency of the power output of each unit; in the formation control of unmanned aerial vehicles, the trajectory planning of multiple aircraft needs to satisfy both the global optimal path search and the formation shape constraint. These typical application scenarios can be modeled as distributed consensus optimization problems of multi-agent systems, and their mathematical models are essentially non-differentiable function optimization problems with set constraints.

[0003] Existing distributed optimization algorithms have significant limitations in terms of network topology adaptability. Traditional methods such as the distributed subgradient algorithm based on gradient descent (Nedic A, 2011), the primal-dual algorithm based on dual decomposition (Zhu M, 2015), etc. all require that the communication topology satisfies the condition of an undirected graph or a balanced directed graph. However, in the actual deployment of industrial Internet of Things, due to physical limitations such as asymmetric attenuation of communication links and directional communication interruptions caused by limited node energy. Especially in the distributed energy management of microgrids, when the communication between photovoltaic inverter nodes and energy storage systems experiences a one-way interruption, the adjacency matrix of the system will no longer satisfy the balanced condition of equal row sum and column sum, resulting in the failure of the key consensus error convergence mechanism in existing algorithms.

[0004] To solve the distributed optimization problem under the condition of unbalanced directed communication topology, the academic community has proposed distributed control methods based on multi-agent systems in recent years. The paper "Distributed adaptive convex optimization on directed graphs via continuous-time algorithms" published in the IEEE Transactions on Automatic Control proposed a consensus control method based on adaptive coupling gain, but the objective function is required to be differentiable, and the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix needs to be pre-computed; the paper "Fully distributed continuous-time algorithm for nonconvex optimization over unbalanced digraphs" published in the 9th International Conference on Control, Decision and Information Technologies proposed a distributed optimization method that can estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, but the objective function is required to be differentiable, and it cannot solve the optimization problem with set constraints; the paper "Fully distributed algorithm for resource allocation over unbalanced directed networks without global Lipschitz condition" published in the IEEE Transactions on Automatic Control proposed a distributed optimization method based on differentiable projection operation, but the objective function is required to be differentiable; the paper "A predefined-time consensus algorithm of multi-agent system for distributed constrained optimization" published in the IEEE Transactions on Network Science and Engineering proposed a consensus control method based on exact penalty function, but it cannot be applied to the scenario where the communication topology is an unbalanced directed graph.

[0005] Although certain progress has been made in recent years in the research on distributed optimization for unbalanced directed graphs, there are still three major technical bottlenecks in terms of engineering applicability: First, existing methods generally require the objective function to satisfy the differentiability condition, while rectifier loss functions, battery charge and discharge efficiency functions, etc., which widely exist in actual systems, have the characteristics of piecewise linear non-differentiability; Second, existing algorithms are difficult to handle set constraints formed by device physical limitations, such as the hard boundary constraints of the state of charge (SOC) of energy storage systems, the safety distance constraints of UAV formations, etc.; Third, most solutions rely on the global eigenvalue information of the Laplacian matrix and require pre-computation or online estimation of its left eigenvectors, which is difficult to achieve in actual dynamic topology scenarios. For example, in the collaborative transportation task of robots, when communication links dynamically switch due to environmental obstacles, the distributed optimizer based on the fixed topology assumption will exhibit a steady-state deviation.

[0006] Therefore, it is urgent to establish a new distributed optimization theory framework for unbalanced directed graphs and focus on breaking through the following key technologies: 1) Design a distributed optimization mechanism that does not require the differentiability of the objective function and is compatible with non-smooth objective functions such as rectifier losses and friction models; 2) Develop a distributed processing technology that embeds set constraints to achieve distributed modeling and solution of device physical limitations; 3) Construct a distributed algorithm architecture that adapts to dynamic topologies to eliminate the dependence on the global eigenvalues of the Laplacian matrix. These technological breakthroughs will effectively improve the optimization control performance in key fields such as distributed energy management systems and intelligent logistics robot clusters, and have important engineering application value. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide a distributed consensus optimization method for multi-agent systems considering unbalanced directed communication graphs. For the consensus optimization problem of multi-agent systems with non-differentiable cost functions, a distributed optimization algorithm considering unbalanced directed communication topologies and set constraints is constructed by combining distance penalty functions and adaptive control methods, which can be widely applied to fields such as smart grids, UAV formations, sensor networks, and robot collaborations, and has high practicality and promotion value.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] Solution 1: A distributed consensus optimization method for multi-agent systems considering unbalanced directed communication graphs, as Figure 1 shown, specifically includes the following steps:

