A strict-feedback nonlinear multi-body system sampling style distributed aggregation optimization method

Abstract

The application discloses a strict feedback nonlinear multi-body system sampling type distributed aggregation optimization method, comprising the following steps: an aggregation adjusting variable integrating neighbor information in each sampling period is designed, and the adjusting variable is updated in combination with an auxiliary sampling function, so that a distributed aggregation optimization problem on a complex nonlinear system with strict feedback dynamics is converted into a variable adjusting problem, and effective adjustment of the aggregation variable can be realized by using a classical control method. A control law fusing a performance function and the aggregation adjusting variable is proposed to cope with the distributed aggregation optimization problem existing state time delay and time-varying directed graph communication topology. The method provided by the application can realize distributed aggregation optimal control of a complex multi-body system under the conditions of unknown dynamics, state delay and directed equilibrium time-varying topology.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent distributed optimization control, specifically relating to a sampling-based distributed aggregation optimization method for strictly feedback nonlinear multi-agent systems. Background Technology

[0002] With technological advancements and growing industrial demands, multi-agent systems have gradually become a research and application hotspot. These systems consist of multiple intelligent agents with autonomous decision-making capabilities and interactive relationships, cooperating to achieve overall optimization tasks. Distributed optimization, as a core approach, is widely used to address problems such as resource allocation, task assignment, and data analysis. In such systems, each agent typically only obtains partial information and relies on communication networks to achieve collaborative optimization, thereby improving overall performance. This method possesses good scalability and anti-interference capabilities, significantly reducing reliance on centralized control while effectively alleviating communication pressure and improving computational efficiency. Therefore, distributed optimization has been widely applied in scenarios such as power dispatching, collaborative control of unmanned systems, and network protection.

[0003] In multi-agent systems, strictly feedback nonlinear models are widely used to enhance system modeling capabilities and adapt to complex and dynamic environments. These models can deeply characterize the nonlinear interactions between agents, encompassing features such as adaptive adjustment, learning behavior, and multi-level control strategies. By introducing a strictly feedback dynamic structure, the system can more fully reflect the uncertainty and time-varying characteristics of the environment, thereby improving control accuracy and predictive performance. Furthermore, strictly feedback nonlinear models have the ability to handle high-dimensional system states, adapting to more complex system requirements without sacrificing modeling accuracy. Simultaneously, this modeling approach enhances the system's adaptability to external disturbances, enabling it to maintain operational efficiency and stability even in unstable or dynamic environments.

[0004] Most existing multi-agent distributed optimization methods tend to assume that each agent's cost function depends only on its own decision variables. However, in real-world applications such as resource contention, traffic scheduling, and load balancing, an individual's cost is not only affected by its own behavior but also coupled with the behavior of other agents. This coupling often manifests as some form of aggregation, such as the average or sum of the states of all agents, forming what is known as an aggregation optimization problem. Traditional methods struggle to effectively handle such structures, especially in environments with dynamically changing communication topologies and limited resources.

[0005] Existing patent application CN 119472776 A proposes a predetermined time proportional consensus control method for multi-agent systems. The consensus control problem studied in this patent is fundamentally different from the aggregation optimization problem studied in this invention; its network topology switching and predetermined time convergence requirements are significantly different from the control techniques used in this paper. Furthermore, patent application CN 116088531 A discloses a finite-time consensus control method for multi-agent systems under directed continuous time-varying communication topologies. The problem studied in this patent is also fundamentally different from the aggregation optimization problem of this invention, and the research in this patent only focuses on first-order continuous algorithms, while this invention considers more complex high-order nonlinear strict feedback systems.

[0006] Existing patent application CN118567226A proposes a high-order nonlinear multi-agent distributed optimization method based on proportional-integral regulation. However, the problem type addressed by this patent is an optimal consensus problem, and its objective function structure differs fundamentally from the aggregation optimization problem addressed in this invention, thus making it unsuitable for direct application in aggregation optimization scenarios. Furthermore, this method is based on a fixed communication topology, resulting in non-time-varying communication connections, and its control strategy relies on continuous communication, failing to consider system performance and implementation costs under conditions of limited communication resources. Therefore, this scheme has certain limitations in application within dynamic communication environments and resource-constrained systems.

