CN117055409A - Multi-intelligent system preset performance consistency control method with event triggering function - Google Patents

Multi-intelligent system preset performance consistency control method with event triggering function Download PDF

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CN117055409A
CN117055409A CN202311129460.XA CN202311129460A CN117055409A CN 117055409 A CN117055409 A CN 117055409A CN 202311129460 A CN202311129460 A CN 202311129460A CN 117055409 A CN117055409 A CN 117055409A
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甄然
王潇飞
武晓晶
孟凡华
李志杰
奚乐乐
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Hebei University of Science and Technology
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Hebei University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/04—Programme control other than numerical control, i.e. in sequence controllers or logic controllers
    • G05B19/042—Programme control other than numerical control, i.e. in sequence controllers or logic controllers using digital processors
    • G05B19/0423—Input/output
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/25—Pc structure of the system
    • G05B2219/25257—Microcontroller
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

The invention relates to a method for controlling the consistency of preset performances of a multi-agent system with event triggering, which estimates the unknown state in the system through a reduced order filter, designs a controller through a distributed self-adaptive control method, adopts a dynamic surface control technology and an event triggering technology in the design process of the controller, and realizes the constraint on the temporary steady state performance of the system under the conditions that the initial state of the multi-agent system is not limited and the state of a part of the system is unknown. The invention can realize the restraint of the temporary steady state performance of the system under the condition that the initial state of the multi-agent is not limited and the partial state of the system is unknown, can save the communication bandwidth resource of the system to prolong the endurance time, and has good anti-interference capability.

Description

Multi-intelligent system preset performance consistency control method with event triggering function
Technical Field
The present invention relates to a control technology of a multi-agent system, and more particularly, to a method for controlling consistency of preset performance of a multi-agent system with event triggering, which allows an initial state of an agent to be not limited when the preset performance is performed on the agent.
Background
Multi-intelligent systems are widely used in various fields such as autonomous vehicles, robotic collaboration and distributed networks. In these applications, it is often necessary to ensure that multiple agents achieve preset performance in a consistent manner to maintain the safety and effectiveness of the system.
The control method for the consistency of the preset performances of the multi-agent system aims at ensuring that the temporary steady-state performances of all agents meet preset standards. Whereas conventional control methods generally require strict restrictions on the initial state of each agent, which may be inconsistent with the actual application in many cases.
In addition, because the intelligent agent is provided with the driving module, the embedded processor and other devices, the intelligent agent is more intelligent and simultaneously provides great challenges for energy supply and limited communication bandwidth. Meanwhile, certain state information of the intelligent agent and self parameters thereof are not easy to measure in consideration of actual conditions. The method has the advantages of reasonably saving resources, prolonging the working time of the system, accurately estimating the unknown state and parameters, improving the stability of the system and better realizing the preset target.
In the existing control method, the initial state of the multi-agent system is strictly limited, however, in engineering application, the initial state may be any value. If the initial state exceeds a preset value, the system cannot well achieve the desired performance, and the existing control method does not consider that the working time is prolonged by properly reducing the consumption of communication resources.
Disclosure of Invention
In order to solve the defects, the method for controlling the consistency of the preset performance of the multi-intelligent system with event triggering saves the waste of communication bandwidth resources and prolongs the working time of the system.
The technical scheme of the invention is as follows:
a method for controlling the consistency of preset performance of multi-intelligent system with event trigger includes such steps as estimating the unknown state in system by order-decreasing filter, designing controller by distributed adaptive control method, and using dynamic surface control technique and event trigger technique to restrict the temporary stable performance of system.
Preferably, the system equation is:
the system is a high-order system, the order n of the system i May be any value; wherein y is i An output track of the ith agent; x is x i2 ,x i3 ,x is Is the status of the ith agent; /> Is state x i1 ，x i2 ,x i3 ,/>Is a derivative of (2); phi (phi) i1 (y i )，φ i2 (y i )，/> Is a known smooth function vector; f (f) i22 (y i ),/> Is a known smooth nonlinear function; θ i A vector that is an unknown constant in the system; u (u) i Is a control input; b i0 ,b i1 ,/>The previous coefficients are input to the controller.
