CN118151523A - PID-based multi-agent system output hysteresis consistency control method - Google Patents
PID-based multi-agent system output hysteresis consistency control method Download PDFInfo
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Abstract
The invention is applicable to the technical field of cooperative control, and provides an output hysteresis consistency control method of a multi-agent system based on PID, which comprises the following steps: establishing a mathematical model and a virtual leader model of the multi-agent system; introducing an error model of the multi-agent system, wherein the error model comprises a position error, a speed error and an output error; setting PD and PI control protocol; constructing a corresponding Lyapunov function for obtaining a condition that the multi-intelligent system realizes output hysteresis consistency; the second-order nonlinear multi-agent system based on PD and PI realizes output hysteresis consistency. The invention requires fewer computing resources and requires a more readily available control volume and has a wide range of applications.
Description
Technical Field
The invention relates to the technical field of cooperative control, in particular to an output hysteresis consistency control method of a multi-agent system based on PID.
Background
Consistency is a fundamental problem in the coordinated control of multiple intelligent systems and has been widely discussed in recent years. To date, a number of important results have been reported regarding the consistency of multi-agent systems. However, in many practical application scenarios, only a portion of the states of the agents are required to be consistent, and thus, one in turn requires that the output of each agent be consistent. This consistency is called output consistency, which is a generalization of the consistency problem. The deep exploration of the research direction provides a more solid foundation and theoretical support for the practical application of the multi-agent system.
In the process of realizing consistency, communication between agents is an indispensable link. However, communication between agents is limited by factors such as limited transmission speed and congestion of information, which may lead to time lags in the communication process. The existence of time lags not only increases the difficulty of realizing consistency, but also can lead to errors or efficiency reduction of the intelligent agent in executing tasks. Therefore, how to overcome the influence of time lags and realize the lag consistency of the multi-agent system becomes a critical research direction.
From the current research results on the consistency of the multi-agent system, it is obvious that it is very meaningful to consider the output lag consistency of the multi-agent system by using the PID control method. However, up to now, research results in this field are still blank.
Disclosure of Invention
In view of the shortcomings of the prior art, the present invention is directed to providing a method for controlling output hysteresis consistency of a PID-based multi-agent system, so as to solve the problems in the prior art.
The invention is realized in that the method for controlling the consistency of the output hysteresis of a multi-agent system based on PID comprises the following steps:
establishing a mathematical model and a virtual leader model of the multi-agent system;
introducing an error model of the multi-agent system, wherein the error model comprises a position error, a speed error and an output error;
Setting PD and PI control protocol;
Constructing a corresponding Lyapunov function for obtaining a condition that the multi-intelligent system realizes output hysteresis consistency;
the second-order nonlinear multi-agent system based on PD and PI realizes output hysteresis consistency.
As a further scheme of the invention: the mathematical model of the multi-agent system is that
，
Wherein the method comprises the steps ofRespectively representing a position vector, a velocity vector, an output vector and a control input of the agent,/>Is a time variable,/>Representing nonlinear dynamics of an agent,/>And/>Is a known constant matrix and is of the form shown below
，
Wherein the method comprises the steps of。
As a further scheme of the invention: the virtual leader model of the multi-agent system is
，
Wherein the method comprises the steps ofRepresenting the position vector, the velocity vector and the output vector of the virtual leader, respectively.
As a further scheme of the invention: define the position error, the speed error and the output error as respectively，/>Obtaining an error model based on the position error, the speed error and the output error according to the multi-agent system, wherein the error model is that
。
As a further scheme of the invention: the PD control protocol is that
，
Wherein the method comprises the steps ofThe following conditions are satisfied:
；
The PI control protocol:
，
Wherein the method comprises the steps of The following conditions are satisfied:
。
compared with the prior art, the invention has the beneficial effects that:
the invention provides an output hysteresis consistency control method of a multi-agent system based on PID, which can realize the output hysteresis consistency control by only using the position and speed information of the agent adjacent to each agent. From an implementation point of view, the invention requires fewer computing resources and the required control amount is easier to obtain; the output hysteresis consistency control method of the second-order nonlinear multi-agent system based on PD and PI is applicable to any practical system modeled by the mathematical model of the single agent considered by the invention, and has wide application range.