[0010] S1: Establish a first-order dynamic model of the multi-agent system;

[0011] S2: Construct an unbalanced directed communication topology network of the multi-agent system, and describe the communication relationship between agents through an adjacency matrix;

[0012] S3: Model the distributed optimization problem, and define the global optimization objective as minimizing the sum of the local cost functions of all agents, and the optimal solution satisfies the set constraints;

[0013] S4: Construct an adaptive exact penalty function based on distance to transform the set-constrained optimization problem into an unconstrained optimization problem;

[0014] S5: Design a distributed algorithm based on the adaptive control method, specifically including: designing an adaptive coupling gain to solve the distributed optimization problem, and designing an auxiliary variable to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix; then update the state variables and auxiliary variables of the agents according to the estimated values.

[0015] Furthermore, in step S1, establish a first-order dynamic model of the multi-agent system (such as a battery energy storage system, etc.), expressed as:

[0016]

[0017] where, is the state variable (such as output power, state of charge, etc.) of the i-th agent (such as a battery pack, etc.), u i (t) is the control input, i = 1, 2, …, N is the agent number, and N is the total number of agents.

[0018] Furthermore, step S2 specifically includes: constructing a non-balanced directed communication topology network of the multi-agent system, where each node in the network topology represents an agent, and the edge represents the communication relationship between agents; the constructed network topology graph is a non-balanced directed graph where, V = v1, …, v N is the agent set, represents the edge set of the communication relationship between agents.

[0019] Then describe the communication relationship between agents through the adjacency matrix A of the network topology structure of the multi-agent system. If the i-th agent can receive information from the j-th agent, then the adjacency matrix element a ij > 0, otherwise a ij = 0, and assume that there is no self-loop in the communication topology graph, that is, a ii = 0; the expression of the adjacency matrix A is:

[0020] The method designed by the present invention exchanges local information through the constructed communication topology graph, enabling each agent to perform optimization adjustments according to the states of adjacent agents.

[0021] Furthermore, in step S3, the total cost function (such as the operation cost of the battery energy storage system, etc.) is defined as the sum of all agents' local cost functions, expressed as:

[0022]

[0023] where, f i (x i ) is the local cost function of the i-th agent. The goal is to minimize the sum of all local cost functions, and at the same time, the optimal solution of the total cost function satisfies the set constraint, that is where represents the optimal solution of each agent, represents the set constraint of each agent's state variables. The above problem is equivalent to the following optimization problem:

[0024]

[0025] s.t. x i ∈Ω i

[0026] x i =x j , i, j ∈ 1, 2, …, N

[0027] where the equality constraint x i =x j means that the state variables of the multi-agent system are consistent.

[0028] Furthermore, step S4 specifically includes: dealing with the set constraint by designing a distance-based adaptive exact penalty function to ensure that the state variables of all agents always satisfy the set constraint. The distance-based adaptive exact penalty function is: where the distance function The subgradient is expressed as:

[0029]

[0030] where, ||·|| represents the Euclidean norm; inf{||y - x i ||, y ∈ Ω i} represents the infimum of the norm ||y - x i ||; int(Ω i ) represents the interior set of Ω i ; bd(Ω i ) represents the boundary set of Ω i ; represents the normal cone of the point x i on the set Ω i , that is y ∈ Ωi , where \(z\) and \(y\) represent elements in the sets and \(\Omega\) i respectively; \(B(0; 1)\) represents the unit ball centered at the origin with a radius of 1, that is, \(B(0; 1)=\{y|\|y\|\leq1\}\);

