A Distributed Constraint Optimization Control Method Based on Iterative Learning Control

Abstract

This invention belongs to the field of intelligent control technology, specifically relating to a distributed constraint optimization control method based on iterative learning control. The method includes establishing a multi-agent system, determining the optimization objective function, building a communication network for the multi-agent system, designing a control protocol based on a terminal iterative learning control method and a distributed projection gradient algorithm, and proving convergence to achieve the optimal solution. This invention aims to solve the problem that multi-agent systems must adhere to specific constraints while completing optimization tasks in an iterative environment. The control method of this invention ensures that constrained multi-agent systems with repetitive motion characteristics complete optimization tasks while avoiding single-point failures and poor robustness.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology, specifically relating to a distributed constraint optimization control method based on iterative learning control. Background Technology

[0002] With the rapid development of communication and sensor technologies, control systems are increasingly characterized by large-scale and networked architectures, such as power networks, transportation networks, and sensor networks. This has led to widespread attention being paid to distributed cooperative control of multi-agent systems. In control systems, many practical problems can be transformed into optimization problems. Centralized optimization algorithms, limited by computational power and inefficient network information transmission, struggle to achieve efficient centralized information processing, thus failing to effectively solve optimization problems in large-scale systems. To address these optimization problems, researchers have conducted in-depth research on distributed optimization algorithms based on distributed cooperative control of multi-agent systems. In this algorithm, each agent is assigned an objective function, and the global objective function is the sum of these objective functions. Agents optimize their own objective functions and interact with their neighbors to optimize the global objective function. Compared to centralized optimization algorithms, distributed optimization algorithms effectively avoid single points of failure and poor robustness.

[0003] It is worth noting that many control systems, such as intelligent manufacturing and industrial automation systems, often need to repeatedly execute control tasks within a finite time frame in practical applications. These systems not only exhibit time-varying dynamic characteristics but also evolve along the iteration axis within a finite time frame, displaying unique two-dimensional dynamic characteristics. For this type of behavior, iterative learning control (ILC) is often employed. It continuously optimizes the control input by utilizing past information, thereby improving the system's tracking performance. Traditional iterative learning control methods typically rely on known target information. However, in optimization problems, since the optimal state is usually unknown, this dependency limits its applicability, making it difficult to effectively solve related optimization problems. Therefore, how to control a class of intelligent agent systems with repetitive motion characteristics to complete optimization tasks is a problem that urgently needs to be solved.

[0004] Currently, for intelligent agent systems with repetitive motion characteristics, existing optimization algorithms can only solve specific problems such as quadratic optimization and unconstrained optimization. They are unable to solve problems where intelligent agents need to follow specific constraints while completing optimization tasks, such as network traffic path selection and economic dispatching of power networks.

[0005] Based on this, the present invention proposes a distributed constraint optimization control method based on iterative learning control to solve the problem of completing optimization tasks for intelligent agent systems with repetitive motion characteristics under constraints. Summary of the Invention

[0006] To address the problem that intelligent agent systems with repetitive motion characteristics struggle to fulfill specific constraints while completing optimization tasks, this invention proposes a distributed constraint optimization control method based on iterative learning control. Primarily targeting optimization problems in large networks, it designs a constraint optimization algorithm based on terminal ILC, which can ensure that multi-agent systems operating in an iterative environment can complete optimization tasks while satisfying constraints.

[0007] The technical solution of this invention is:

[0008] A distributed constraint optimization control method based on iterative learning control includes the following steps:

[0009] Step 1: Establish a multi-agent system;

[0010] Step 2: Determine the objective function for optimization;

[0011] Step 3: Construct a directed graph G ( V , E , A The communication network of a multi-agent system is represented by ), where the node set is... express n There are 1 intelligent agents, each node represents an intelligent agent, and the edge set... This represents the communication connection between intelligent agents; Represents the adjacency matrix;

[0012] Step 4: Based on the terminal iterative learning control method and the distributed projection gradient algorithm, design a distributed control protocol: in Represents learning gain, scalar Indicates non-negative weights. Let represent a positive step size, and satisfy . ; Represents intelligent agents Local objective function exist The gradient at each function The gradient set in the set X The upper limit is bounded, that is... ;

[0013] Step 5: Prove that the state of the controlled system converges to the optimal solution of the objective function at the terminal time as the number of iterations increases, thereby verifying the effectiveness of the distributed control protocol.

[0014] Furthermore, in step 1, a system is established by... n A multi-agent system consisting of 3 agents, the first i The agent in the th... k The dynamic description in this iteration is as follows: in, Indicates the first i The state of an agent, Indicates control input; Indicates the number of iterations / repetitions; Indicates time, where T Indicates the terminal time; .