[0007] To address the aforementioned issues, this invention introduces aggregate adjustment variables, transforming the aggregate optimization problem into a distributed variable adjustment problem. Furthermore, it constructs a sampling-based information interaction mechanism within a time-varying directed graph communication structure. This significantly reduces communication frequency while ensuring the system's effective perception and coordination of global aggregate information and its gradients, thereby achieving an efficient and practical optimization control strategy. Therefore, researching a distributed aggregate optimization method applicable to nonlinear multibody systems with strict feedback structures under time-varying directed equilibrium communication topologies has significant practical implications and application value. Summary of the Invention

[0008] To address the aforementioned problems, this invention discloses a sampling-based distributed aggregation optimization method for strictly feedback nonlinear multibody systems. It proposes an aggregation adjustment variable based on sampling technology and independent of communication topology information. This variable reconstructs the original distributed aggregation optimization problem into an equivalent variable adjustment problem. Furthermore, classical control methods are combined to effectively regulate this aggregation adjustment variable, enabling the proposed optimization method to be applied to nonlinear multibody systems with strictly feedback structures, thereby achieving distributed aggregation optimization control for complex systems.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A sampling-based distributed aggregation optimization method for strictly feedback nonlinear multibody systems includes the following steps:

[0011] Step A: Define the dynamic model of the rigorous feedback nonlinear multibody system.

[0012] Preferably, the dynamic model of the strictly feedback nonlinear many-body system described in step A is as follows:

[0013]

[0014] in, Indicates the system status. The vector form representing the state. The system's latency effect was captured, among which .also, and These represent the measurable control output and input, respectively, and the function. and Assume it is an unknown nonlinear function. Each agent has a local cost function. . This indicates bounded interference. For all .

[0015] Preferably, the auxiliary function used in the sampling technique The definition is as follows:

[0016]

[0017] in This represents the largest integer less than or equal to this number. Indicates the sampling period; Indicates the maximum allowable delay; It is a regular constant.

[0018] The ultimate goal of the proposed algorithm is to make the system state satisfy the inequality:

[0019]

[0020] in It is a positive number that can be adjusted to any small value; To and Irrelevant constants; Indicates the system status; Indicate the problem The optimal solution, where This indicates aggregated information.

[0021] Step B: Model the directed time-varying balanced communication topology between agents as a set of time-varying directed graph sequences (joint connected graphs), each graph consisting of a set of agents. edge set and weighted adjacency matrix The set of edges describes the information transmission relationships between the agents; for any given time, its communication structure is composed of a weighted adjacency matrix. It means that when the intelligent agent Able to be in time To intelligent agents When sending a message, satisfy the following conditions: ,otherwise The weighted adjacency matrix is ​​used to describe communication patterns and supports the construction of a product of communication weight matrices over multiple consecutive time points to characterize the time-varying nature of the communication topology. satisfy And the lower bound of all non-zero elements is some positive number. In addition, there exists a positive integer This makes it possible at any time The beginning of the continuous Within each time step, their joint communication graph maintains strong connectivity within that time window.

[0022] Step C: Propose an aggregate adjustment variable based on sampling technology and independent of communication topology information; reconstruct the distributed aggregation optimization problem into a variable adjustment problem using this aggregate adjustment variable; adjust the aggregate adjustment variable using a classical control method (preset performance control) to make the optimization method applicable to nonlinear multibody systems with strict feedback structures, thereby realizing aggregation optimization control in complex systems. Preferably, the aggregate adjustment variable proposed in step C based on sampling technology and independent of communication topology information includes:

[0023]

[0024] Represents the aggregate adjustment variable, where

[0025]

[0026]

[0027]

[0028] Among them, parameters The adjacency matrix has been determined. Elements in the set. Positive numbers. This represents the learning rate of the algorithm. For the constructed discrete form auxiliary function, the local estimator and Its purpose is to enable each agent to estimate the aggregate variables. and its gradient .