[0031] The set-constrained optimization problem is transformed into an optimization problem without set constraints according to the distance-based adaptive exact penalty function, that is:

[0032]

[0033] s.t. \(x\) i = \(x\) j , \(i,j\in1,2,\cdots,N\)

[0034] where is the adaptive exact penalty factor, which is used to dynamically adjust the control signal during the optimization process. Through \(r\) i , the algorithm can automatically adjust the gain parameters according to the changes in the system state, thereby improving the convergence speed of the system. This method effectively reduces the parameters that need to be pre-calculated and adjusted in the traditional method, improves the flexibility and adaptability of the system, thus reducing the parameter adjustment cost and improving the system robustness. The update formula of the penalty factor is: where represents the derivative of \(r\) i with respect to time \(t\), that is

[0035] Furthermore, in step S5, an auxiliary variable is designed to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, specifically including estimating the left eigenvector corresponding to the zero eigenvalue of the communication topology Laplacian matrix \(L\) by means of the auxiliary variable , so as to solve the consensus optimization problem under the condition of an unbalanced directed communication topology graph.

[0036] The initialization condition of \(z\) i is \(k\neq i\), \(k = 1,2,\cdots N\), where is the \(k\)-th component of \(z\) i . The update formula of \(z\) i is: where represents the derivative of \(z\) i with respect to time \(t\), that is

[0037] Furthermore, in step S5, an adaptive coupling gain is designed to solve the distributed optimization problem, specifically including: adjusting the gain through an adaptive control method, designing the control input \(u\) i(t) makes the system reach consistency and finally converge to the global optimal solution under the condition of unbalanced directed network topology. The state variable x i (t) is updated by the following algorithm:

[0038]

[0039] where e i is the relative error, x i is the state variable, is the auxiliary variable, a ij is the element in the i-th row and j-th column of the adjacency matrix A; is the subgradient of the cost function f i (x i ), d(x i , Ω i ) is the distance penalty function, is used to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix; b i , represents the adaptive coupling gain; r i is the adaptive penalty factor, with the initial conditions b i (0) > 0, r i (0) > 0, k and β are adjustable parameters greater than 0; represents the derivative of v i with respect to time t, that is

[0040] In the algorithm, the gradient term is used to optimize the state variable, the state error term and the integral error term are used to achieve the consistency of the state variable; in addition, the algorithm uses a distance-based exact penalty function to handle set constraints and can obtain the consistent optimal solution of the problem under an unbalanced directed graph, that is

[0041] Furthermore, the consistency optimization method designed through the above steps does not require the assumption that the cost function is differentiable and does not require the initialization of the state variable. In addition, the designed algorithm is fully distributed.

[0042] Furthermore, this method is applicable to scenarios where the cost function is non-differentiable, including the optimization of the output power of a battery energy storage system or the trajectory planning of an unmanned aerial vehicle formation, etc.

[0043] Solution 2: A computer-readable storage medium, on which a computer program is stored, characterized in that when the program is executed by a processor, it implements the multi-agent system distributed consistency optimization method as described in Solution 1.

[0044] Solution 3: A multi-agent system control device, comprising a memory, a processor, and a communication module, wherein the processor is configured to run the multi-agent system distributed consistency optimization method as described in Solution 1, and exchange status information with adjacent agents through the communication module.

[0045] The beneficial effects of the present invention are as follows:

[0046] (1) Breaking through the optimization limitations under unbalanced directed communication topologies: The method of the present invention effectively solves the problem of difficult convergence caused by the asymmetry of the adjacency matrix in traditional distributed optimization methods in unbalanced directed communication networks by designing a distributed consistency algorithm based on a dynamic compensation mechanism. In typical application scenarios such as the optimization of the output power of battery energy storage systems and the trajectory planning of UAV formations, this method can achieve the convergence of the global optimal solution of the multi-agent system under asymmetric communication conditions, and is particularly suitable for complex working conditions where there are one-way transmissions or node failures in the communication links.