[0015] Furthermore, the multi-agent system satisfies: the initial state of the system It is the same in each iteration, that is .

[0016] Furthermore, the objective function in step 2 P 1 is in, Indicates minimization. It is an intelligent agent i The corresponding differentiable local objective function, and the function Only for intelligent agents Known; for any Each function yes -Strongly convex, and possessing -Lipschitz continuous gradient, i.e., for any ,satisfy and ,in , ; It is a closed convex set, representing the constraint set of all intelligent agents.

[0017] Furthermore, in step 3, the communication connection... Indicates from the intelligent agent Receiving intelligent agents Information, nodes The neighbor set is defined as ; Let represent the adjacency matrix, where if ,otherwise For all They all ,if ,but ,in, Communication networks It is strongly connected and satisfies .

[0018] Furthermore, in step 5, the method for proving the optimal solution includes the following steps:

[0019] (1) Utilization The multi-agent system can be written in the following form: (6-1)

[0020] (2) Due to Equation (6-1) can be expressed as: (6-2)

[0021] (3) Let Construct it in the following form: (6-3)

[0022] (6-4)

[0023] (6-5)

[0024] (4) By Equation (6-3) can be expressed in the following compact form: (6-6)

[0025] in , , ; L = D - A ,in , ;

[0026] (5) Due to ,Right now It is a double random matrix, from which we can obtain: in , because ,in Representation matrix The spectral norm and satisfy , ,as well as ,but (6-7)

[0027] Define norm ,in Through analysis, we obtained , (6-8)

[0028] Construct the norm relationship between the system state and the optimal solution of the objective function, and further analyze and simplify using equation (6-8) to obtain... .

[0029] The beneficial effects of this invention are:

[0030] (1) Based on terminal ILC and projection gradient algorithm, this invention proposes a distributed optimization control method for the optimization control problem of multi-agent systems with repetitive motion characteristics under constraints. The method includes establishing a multi-agent system, determining the optimization objective function, building a communication network for the multi-agent system, designing a control protocol based on terminal iterative learning control method and distributed projection gradient algorithm, and proving convergence to achieve the optimal solution. It aims to solve the problem that multi-agent systems need to follow specific constraints while completing optimization tasks in an iterative environment, and can enable networked industrial systems with repetitive motion characteristics and constraints to efficiently complete optimization tasks.

[0031] (2) The distributed optimization control method proposed in this invention adopts a decentralized architecture to avoid centralized information processing. While ensuring that the intelligent agent system completes the optimization task, it can effectively avoid problems such as single point failure and poor robustness. It is suitable for the optimization control of large-scale network systems such as industrial robot collaborative systems, smart grids and logistics transportation. Its distributed characteristics support multi-node parallel computing and dynamic constraint collaborative decomposition, which has significant engineering application value. Attached Figure Description

[0032] Figure 1 This is a flowchart of the distributed constraint optimization control method based on iterative learning control proposed in this invention;

[0033] Figure 2 This is a diagram of a communication network consisting of eight agents.

[0034] Figure 3 This is a schematic diagram of the state of each agent under the distributed constraint optimization control method proposed in this invention, as shown in Example 1.

[0035] Figure 4 This is a schematic diagram showing the average state of all intelligent entities under the distributed constraint optimization control method proposed in this invention, as shown in Example 1.

[0036] Figure 5 This is a schematic diagram of the state of each agent under the distributed constraint optimization control method proposed in this invention, as shown in Example 2.

[0037] Figure 6 This is a schematic diagram showing the average value of all intelligent body states under the distributed constraint optimization control method proposed in this invention, as shown in Example 2. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] To further understand the present invention, it will be further described in conjunction with the accompanying drawings and embodiments.

[0040] This invention addresses the optimization problem in constrained networked industrial systems with repetitive motion characteristics, proposing a distributed constrained optimization control method based on iterative learning control, comprising the following steps: Step 1, establishing a distributed constrained optimization control method based on iterative learning control. n A multi-agent system consisting of 3 agents, the first i The agent in the th... k The dynamic description in this iteration is as follows: in, Indicates the first i The state of an agent, Indicates control input; Indicates the number of iterations / repetitions; Indicates time, where T Indicates the terminal time; ;

[0041] The system satisfies: the initial state of the system It is the same in each iteration, that is .

[0042] Step 2: Determine the objective function. P 1 is in, Indicates minimization. It is an intelligent agent i The corresponding differentiable local objective function, and the function Only for intelligent agents Known; for any Each function yes -Strongly convex, and possessing -Lipschitz continuous gradient, i.e., for any ,satisfy and ,in , ; It is a closed convex set, representing the constraint set of all intelligent agents.