[0029] Step D: Combining with Step C, and under the convergence analysis of distributed preset performance control, a distributed control algorithm based on aggregate adjustment variables and preset performance functions is designed to ensure that, under a time-varying equilibrium communication topology, all agents can collaboratively find the optimal aggregate state of the system. Specifically, the aggregate adjustment variable is constructed using the neighbor information received by each agent in each sampling period, and this variable is adjusted to approximate the optimal aggregate solution. A preset performance function is introduced to constrain the error evolution process of the system, enabling the states of each agent to achieve aggregate optimization control while satisfying performance indicators.

[0030] Preferably, the control algorithm in step D, which combines aggregated adjustment variables and preset performance functions, is described as follows:

[0031] First, we introduce logarithmic transformation. ,in .

[0032] Secondly, design virtual control inputs: With actual control input .parameter This represents a positive control gain. Represents the standardized error variables, where the first error variable , Represents a positive performance function. This is the aggregate adjustment variable defined earlier.

[0033] For the standardized error variable of the intermediate step, it is defined as follows: ,in .

[0034] Step E: The distributed control algorithm based on aggregated adjustment variables and preset performance functions is loaded into each intelligent agent through programming, and then reasonable variable initialization is performed. Finally, the distributed operation and real-time response of the control algorithm are realized.

[0035] The beneficial effects of this invention are:

[0036] Compared with existing nonlinear optimization strategies that rely on embedded reference trajectories or auxiliary systems, this invention does not rely on global reference signals. Instead, it constructs aggregate adjustment variables solely through neighbor information obtained from sampling, thereby transforming the aggregate optimization problem into a local variable adjustment problem and effectively reducing implementation complexity.

[0037] The sampling technique introduced in this invention not only avoids the need for continuous communication but also allows for a certain degree of communication latency, significantly reducing the communication burden of the system and improving the algorithm's adaptability in real-world resource-constrained environments.

[0038] Furthermore, the system targeted by this invention is a strictly feedback nonlinear structure with state delay, which exhibits higher dynamic complexity and modeling challenges compared to traditional delay-free systems. By combining aggregated adjustment variables and performance function constraints, this method achieves stable optimization control of complex systems while ensuring convergence performance.

[0039] Meanwhile, this method is applicable to time-varying directed balanced communication topologies, breaking through the dependence of traditional methods on static undirected graphs. It has stronger topology adaptability and engineering versatility, making it suitable for deployment in practical application scenarios such as collaborative control and resource optimization of multi-agent systems. Attached Figure Description

[0040] Figure 1 This is the time-varying directed communication topology network of the multi-body system in this embodiment.

[0041] Figure 2 For agent state The evolution curve.

[0042] Figure 3 For agent state The evolution curve.

[0043] Figure 4 Aggregate adjustment variables The evolution curve. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention.

[0045] To achieve the above objectives, this invention proposes a sampling-based distributed aggregation optimization method for strictly feedback nonlinear multibody systems, comprising the following steps:

[0046] Step A: Define the dynamic model of the rigorous feedback nonlinear multibody system.

[0047] This type of high-order nonlinear many-body system with strict feedback contains N agents, of which the first agent is... The dynamic model of the agent is as follows:

[0048]

[0049] in, Indicates the system status. The vector form representing the state. The system's latency effect was captured, among which .also, and These represent the measurable control output and input, respectively, and the function. and Assume it is an unknown nonlinear function. Each agent has a local cost function. . This indicates bounded interference. For all .

[0050] Auxiliary functions used in sampling techniques The definition is as follows:

[0051]

[0052] in This represents the largest integer less than or equal to this number. Indicates the sampling period; Indicates the maximum allowable delay; It is a regular constant.

[0053] The ultimate goal of the proposed algorithm is to make the system state satisfy the inequality:

[0054]

[0055] in It is a positive number that can be adjusted to any small value; To and Irrelevant constants; Indicates the system status; Indicate the problem The optimal solution, where This indicates aggregated information.