Drawings
FIG. 1 is a flow chart of a PID-based multi-agent system output hysteresis consistency control method;
FIG. 2 is a communication topology of a multi-agent system;
Fig. 3 and 4 are analysis diagrams of simulation results of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Specific implementations of the invention are described in detail below in connection with specific embodiments.
As shown in fig. 1, an embodiment of the present invention provides an output hysteresis consistency control method of a PID-based multi-agent system, the method comprising:
establishing a mathematical model and a virtual leader model of the multi-agent system;
introducing an error model of the multi-agent system, wherein the error model comprises a position error, a speed error and an output error;
Setting PD and PI control protocol;
Constructing a corresponding Lyapunov function for obtaining a condition that the multi-intelligent system realizes output hysteresis consistency;
the second-order nonlinear multi-agent system based on PD and PI realizes output hysteresis consistency.
In the embodiment of the invention, for each intelligent agent, the consistency control of the output lag can be realized only by using the position and speed information of the intelligent agent adjacent to the intelligent agent. From an implementation point of view, the invention requires fewer computing resources and the required control amount is easier to obtain; the output hysteresis consistency control method of the second-order nonlinear multi-agent system based on PD and PI is applicable to any practical system modeled by the mathematical model of the single agent considered by the invention, and has wide application range.
As a preferred embodiment of the invention, a single agent model in a second-order nonlinear multi-agent system is constructed as follows:
， (1)
Wherein the method comprises the steps of Respectively representing a position vector, a velocity vector, an output vector and a control input of the agent,/>Is a time variable,/>And/>Is a known constant matrix and is of the form shown below
，
Wherein the method comprises the steps of。
Representing nonlinear dynamics of an agent and satisfying the following inequality
，
For any oneIs a positive constant.
To obtain the desired result, the virtual leader is selected as follows:
， (2)
Wherein the method comprises the steps of Representing the virtual leader's position, velocity and output vector.
Multiple agent systems capable of achieving output lag uniformity if for arbitraryThe following conditions can be satisfied:
，
Wherein the method comprises the steps of Is a normal number representing the communication time lag between the agent and the virtual leader.
As a preferred embodiment of the invention, the position error, the speed error and the output error are defined as respectively，/>. The following error model can be obtained from (1) and (2):
。 (3)
As a preferred embodiment of the present invention, considering that differential control can enhance the stability of a closed loop system and improve the response speed of a controller, the following PD control protocol based on state feedback is proposed:
， (4)
Wherein the method comprises the steps of The following conditions are satisfied:
；
Considering that integral control can force the steady state error of the system to approach zero, the following PI control protocol based on state feedback is proposed:
， (5)
Wherein the method comprises the steps of The following conditions are satisfied:
。
The bringing of the PD control protocol (4) into the error model (3) can be expressed as
； (6)
The bringing of the PI control protocol (5) into the error model (3) can be expressed as
。 (7)
As a preferred embodiment of the present invention, if presentSo that the following inequality is satisfied:
， (8)
Wherein the method comprises the steps of Under the action of the PD controller (4), the multi-agent system (1) can realize output hysteresis consistency.
If presentSo that the following inequality is satisfied:
， (9)
Under the action of the PI controller (5), the multi-agent system (1) can realize output hysteresis consistency.
For the error model (6), the following Lyapunov function is constructed:
。 (10)
Can obtain the derivative of the above type ；
。 (11)
Based on non-linear functionsIs available on the assumption of
， (12)
。 (13)
The combinations (11) - (13) can be obtained
，
Wherein the method comprises the steps of。
Combining inequality techniques with Lyapunov functions (10) can result in
，
，
，
Further obtainExist and are bounded.
From the error model (3), it is possible to obtainIs bounded and because of/>Is bounded, can deduce/>Is consistently continuous, can be obtained according to Barbalat's lemma/>. That is to sayThus, the multi-agent system (1) is capable of achieving output hysteresis consistency under the influence of the PD controller.
As a preferred embodiment of the invention, for the error model (7), the following Lyapunov function is constructed:
。 (14)
Can obtain the derivative of the above type ；
， (15)
Wherein the method comprises the steps of。
Combining inequality techniques with Lyapunov functions (14) can result in
，
，/>
，
。
Further obtainExist and are bounded.