Preferably, the reduced order filter is designed to:
wherein the method comprises the steps ofIs a function vector; zeta type toy i ＝[ξ i2 ,ξ i3 ,…,ξ in ] T ,o i ＝[o i2 ,o i3 ,…,o in ] T ,Ξ i ＝[Ξ i2 ,Ξ i3 ,...,Ξ in ] T ,ν ik ＝[ν ik2 ,ν ik3 ,...,ν ikn ] T ,k＝0,...,m,/>Are all parameter vectors in the reduced order filter; /> Are normal number vectors; />Is a constant vector; u (u) i Is a control input;
dynamic gainl i Dynamic gain for ith reduced order filter,/->Is l i Is a derivative of (2); k (k) i Is a coefficient that can be designed, Φ i Is a designed nonlinear function; pi i1 ＝π i βρ i Wherein->The error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; beta is a time-varying function to be designed, ζ i (t)＝β(t)η i (t) is based on β (t) and the introduced transfer function; />Is a designed calculation function, where l is a constant greater than 0; e, e i0 Is the consistency error of the multi-agent system; sigma (sigma) i10 ，σ i14 ,σ i15 A constant greater than 0; sigma (sigma) -1 i14 ，σ -1 i15 Is sigma (sigma) i10 ，σ i14 Is the reciprocal of (2);the sum of communication coefficients of the multi-intelligent system; a, a iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
Preferably, a barrier function suitable for a multi-agent system is designed according to a time-varying restriction function beta (t) to achieve multi-agent preset performance control with unlimited initial state;
if a function β (t) meets the following requirement, called a time-varying constraint function:
beta (t) is a strict one-way increasing function and needs to satisfy beta (0) =1 when time t=0; when the time t is infinityAnd 0 < b f ＝1；
B:β (k) K=1, 2,3. N is at the time the boundary segments are continuous;
constructing a preset function according to the time-varying limiting function as follows:where l is a constant greater than 0, ψ (t) is the inverse of the real variable restriction function β (t), i.e +.>
Preferably, the barrier function of designing the multi-agent system in accordance with the time-varying restriction function is:
zeta in i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 The transfer function to be introduced is that,the error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; e, e i0 Uniformity error for a multiple agent system>a iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
Preferably, the following coordinate transformation is performed according to the barrier function:
wherein z is i1 ,z ij Is the error needed in the back-stepping method; s is(s) ij Filtering errors before and after the virtual controller; alpha i,(j-1) Andthe method is a virtual controller which is designed in a back-stepping method and a filtered virtual controller; v imij Is a parameter in the reduced order filter;
for z i1 The derivation designs the virtual controller of the first step as:
in the middle ofRepresents->The sign, z of i1 Error for the first step of the backstepping method, < >>Is a virtual controller alpha i1 A positive constant; beta i 、β iq 、λ i 、χ i Is adaptive parameter->Is self-adaptive parameter beta i 、β iq 、λ i 、χ i Is a function of the estimated value of (2); />c i1 ,σ i11 ,σ i12 ,σ i14 ,σ i15 ,a i A constant greater than zero; />Sum of communication coefficients of multi-intelligent system, a iq Representing the communication coefficient between the ith agent and the qth agent, a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, and if the information of the leader is directly acquired, mu i =1, vice versa μ i ＝0；ξ i2 Reduced order filter parameters, ζ, for the ith agent q2 The reduced order filter parameter of the q-th agent; l (L) i Dynamic gain for the reduced order filter; pi i1 And pi i2 Simplifying the function after deriving the barrier function; pi i1 ＝π i βρ i ，/>Wherein-> Is an error conversion function designed for realizing the preset transient steady state performance of the ith intelligent agent, beta is a time-varying function which needs to be designed, and zeta is a time-varying function i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 (t) introduced transfer function, +.>Is a designed computable function, where l is a constant greater than 0, e i0 Is the consistency error of the multi-agent system;/>andparameter vector +.f. for reduced order dynamic gain filter obtained by scaling with Young's inequality>And->A function of the correlation.