[0056] Step B: Model the directed time-varying balanced communication topology between agents as a sequence of time-varying directed graphs, each graph consisting of a set of agents. edge set and weighted adjacency matrix The set of edges describes the information transmission relationships between the agents; for any given time, its communication structure is composed of a weighted adjacency matrix. It means that when the intelligent agent Able to be in time To intelligent agents When sending a message, satisfy the following conditions: ,otherwise Adjacency matrix satisfy And the lower bound of all non-zero elements is some positive number. In addition, there exists a positive integer This makes it possible at any time The beginning of the continuous Within each time step, the joint communication graph maintains strong connectivity within that time window. Compared to fixed communication topologies, time-varying directed graph structures can more realistically reflect the dynamically changing communication connections in real-world systems, thereby improving the algorithm's adaptability and practicality under complex network conditions.

[0057] Step C: A sampling-based aggregation adjustment variable, independent of communication topology information, is proposed. This variable reconstructs the original distributed aggregation optimization problem into an equivalent variable adjustment problem. Classical control methods are then combined to effectively adjust this aggregation adjustment variable, enabling the proposed optimization method to be applied to nonlinear multibody systems with strict feedback structures, thereby achieving distributed aggregation optimization control of complex systems. It can be observed that the auxiliary function in this design... It plays a crucial role in linking discrete-time decision updates with the evolution of continuous systems, significantly reducing the communication burden of the algorithm. Furthermore, the function's design structure indicates that it allows for a certain degree of communication delay, thus increasing the algorithm's robustness to some extent.

[0058] The proposed aggregate adjustment variables based on sampling techniques are as follows:

[0059]

[0060] Represents the aggregate adjustment variable, where

[0061]

[0062]

[0063]

[0064] Among them, parameters The adjacency matrix has been determined. Elements in the set. Positive numbers. This represents the learning rate of the algorithm. For the constructed discrete form auxiliary function, the local estimator and Its purpose is to enable each agent to estimate the aggregate variables. and its gradient .

[0065] Step D: Combining with Step C, under the convergence analysis of distributed preset performance control, a distributed control algorithm based on aggregate adjustment variables and preset performance functions is designed to ensure that all agents can collaboratively find the optimal aggregate state of the system under the time-varying equilibrium communication topology.

[0066] Preferably, the control algorithm in step D, which combines aggregated adjustment variables and preset performance functions, is described as follows:

[0067] First, we introduce logarithmic transformation. ,in .

[0068] Secondly, design virtual control inputs: With actual control input .parameter This represents a positive control gain. Represents the standardized error variables, where the first error variable , Represents a positive performance function. This is the aggregate adjustment variable defined earlier.

[0069] For the standardized error variable of the intermediate step, it is defined as follows: ,in .

[0070] Step E: The distributed control algorithm based on aggregated adjustment variables and preset performance functions is loaded into each intelligent agent through programming, and then reasonable variable initialization is performed. Finally, the distributed operation and real-time response of the control algorithm are realized.

[0071] In this implementation example, a multi-stirred reactor system is used as an example of an intelligent agent. Its strictly feedback multi-agent system communication structure is as follows: Figure 1 As shown. The number of agents N=5.

[0072] Among them, the The dynamics of an agent are as follows:

[0073]

[0074] in, and They represent concentrations respectively. and The deviation from its equilibrium point, i.e. , The nonlinearity representing the uncertainty of the system is: and The system state delay is , 1) For each reactor, full-state measurements are used, and the output of the nth reactor is... The initial value in the aggregation optimization algorithm is set to... , .

[0075] Preferably, the bounded interference is The control gain is , The pre-defined performance function in exponential decay form is designed as follows: , The learning rate is The cost function for each agent is in the form of: Importance trade-off parameters The target concentration difference vector is The aggregate function is chosen as... In addition, the sampling period is selected as... The maximum allowable latency is .

[0076] from Figure 2 and Figure 3 It can be seen that each agent reactor converges to the target concentration difference. Furthermore, from... Figure 4 It can be seen that the aggregation adjustment variable designed in this invention was also successfully adjusted to near 0. This indicates that the algorithm proposed in this invention can solve the aggregation optimization problem of strictly feedback nonlinear multibody systems.

[0077] It should be understood that the technical solutions disclosed in this invention are not limited to the specific contents described in the above embodiments, but also include various variations and alternative solutions formed by combining the above technical features in any reasonable manner, all of which should be considered within the scope of protection of this invention.