[0043] Step 3: Construct a directed graph G (V , E , A The communication network of a multi-agent system is represented by ), where the node set is... express n There are 1 intelligent agents, each node represents an intelligent agent, and the edge set... Represents the communication connection between intelligent agents; communication connection Indicates from the intelligent agent Receiving intelligent agents Information, nodes The neighbor set is defined as ; Let represent the adjacency matrix, where if ,otherwise For all They all ,if ,but ,in, Communication networks It is strongly connected and satisfies .

[0044] Step 4: Based on the terminal iterative learning control method and the distributed projection gradient algorithm, design a distributed control protocol: in Represents learning gain, scalar Indicates non-negative weights. Let represent a positive step size, and satisfy . ; Represents intelligent agents Local objective function exist The gradient at each function The gradient set in the set X The upper limit is bounded, that is... .

[0045] Step 5: Prove convergence and achieve the optimal solution, i.e., prove: ,in It is the first At the terminal moment, an intelligent agent state, Representing the optimization problem P The optimal solution for 1;

[0046] (1) First utilize The multi-agent system can be written in the following form: (6-1)

[0047] (2) Due to Equation (6-1) can be expressed as: (6-2)

[0048] (3) Let Construct it in the following form: (6-3)

[0049] (6-4)

[0050] (6-5)

[0051] because Then (6-3) can be written in the following matrix compact form for the system: (6-6)

[0052] in , , ; L = D - A ,in , ;

[0053] (5) Due to ,Right now It is a double random matrix, from which we can obtain: in , because ,in Representation matrix The spectral norm and satisfy , ,as well as ,but (6-7)

[0054] Define norm ,in Through analysis, we obtained , (6-8)

[0055] (6) Construct the norm relationship between the system state and the optimal solution of the objective function, and further analyze and simplify using equation (6-8) to obtain .

Claims

1. A distributed constraint optimization control method based on iterative learning control, characterized in that, Includes the following steps: Step 1: Establish a system based on... n A multi-agent system consisting of 3 agents, the first i The agent in the th... k The dynamic description in this iteration is as follows: , in, Indicates the first i The state of an agent, Indicates control input; Indicates the number of iterations / repetitions; Indicates time, where T Indicates the terminal time; ; The multi-agent system satisfies: the initial state of the system It is the same in each iteration, that is ; Step 2: Determine the optimization objective function. P 1 is , in, Indicates minimization. It is an intelligent agent i The corresponding differentiable local objective function, and the function Only for intelligent agents i Known; for any Each function yes -Strongly convex, and possessing -Lipschitz continuous gradient, i.e., for any ,satisfy and ,in , ; It is a closed convex set, representing the constraint set of all agents; Step 3: Construct a directed graph G ( V , E , A The communication network of a multi-agent system is represented by ), where the node set is... express n There are 1 intelligent agents, each node represents an intelligent agent, and the edge set... This represents the communication connection between intelligent agents; Represents the adjacency matrix; Step 4: Based on the terminal iterative learning control method and the distributed projection gradient algorithm, design a distributed control protocol: , in Represents learning gain, scalar Indicates non-negative weights. Let represent a positive step size, and satisfy . , , ; Represents intelligent agents i Local objective function exist The gradient at each function The gradient set in the set X The upper limit is bounded, that is... ; Step 5: Prove that the state of the controlled system converges to the optimal solution of the objective function at the terminal time as the number of iterations increases, thereby verifying the effectiveness of the distributed control protocol.

2. The method according to claim 1, characterized in that, In step 3, the communication connection Indicates from the intelligent agent Receiving intelligent agents Information, nodes The neighbor set is defined as ; Let represent the adjacency matrix, where if ,otherwise For all They all ,if ,but ,in, Communication networks It is strongly connected and satisfies .

3. The method according to claim 1, characterized in that, In step 5, the method for proving the optimal solution includes the following steps: (1) Utilization The multi-agent system can be written in the following form: (6-1) (2) Due to Equation (6-1) can be expressed as: (6-2) (3) Let Construct it in the following form: (6-3) (6-4) (6-5) (4) Due to Equation (6-3) can be expressed in the following compact form: （6-6） in , , ; L = D - A ,in , ; (5) Due to ,Right now It is a double random matrix, from which we can obtain: ， in , , because ,in Representation matrix The spectral norm and satisfy , ,as well as ,but (6-7) Define norm ,in Through analysis, we obtained ， （6-8） (6) Construct the norm relationship between the system state and the optimal solution of the objective function, and further analyze and simplify using equation (6-8) to obtain .

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