CN115469548A - Unknown nonlinear multi-agent finite time clustering consistency control method with input saturation - Google Patents
Unknown nonlinear multi-agent finite time clustering consistency control method with input saturation Download PDFInfo
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Abstract
The invention discloses an unknown nonlinear multi-agent finite time grouping consistency control method with input saturation, which comprises the following steps: the method comprises the steps of adopting a radial basis function neural network to carry out online identification on unknown items in a system, introducing a hyperbolic tangent function to carry out smooth approximation on saturated items in dynamics on the basis, and then combining information of an agent node, reference model information and information of neighbor agent nodes of the agent node to design a finite time distributed controller based on the neural network, so that the multi-agent can achieve finite time clustering consistency. The invention realizes the on-line identification and the limited time grouping consistency control of a multi-agent system with unknown models, thereby solving the problems of unknown multi-agent models and physical constraint influence.
Description
Technical Field
The invention relates to the technical field of multi-agent control, in particular to a finite time clustering consistency control method for an unknown nonlinear multi-agent with input saturation.
Background
In recent years, as multi-agent systems have wide application potential in fields such as micro-grids, unmanned aerial vehicles and sensors, the problem of coordination control of multi-agent systems is widely researched. The problem of consistency control of multi-agent systems is one of the most essential problems of coordination control of multi-agent systems, and the problem is widely applied to the control fields of formation control, cluster control, aggregation and swarming and the like.
First, a definition of an agent is given, which is a device or machine with autonomy, responsiveness, aggressiveness, sociality, and progressiveness. The multi-agent system is a network formed by a plurality of agents, and the agents communicate with each other through the topological rules of the network, so that the complex tasks are solved through cooperation.
With the development of the multi-agent system, the multi-agent system is applied to more practical projects, the problems to be solved are more complicated, and the simple consistency control cannot well solve the complicated problems in the practical projects. For these problems, sometimes the system needs to be autonomously divided into multiple groups to complete different subtasks, that is, all the smartphones in the system need to eventually present multiple different consistent states, so that the group consistency is more general than the consistency.
The group consistency means that all agents in the system are divided into a plurality of subgroups, all agents in the same subgroup can reach a consistent state, different subgroups keep respective independent states, and the diversity among the subgroups is more universal. In particular, when agents in different subgroups can eventually reach the same state, the group consistency becomes complete consistency, and thus the complete consistency can be regarded as a special case of the group consistency.
Most of the research results on grouping consistency in the prior art are obtained based on known model information. In fact, most of the systems in practical application are unknown in dynamics, and a model of a controlled system is difficult to establish. Therefore, the research on the grouping consistency of the unknown nonlinear multi-agent system has practical significance.
Meanwhile, in practical applications, various physical constraints existing in a practical system should be considered when designing a controller, so that it is necessary to consider the influence caused by input saturation. In addition, the limited time control is introduced, so that the convergence speed of the system can be improved, and the designed controller has better performance.
Disclosure of Invention
The present invention aims to provide a method for controlling finite time clustering consistency of unknown nonlinear multi-agent with input saturation, so as to solve the problems in the background art.
In order to achieve the purpose, the invention adopts the following technical scheme:
an unknown nonlinear multi-agent finite time clustering consistency control method with input saturation comprises the following steps:
s1, clearly researching a problem dynamics model;
s2: aiming at unknown items in the dynamic model, an adaptive algorithm based on an RBF artificial neural network is adopted to carry out online identification on the unknown items so as to meet the requirements of real-time performance and rapidity of the system;
s3: introducing a hyperbolic tangent function to approximate an input saturation function so as to eliminate the influence caused by input saturation constraint;
s4: by combining S2 and S3, a distributed controller is designed by utilizing the information of the intelligent agent node and the information of the adjacent intelligent agent nodes under the Lyapunov stability theorem, so that the unknown nonlinear multi-intelligent agent with input saturation can reach grouping consistency in a limited time;
s5: and injecting the unknown model identification strategy and the control algorithm into each multi-agent through programming.
Compared with the prior art, the invention has the technical bright points that: the self-adaptive algorithm based on the RBF artificial neural network can perform an online identification algorithm on an unknown model of the system, so that the real-time performance of the system is met; meanwhile, the influence of control input saturation is considered, and the problem of input saturation constraint in an actual physical system can be better solved; in addition, a distributed finite time control algorithm is designed, and clustering consistency can be realized more quickly.
Drawings
FIG. 1 is a diagram of a multi-agent communication topology in this embodiment.
FIG. 2 is a state response diagram of the multi-agent in the method proposed herein.
FIG. 3 is a control input diagram for the multi-agent under saturation constraints for this embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.
An unknown nonlinear multi-agent finite time clustering consistency control method with input saturation comprises the following steps:
s1, clearly researching a problem dynamics model;
the unknown multi-agent dynamic model of the model comprises N agents, and the ith agent dynamic model is as follows:
wherein x is i1 (t)∈R n ,x i2 (t)∈R n ,u i (t)∈R n ,f i (x i1 (t),x i2 (t))∈R n Respectively representing the position state, velocity state, control input and unknown nonlinear function of the agent, sat (u) i (t)) satisfies the following form:
and herein defines the reference model:
wherein N is i Representing a neighbor set of agent i.
The tracking error is further defined:
in S1, the communication network topology of the agent is as shown in fig. 1.
The following definitions are provided for the directional strong connectivity:
wherein:
the use of a novel Laplace matrix in the present invention
Wherein
In addition, in the case of the present invention,
s2: for the unknown item f in (1) i (x 1i (t),x i2 And (t)), adopting an adaptive algorithm based on the RBF artificial neural network to perform online identification on the system so as to meet the requirements of real-time performance and rapidity of the system.