To avoid the overestimation problem, we define the adaptive parameters as follows and estimate the following adaptive parameters:
β i ＝sup‖Θ i ‖,β iq ＝sup‖Θ iq ‖
wherein Θ i For all unknown constant vectors in the ith agent system, Θ iq All unknown constant vectors in the q-th intelligent agent system; sup|theta i II is theta i An upscaling of the norm; sup|theta iq II is theta iq An upscaling of the norm;is thatIs the minimum of (2); />Is->Is the upper bound of (2); />And->Reduced order dynamic gain filter parameter vector, v for the ith agent and the jth agent i(mi-2)2 ,…,ν i02 ,Ξ i2 ,φ i1 ，/>Is a parameter in the reduced order dynamic gain filters i and q.
Preferably, the adaptation rate is designed as:
wherein the method comprises the steps ofA constant greater than zero; />Estimated value for adaptive parameter +.>Is a derivative of (2); />Andparameter vector +.f. for reduced order dynamic gain filter obtained by scaling with Young's inequality>And->A function of the correlation.
Preferably, the virtual controller of the second step is designed to:
j (j is not less than 3 and not more than ρ) i ) The virtual controller is designed as follows:
in c ij ,σ ij1 、σ ij2 、σ i(j-1)1 Is a normal number of times, and the number of times is equal to the normal number,the method is designed in the following form:
τ in ij All c and σ are constants greater than zero, no matter what the subscript is, positive constants.
Preferably, the controller of the system is:
in the middle ofδ i1 ，/>Is a positive constant; />The ith P.o. of the ith agent i A step consistency error; />Is a nonlinear term in the system, l i ,/>Is a term in the reduced order filter; />For virtual controller->Is a derivative of (2); tanh is a function.
Multi-agent system: a multi-agent system is a collection of agents that are able to autonomously perceive an environment, make decisions, and achieve a common goal or task through interactions. Each agent can be considered as a separate entity with some autonomy and intelligence. Multi-agent systems are often used to solve complex problems that require collaboration, coordination, or competition.
The preset performance control is a control method: it is intended to ensure that a system is able to meet or maintain a predetermined performance standard or performance goal when performing tasks or completing work. Such methods typically involve defining, measuring and monitoring the performance of the system and taking the necessary measures to ensure that the performance of the system is always within the expected range.
The invention has the beneficial effects that:
the invention adopts a barrier function to limit the transient steady state performance of the intelligent agent, and the barrier function can relax the initial state to any value. Meanwhile, an event triggering controller is designed by adopting an event triggering technology, so that the waste of communication bandwidth resources is saved, and the working time of the system is prolonged.
The invention can realize the restraint of the temporary steady state performance of the system under the condition that the initial state of the multi-agent is not limited and the partial state of the system is unknown, can save the communication bandwidth resource of the system to prolong the endurance time, and has good anti-interference capability.
The following points are specifically shown:
1. the invention realizes the preset performance consistency control of the high-order nonlinear multi-agent system with the initial state not limited.
2. The nonlinear output feedback high-order system comprising unknown parameters and uncertain disturbance is adopted, so that the application is wider. The unknown state is estimated by using the reduced order filter, the order is lower, unnecessary resource waste is avoided, and meanwhile, the error of the filter can be arbitrarily small by reasonably selecting parameters.
3. The back-stepping method is optimized by utilizing the dynamic surface technology in the design process of the controller, so that the calculated amount is greatly reduced, the communication bandwidth resource is saved by adopting the event triggering technology, and the working time of the system is prolonged.
Multi-agent system: a multi-agent system is a collection of agents that are able to autonomously perceive an environment, make decisions, and achieve a common goal or task through interactions. Each agent can be considered as a separate entity with some autonomy and intelligence. Multi-agent systems are often used to solve complex problems that require collaboration, coordination, or competition.
The preset performance control is a control method, and aims to ensure that a system can reach or maintain a preset performance standard or performance target when performing tasks or completing work. Such methods typically involve defining, measuring and monitoring the performance of the system and taking the necessary measures to ensure that the performance of the system is always within the expected range.
Drawings
Fig. 1 is a trace-graph of an embodiment of the present invention.