[0047] (2) Innovatively handling the distributed optimization of non-differentiable objective functions: Aiming at the industry pain point that traditional gradient-based methods cannot handle non-differentiable cost functions, the method of the present invention successfully expands the optimization object to the field of non-differentiable functions by introducing a subgradient optimization mechanism and a consistency error compensation strategy. This method does not require complex initialization operations on the agent state variables, and the algorithm is fully distributed. Each node can complete the optimization calculation only through local communication, significantly reducing the system calculation complexity and providing scalability guarantees for scenarios such as the optimization of large-scale sensor network resources.

[0048] (3) Adaptive parameter adjustment to enhance engineering practicality: The present invention realizes the autonomous optimization configuration of the key parameters of the system by constructing a double-loop adaptive control system (including a precise penalty factor dynamic adjustment module and a coupling gain automatic tuning module), and an auxiliary variable estimation algorithm based on distributed average tracking. This design effectively avoids the disadvantages of traditional methods that require manual repeated adjustment of the penalty factor and rely on centralized calculation of eigenvectors, and is particularly suitable for industrial field environments with dynamically changing communication topologies.

[0049] (4) Fully distributed architecture to enhance system reliability: The method of the present invention completely eliminates the dependence on global network information by designing a decentralized auxiliary variable update rule. Each agent only needs to obtain first-order neighbor information to complete all calculation steps, and can maintain the degraded operation ability in case of communication interruption or node failure. The system fault tolerance is improved compared with traditional centralized optimization methods, providing reliable guarantees for safety-critical applications such as UAV formations.

[0050] Other advantages, objects, and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and obtained by the following description of the specification. Description of the Drawings

[0051] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0052] Figure 1 It is a flowchart of a distributed consensus optimization method for a multi-agent system considering an unbalanced directed communication graph proposed by the present invention;

[0053] Figure 2 It is the distributed control strategy for the i-th battery pack of the BESS in Embodiment 1;

[0054] Figure 3 It is an unbalanced directed communication topology graph with 6 battery packs in Embodiment 1;

[0055] Figure 4 It is a trajectory graph of the output power of each battery pack changing with time in Embodiment 1;

[0056] Figure 5 It is the output power error ‖x - x * ‖ 2 changing with time trajectory graph;

[0057] Figure 6 It is a trajectory graph of the total cost function f(x) of the BESS changing with time in Embodiment 1;

[0058] Figure 7 It is the adaptive coupling gain b of each battery pack in Embodiment 1 i changing with time trajectory graph;

[0059] Figure 8 It is a trajectory graph of the output power of each battery pack changing with time in Embodiment 2;

[0060] Figure 9 It is the output power error ‖x - x * ‖ 2 changing with time trajectory graph;

[0061] Figure 10 It is a trajectory graph of the output power of each battery pack changing with time in Embodiment 3;

[0062] Figure 11 It is the output power error ‖x - x* ‖ 2 Time-varying trajectory diagram. Detailed implementation manners

[0063] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0064] Among them, the accompanying drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0065] Embodiment 1:

[0066] This embodiment focuses on the problem of state of charge (SOC) equalization control at the battery pack level of a battery energy storage system (BESS) operating in parallel, that is, keeping the SOC of all battery packs consistent. BESS has important application values in energy management and storage, especially in providing energy storage for renewable energy power generation. A battery energy storage system may include multiple battery packs, and each battery pack is composed of several battery cells. For each battery pack, a battery management system is used to balance the SOC of all battery cells to ensure the overall operating efficiency of the energy storage system. In addition, the SOC equalization control at the battery pack level can play a role in redundant protection, effectively avoiding the damage of overcharging or over-discharging of the battery during the charging and discharging process. Specifically, the output power x of the i-th battery pack i and its state SOC can be represented by the following relational expression:

[0067]

[0068] where, EFF i is determined by the coulomb efficiency of the i-th battery pack and the converter conversion efficiency, Q represents the capacity of each battery pack, and V d represents a constant related to the battery. The distributed control block diagram of the i-th battery pack of BESS is as Figure 2 shown, where v i and i irespectively represent the output voltage and current of the i-th converter, v represents the distribution bus voltage, and c i is an auxiliary variable of the energy coordinator, is the output power value of the final convergence, which is obtained through the distributed optimization process, while represents the adjusted local reference output power of the i-th battery pack. Each battery pack can determine the required power output based on the local optimization control protocol by communicating with the neighbor battery pack nodes, which provides additional flexibility for the overall BESS. The control system of each battery pack can be represented as the following single-integral dynamic system:

[0069]

[0070] When each battery pack obtains the optimal output power then, the SOC balance at the battery pack level can be achieved through other existing technologies. Therefore, the goal of this embodiment is to achieve the consistency of the power output of each battery pack in the battery energy storage system through the consistency optimization method of the present invention and minimize the local cost, that is, to obtain the where the local cost can be modeled into a specific local cost function to quantitatively describe the "cost" or "loss" generated by a single battery pack during operation, which reflects the comprehensive performance of the battery pack in aspects such as energy management, power output, and health status.

[0071] For this embodiment, it is assumed that the battery energy storage system has 6 battery packs (i.e., N = 6), and its communication topology network diagram is as shown in Figure 3 shown. In addition, the output power of each battery pack is a three-dimensional vector, that is, x i ∈R 3 .

[0072] (1) The adjacency matrix corresponding to the communication topology network diagram is as follows:

[0073]

[0074] (2) It is assumed that the local cost function of each battery pack is as follows:

[0075] f i ( x i)=(x i1 +i) 2 -2.1x i1 i+(x i2 -i) 2 +2.1x i2 i+(x i3 -0.5i) 2 , i = 1, 2,..., 6

[0076] (3) Assume the output power of each battery pack is \(x\). i The constraint conditions are as follows:

[0077] 0.5 ≤ \(x\) ij ≤ 2, \(j = 1, 2, 3\)

[0078] Randomly initialize the state variables \(x\) i (0) and the auxiliary variable \(v\) i (0), and set \(r\) i (0) = 0.01, \(k = 0.1\), \(β = 1\), \(b\) i (0) = 0.01, step size \(step = 0.001\). From the experimental result graphs ( Figure 4 、 Figure 5 ), it can be seen that the three components of the output powers of the 6 battery packs accurately converge to 0.50, 0.50, 1.75 respectively and satisfy the set constraints. Figure 5 In it, \(x\) * represents the exact optimal solution of the consensus optimization problem, so the consensus optimization method of the present invention can obtain the optimal solution of this problem. In addition, the change trajectory graph of the total cost function is as shown in Figure 6 , and finally the optimal value \(f(x\) * ) = 189.4 of the distributed optimization problem is obtained. The adaptive coupling gain \(b\) i of each battery pack over time is as shown in Figure 7 , and it can be seen that \(b\) i finally converges to a constant. Therefore, the distributed consensus optimization method considering the unbalanced directed communication graph proposed by the present invention can obtain the optimal output powers of each battery pack of the BESS

[0079] Example 2:

[0080] For the consensus optimization problem of the battery pack output powers in Example 1, this example considers a more complex cost function. Assume that the unbalanced directed communication topology graph of 6 battery packs (i.e., \(N = 6\)) is as shown in Figure 3 , and the output power of each battery pack is a two-dimensional vector, i.e., \(x\) i ∈\(R\) 2 . In addition, consider the following local cost function and the constraint conditions for the output power \(x\) i of each battery pack:

[0081] (1) Local cost function:

[0082]

[0083] \(f_2(x)=0.6(x\) 21 - 1) 2 + 0.4x21 x 22 +0.2(x 22 +0.6) 2

[0084]

[0085] (2) Set constraint: 1.5 ≤ x ij ≤ 5.0, i = 1, 2, …, 6, j = 1, 2

[0086] Randomly initialize the state variable x i (0) and the auxiliary variable v i (0), and set r i (0) = 0.1, k = 0.5, β = 1, b i (0) = 0.1, step size step = 0.001. From the numerical simulation result graph ( Figure 8 、 Figure 9 ), it can be seen that the two components of the output power of the 6 battery packs converge precisely to 2.215 and 1.500 respectively, and satisfy the set constraint. Figure 9 In it, x * represents the exact optimal solution of the consensus optimization problem. Therefore, the distributed consensus optimization method considering the unbalanced directed communication graph proposed by the present invention can obtain the optimal output power of each battery pack of the BESS under complex cost function conditions

[0087] Example 3:

[0088] For the consensus optimization problem of the battery pack output power in Example 1, this example considers a BESS with 8 battery packs (i.e., N = 8) and non - differentiable local cost functions. Assume that the adjacency matrix A corresponding to the unbalanced directed communication topology graph of the multi - agent system and the local cost function and constraint conditions of each agent are as follows:

[0089] (1) Adjacency matrix A:

[0090]

[0091] (2) Local cost function:

[0092] (3) Set constraint: 4.5 ≤ x i ≤ 9.0, i = 1, 2, …, 8;

[0093] Randomly initialize the state variable x i (0) and the auxiliary variable v i (0), and set r i (0) = 0.1, k = 0.5, β = 1, b i(0) = 0.1, step size step = 0.001. From the experimental result graphs ( Figure 10 and Figure 11 ), it can be seen that the output powers of the 8 battery packs converge precisely to 4.50 and satisfy the set constraints. Figure 11 In * , x represents the exact optimal solution of the consensus optimization problem. Therefore, the distributed consensus optimization method considering unbalanced directed communication graphs proposed in the present invention can obtain the optimal output powers of each battery pack of the BESS under the condition that the cost function is non-differentiable.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A distributed consensus optimization method for multi-agent systems considering unbalanced directed communication graphs, characterized in that The method specifically includes the following steps: S1: Establish a first-order dynamic model of the multi-agent system; S2: Construct a non-equilibrium directed communication topology network of the multi-agent system, and describe the communication relationship between agents through an adjacency matrix; S3: Model the distributed optimization problem, and define the global optimization objective as minimizing the sum of the local cost functions of all agents, and the optimal solution satisfies the set constraints; S4: Construct a distance-based adaptive exact penalty function to transform the set-constrained optimization problem into an unconstrained optimization problem; S5: Design a distributed algorithm based on the adaptive control method, specifically including: designing an adaptive coupling gain to solve the distributed optimization problem, and designing an auxiliary variable to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix; then update the state variables and auxiliary variables of the agent according to the estimated value.

2. The distributed consistency optimization method for the multi-agent system according to claim 1, wherein In step S1, establish a first-order dynamic model of the multi-agent system, expressed as: Among them, is the state variable of the $i$-th agent, and $u$ i (t) is the control input, where $i = 1, 2, \ldots, N$ is the agent number, and $N$ is the total number of agents.