Claims

1. A sampling-based distributed aggregation optimization method for strictly feedback nonlinear multibody systems, characterized in that, Includes the following steps: Step A: Define the dynamic model of the rigorous feedback nonlinear multibody system; Step B: Model the directed time-varying balanced communication topology as a sequence of time-varying directed graphs, each graph consisting of a set of agents. edge set and weighted adjacency matrix Composition, in which Indicates at time intelligent agent To intelligent agents Send a message; if no message is received, then... The weighted adjacency matrix is ​​used to describe the communication pattern and supports the construction of a product of communication weight matrices over multiple consecutive time points to characterize the time-varying nature of the communication topology. Step C: Propose an aggregate adjustment variable based on sampling techniques and independent of communication topology information; The distributed aggregation optimization problem is refactored into a variable adjustment problem by aggregating adjustment variables; The aggregate adjustment variable is adjusted by using preset performance control, so that the optimization method is applicable to nonlinear multibody systems with strict feedback structure, thereby realizing aggregate optimization control in complex systems; Step D: Design a distributed control algorithm based on aggregated adjustment variables and preset performance functions to realize aggregated optimization control of multibody systems under performance constraints; Step E: The distributed control algorithm based on aggregated adjustment variables and preset performance functions is loaded into each intelligent agent through programming, then the variables are initialized appropriately, and finally the distributed operation and real-time response of the control algorithm are realized. In step A: Define the dynamic model of a strictly feedback nonlinear multibody system: in, Indicates the system status. The vector form representing the state. The system's latency effect was captured, among which ;also, and These represent the measurable control output and input, respectively, and the function. and Assume the function is an unknown nonlinear function; each agent has a local cost function. , This indicates bounded interference, applicable to all ; Auxiliary functions used in sampling techniques The definition is as follows: in This represents the largest integer less than or equal to this number. Indicates the sampling period; Indicates the maximum allowable delay; It is a regular constant; The ultimate goal is to make the system state satisfy the inequality: in It is a positive number that can be adjusted to any small value; To and Irrelevant constants; Indicates the system status; Indicate the problem The optimal solution, where Represents aggregate variables; In step C, an aggregate adjustment variable based on sampling techniques and independent of communication topology information is proposed, including: Represents the aggregate adjustment variable, where Among them, parameters The adjacency matrix has been determined. Elements in; positive constants Indicates the learning rate of the algorithm; For the constructed discrete form auxiliary function, the local estimator and Its purpose is to enable each agent to estimate aggregate variables. and its gradient .

2. The sampling-based distributed aggregation optimization method for a strictly feedback nonlinear multibody system according to claim 1, characterized in that: In step B, the communication topology between agents is modeled as a sequence of time-varying directed graphs, each graph consisting of a set of agents. edge set and weighted adjacency matrix The set of edges describes the information transmission relationships between the agents; for any given time, its communication structure is composed of a weighted adjacency matrix. It means that when the intelligent agent Able to be in time To intelligent agents When sending a message, satisfy the following conditions: ,otherwise Weighted adjacency matrix satisfy And the lower bound of all non-zero elements is some positive number. In addition, there exists a positive integer This makes it possible at any time The beginning of the continuous Within each time step, their joint communication graph maintains strong connectivity within that time window.

3. The sampling-based distributed aggregation optimization method for a strictly feedback nonlinear multibody system according to claim 2, characterized in that: In step D, for the time-varying balanced communication topology, a distributed control algorithm based on aggregate adjustment variables and preset performance functions is designed. The aggregate adjustment variables are constructed using the neighbor information received by each agent in each sampling period. The aggregate adjustment variables are adjusted to approximate the aggregate optimal solution. Furthermore, a preset performance function is introduced to constrain the error evolution process of the system, enabling aggregated optimization control to be achieved while satisfying performance indicators for each agent's state; specifically including: First, we introduce logarithmic transformation. ,in ; Secondly, design virtual control inputs: With actual control input ;parameter Indicates a positive control gain; Represents the standardized error variables, where the first error variable , Represents a positive performance function. This refers to the previously defined aggregate adjustment variable; For the standardized error variable of the intermediate step, it is defined as follows: ,in .

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