Under ideal conditions
Ideal weight matrix, G, representing optimal RBF artificial neural network i (. Cndot.) denotes RBF Artificial neural network activation function, ε i And (t) represents an RBF artificial neural network approximation error.
The optimal weight matrix can be obtained according to the following formula:
preferably, G i (. Cndot.) is a Gaussian function.
The formula (3) is generally used for qualitative analysis, and is practically used
Approximation to an unknown function.
Further preferably, the weight matrix update rate is given by combining an adaptive algorithm:
wherein, delta i The control parameter of the design is more than 0,
s3: introducing a hyperbolic tangent function to smoothly approximate an input saturation function so as to eliminate the influence caused by input saturation constraint;
first, the hyperbolic tangent function is introduced as follows:
wherein:
upper limit of controller saturation constraint for ith agent
Thus sat (u) i (t)) may be expressed as follows:
sat(u i (t))＝h(u i (t))+ε(u i (t)) (7)
wherein epsilon (u) i (t)) is smoothingError in the approximation.
S4: in summary of the above method, the controller of agent i is designed to:
wherein
Weight value updating
As shown in the above equation (5), and each control parameter is designed to satisfy the following equation:
s5: and injecting the unknown model identification strategy and the control algorithm into each multi-agent through programming.
In the present embodiment, preferably, x i1 (t)∈R,x i2 (t)∈R,u i (t)∈R，f i (x i1 (t),x i2 (t))∈R。
The novel laplacian corresponding to the multi-agent communication topology in this embodiment is as follows:
the system is divided into three subgroups, where {1,2} constitutes one subgroup, {3} constitutes one subgroup, {4,5} constitutes one subgroup,
the initial value of the system is randomly generated at (0, 1), x (0) = z (0), and the saturation threshold is selected to be
Preferably, the control parameters of the system are designed as follows:
k 1i ＝100,k 2i ＝0.01,k 3i ＝10,δ i =2,i =1, \8230, N, and the remaining corresponding parameters can be calculated from known information.
According to fig. 2, it can be seen that the states of the agents can be grouped to be consistent within 2s according to the setting, and according to fig. 3, it can be seen that the control amplitude of each agent is constrained between-1.5 and 1.5, that is, the algorithm can realize the finite time grouping consistency control of the unknown nonlinear multiple intelligent system with input saturation.
The above examples are only preferred embodiments of the present invention, it should be noted that, for those skilled in the art, many variations and modifications can be made without departing from the spirit of the present invention, and these should be considered as the protection scope of the present invention, which will not affect the effect of the implementation of the present invention and the utility of the patent.
Claims (8)
1. An unknown nonlinear multi-agent finite time clustering consistency control method with input saturation is characterized in that: the method comprises the following steps:
s1: a problem dynamics model is definitely researched;
s2: aiming at unknown items in the dynamic model, an adaptive algorithm based on an RBF artificial neural network is adopted to perform online identification on the unknown items so as to meet the requirements of real-time performance and rapidity of the system;
s3: introducing a hyperbolic tangent function to smoothly approximate an input saturation function so as to eliminate the influence caused by input saturation constraint;
s4: by combining S2 and S3, a distributed controller is designed by utilizing the information of the intelligent agent node and the information of the adjacent intelligent agent nodes under the Lyapunov stability theorem, so that the unknown nonlinear multi-intelligent agent with input saturation can reach grouping consistency in a limited time;
s5: and injecting the unknown model identification strategy and the control algorithm into each multi-agent through programming.
2. The class of unknown nonlinear multi-agent finite time clustering consistency control method with input saturation as recited in claim 1, characterized by: in S1:
defining an unknown nonlinear multi-agent dynamic model with input saturation to contain N agents, wherein the ith agent dynamic model is as follows:
wherein x is i1 (t)∈R n ,x i2 (t)∈R n ,u i (t)∈R n ,f i (x i1 (t),x i2 (t))∈R n Respectively representing the position state, velocity state, control input and unknown nonlinear function of the agent, sat (u) i (t)) satisfies the following form:
3. the class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 2, characterized by: defining a reference model:
wherein N is i Set of neighbors, k, representing agent i 3i > 0, and furthermore for initial values within a tight set:
4. the class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 1, characterized by: the communication network of the agent is a directed strong connectivity topology and the system has feasible inputs to achieve the control objective.
5. The class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 1, characterized by: in S2: for unknown item f i (x i1 (t),x i2 (t)) adopting an adaptive algorithm based on an RBF artificial neural network to perform online identification, wherein the adaptive algorithm comprises the following steps:
defining a tracking error:
approximating an unknown function:
wherein, delta i And > 0 is a designed control parameter.
6. The class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 1, characterized by: in S3: introducing a hyperbolic tangent function to smoothly approximate an input saturation function, wherein the method comprises the following steps:
first, the hyperbolic tangent function is introduced as follows:
wherein:
upper limit of controller saturation constraint for ith agent
Thus sat (u) i (t)) may be expressed as follows:
sat(u i (t))＝h(u i (t))+ε(u i (t))
wherein epsilon (u) i (t)) is the error present in the smooth approximation.
7. The class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 1, characterized by: in S4:
the controller design of agent i is:
wherein
Weight value updating
As shown in claim 5, and each control parameter is designed to satisfy the following equation:
8. the class of unknown nonlinear multi-agent finite time clustering consistency control methods with input saturation of claim 1, characterized by: in S5:
and injecting the unknown model identification strategy and the control algorithm into each multi-agent through programming.
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