3. The distributed consistency optimization method for the multi-agent system according to claim 2, wherein Step S2 specifically includes: constructing a non - balanced directed communication topology network of a multi - agent system, where each node in the network topology represents an agent, and the edge represents the communication relationship between agents; the constructed network topology graph is a non - balanced directed graph where \(V = \{v_1,\ldots,v_n\}\) N is the set of agents, and \(E\) represents the set of edges of the communication relationship between agents; Then, the communication relationship between agents is described by the adjacency matrix A of the multi-agent system network topology. If the i-th agent can receive information from the j-th agent, then the adjacency matrix element a ij > 0; otherwise, a ij = 0. It is assumed that there are no self-loops in the communication topology graph, that is, a ii = 0. The expression of the adjacency matrix A is:

4. The distributed consistency optimization method for a multi-agent system according to claim 3, characterized in that In step S3, define the global optimization objective as: s.t.x i ∈Ω i where f i (x i ) is the local cost function of the i-th agent; f(x) is the total cost function, that is, the sum of the local cost functions of all agents; the optimal solution of the total cost function satisfies the set constraint, that is where represents the optimal solution of each agent, represents the set constraint of the state variables of each agent.

5. The distributed consensus optimization method for the multi-agent system according to claim 4, characterized in that, Step S4 specifically includes: constructing an adaptive exact penalty function based on distance as follows: where the distance function Secondly, the gradient is expressed as: where, ||·|| represents the Euclidean norm; inf{||y - x i ||, y ∈ Ω i} represents the infimum of the norm ||y - x i ||; int(Ω i ) represents the interior set of Ω i ; bd(Ω i ) represents the boundary set of Ω i ; represents the normal cone of the point x i on the set Ω i , that is y ∈ Ω i , z and y respectively represent the elements of the sets and Ω i ; B(0; 1) represents the unit ball centered at the origin with a radius of 1, that is, B(0; 1) = {y ∣ ||y|| ≤ 1}; According to the distance-based adaptive exact penalty function, transform the set-constrained optimization problem into an unconstrained optimization problem, that is: Among them, is an adaptive precise penalty factor, which is used to dynamically adjust the control signal during the optimization process; the update formula of the penalty factor is: where represents the derivative of r i with respect to time t, that is 6. The distributed consensus optimization method for a multi-agent system according to claim 5, characterized in that In step S5, a design auxiliary variable is used to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix, specifically including: with the aid of the auxiliary variable estimate the left eigenvector corresponding to the zero eigenvalue of the communication topology Laplacian matrix L; z i The initialization condition of is k ≠ i, k = 1, 2, … N, where is the k-th component of z i ; z i The update formula for is as follows: where i denotes the derivative of z with respect to time t, that is 7. The distributed consensus optimization method for a multi-agent system according to claim 6, wherein In step S5, an adaptive coupling gain is designed to solve the distributed optimization problem, specifically including: adjusting the gain through an adaptive control method, and designing the control input u i (t) to make the system reach consensus and finally converge to the global optimal solution under the condition of unbalanced directed network topology; the update algorithm of the state variable x i (t) is as follows: Among them, e i is the relative error, x i is the state variable, is the auxiliary variable, a ij is the element in the i-th row and j-th column of the adjacency matrix A; is the subgradient of the cost function f i (x i ), d(x i , Ω i ) is the distance penalty function, is used to estimate the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix; b i , represents the adaptive coupling gain; r i is the adaptive penalty factor, initial condition b i (0) > 0, r i (0) > 0, k and β are adjustable parameters greater than 0; represents the derivative of v i with respect to time t, that is In the algorithm, the gradient term is used to optimize the state variable, and the state error term and the integral error term are used to achieve the consistency of the state variable; in addition, the set constraints are processed by using the distance-based exact penalty function, and the consistent optimal solution of the problem can be obtained under the unbalanced directed graph, that is 8. The distributed consensus optimization method for the multi-agent system according to any one of claims 1 to 7, characterized in that, This method is applicable to scenarios where the cost function is non-differentiable, including the optimization of the output power of a battery energy storage system or the trajectory planning of a UAV formation.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the distributed consensus optimization method of the multi-agent system according to any one of claims 1 to 7.

10. A multi-agent system control device, comprising a memory, a processor and a communication module, characterized in that, The processor is configured to run the distributed consensus optimization method of the multi-agent system according to any one of claims 1 to 7, and exchange state information with adjacent agents through a communication module.

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