From the error model (7), it is possible to obtainIs bounded and because of/>Is bounded, can deduce/>Is consistently continuous,/>. From Barbalat's lements can be found/>. That is, the multi-agent system (1) can achieve output hysteresis consistency under the action of the PI controller.
As an extended embodiment of the invention, selecting an example for simulation verification;
consider a multi-agent system consisting of 5 single-link robots, which are dynamically represented as follows:
，
Wherein the method comprises the steps of Representing the included angle between the connecting rod and the horizontal ground,/>Representing input torque,/>Representing moment of inertia of the joint,/>Representing gravitational acceleration,/>Representing quality,/>Indicating the length of the link. Wherein the communication diagram is shown in fig. 2.
Order theThe system can be converted into the following second-order nonlinear multi-agent system
， (16)
Wherein the method comprises the steps ofObviously/>Satisfies the following inequality
，
Wherein the method comprises the steps of。
By means of the YALMIP kit in MATLAB, the following parameters can be found so that condition (8) holds:
。
For intelligent agent Taking the communication time lag/>, between the agent and the virtual leaderController parameters/>，/>。
Setting discrete time steps asLet/>Setting the state initial value/>, of the virtual leaderState initial value/>，/>，/>Initial state values of 5 agents/>Respectively/>,/>,/>,/>,/>. State initial value/>Respectively/>,/>,/>,/>,/>. Initial value of state derivative/>Respectively/>,,/>,/>, />. The simulation results are shown in fig. 3.
By means of the YALMIP kit in MATLAB, the following parameters can be found so that condition (9) holds:
，
For intelligent agent Taking the communication time lag/>, between the agent and the virtual leaderController parameters/>，/>。
Setting discrete time steps asLet/>Setting a state initial value of a virtual leaderState initial value/>Initial state values of 5 agents/>Respectively is,/>,/>，/>，/>. State initial value/>Respectively/>，/>,/>,/>，. The simulation results are shown in fig. 4. Fig. 4 shows a graph of the output state of each agent and leader in a multi-agent system over time at different times under the action of a PI controller. As can be seen from fig. 4, the multi-agent system eventually achieves output lag consistency over time.
The foregoing description of the preferred embodiments of the present invention should not be taken as limiting the invention, but rather should be understood to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
It should be understood that, although the steps in the flowcharts of the embodiments of the present invention are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in various embodiments may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of the sub-steps or stages of other steps or other steps.
Those skilled in the art will appreciate that all or part of the processes in the methods of the above embodiments may be implemented by a computer program for instructing relevant hardware, where the program may be stored in a non-volatile computer readable storage medium, and where the program, when executed, may include processes in the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (SYNCHLINK) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
Other embodiments of the present disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure. This application is intended to cover any adaptations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
Claims (5)
1. A method for controlling output hysteresis consistency of a PID-based multi-agent system, the method comprising:
establishing a mathematical model and a virtual leader model of the multi-agent system;
introducing an error model of the multi-agent system, wherein the error model comprises a position error, a speed error and an output error;
Setting PD and PI control protocol;
Constructing a corresponding Lyapunov function for obtaining a condition that the multi-intelligent system realizes output hysteresis consistency;
the second-order nonlinear multi-agent system based on PD and PI realizes output hysteresis consistency.
2. The method for controlling the consistency of output hysteresis of a PID-based multi-agent system according to claim 1, wherein the mathematical model of the multi-agent system is
，
Wherein the method comprises the steps ofRespectively representing a position vector, a velocity vector, an output vector and a control input of the agent,/>Is a time variable,/>Representing nonlinear dynamics of an agent,/>And/>Is a known constant matrix and is of the form shown below
，
Wherein the method comprises the steps of。
3. The method of claim 2, wherein the virtual leader model of the multi-agent system is
，
Wherein the method comprises the steps ofRepresenting the position vector, the velocity vector and the output vector of the virtual leader, respectively.
4. The method for controlling the output lag uniformity of a PID-based multi-agent system according to claim 1, wherein the position error, the velocity error, and the output error are defined as respectively，Obtaining an error model based on the position error, the speed error and the output error according to the multi-agent system, wherein the error model is that
。
5. The method of claim 1, wherein the PD control protocol is
，
Wherein the method comprises the steps ofThe following conditions are satisfied:
；
The PI control protocol:
，
Wherein the method comprises the steps of The following conditions are satisfied:
。
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