FIG. 2 is an error-limited graph of an embodiment of the present invention.
Fig. 3 is a diagram of output signals of a controller according to an embodiment of the present invention.
Detailed Description
A method for controlling the consistency of preset performance of multi-intelligent system with event trigger includes such steps as estimating the unknown state in system by order-decreasing filter, designing controller by distributed adaptive control method, and using dynamic surface control technique and event trigger technique to restrict the temporary stable performance of system.
Preferably, the system equation is:
the system is a high-order system, the order n of the system i May be any value; wherein y is i An output track of the ith agent; x is x i2 ,x i3 ,x is Is the status of the ith agent; /> Is state x i1 ，x i2 ,x i3 ,/>Is a derivative of (2); phi (phi) i1 (y i )，φ i2 (y i )，/> Is a known smooth function vector; f (f) i22 (y i ),/> Is a known smooth nonlinear function; θ i A vector that is an unknown constant in the system; u (u) i Is a control input; b i0 ,b i1 ,/>The previous coefficients are input to the controller.
Preferably, the reduced order filter is designed to:
wherein the method comprises the steps ofIs a function vector;ξ i ＝[ξ i2 ,ξ i3 ,...,ξ in ] T ,o i ＝[o i2 ,o i3 ,...,o in ] T ,Ξ i ＝[Ξ i2 ,Ξ i3 ,...,Ξ in ] T ,ν ik ＝[ν ik2 ,ν ik3 ,...,ν ikn ] T ,k＝0,...,m,/>are all parameter vectors in the reduced order filter; /> Are normal number vectors; />Is a constant vector; u (u) i Is a control input;
dynamic gainl i Dynamic gain for ith reduced order filter,/->Is l i Is a derivative of (2); k (k) i Is a coefficient that can be designed, Φ i Is a designed nonlinear function; pi i1 ＝π i βρ i Wherein->The error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; beta is a time-varying function to be designed, ζ i (t)＝β(t)η i (t) is a baseAt β (t) and the introduced transfer function; />Is a designed calculation function, where l is a constant greater than 0; e, e i0 Is the consistency error of the multi-agent system; sigma (sigma) i10 ，σ i14 ,σ i15 A constant greater than 0; sigma (sigma) -1 i14 ，σ -1 i15 Is sigma (sigma) i10 ，σ i14 Is the reciprocal of (2); />The sum of communication coefficients of the multi-intelligent system; a, a iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
Preferably, a barrier function suitable for a multi-agent system is designed according to a time-varying restriction function beta (t) to achieve multi-agent preset performance control with unlimited initial state;
if a function β (t) meets the following requirement, called a time-varying constraint function:
beta (t) is a strict one-way increasing function and needs to satisfy beta (0) =1 when time t=0; when the time t is infinityAnd 0 < b f ＝1；
B:β (k) K=1, 2,3. N is at the time the boundary segments are continuous;
constructing a preset function according to the time-varying limiting function as follows:where l is a constant greater than 0, ψ (t) is the inverse of the real variable restriction function β (t), i.e +.>
Preferably, the barrier function of designing the multi-agent system in accordance with the time-varying restriction function is:
zeta in i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 The transfer function to be introduced is that,the error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; e, e i0 Uniformity error for a multiple agent system>a iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
Preferably, the following coordinate transformation is performed according to the barrier function:
wherein z is i1 ,z ij Is the error needed in the back-stepping method; s is(s) ij Filtering errors before and after the virtual controller; alpha i,(j-1) Andthe method is a virtual controller which is designed in a back-stepping method and a filtered virtual controller; v imij Is a parameter in the reduced order filter;
for z i1 The derivation designs the virtual controller of the first step as:
in the middle ofRepresents->The sign, z of i1 Error for the first step of the backstepping method, < >>Is a virtual controller alpha i1 A positive constant; beta i 、β iq 、λ i 、χ i Is adaptive parameter->Is self-adaptive parameter beta i 、β iq 、λ i 、χ i Is a function of the estimated value of (2); />c i1 ,σ i11 ,σ i12 ,σ i14 ,σ i15 ,a i A constant greater than zero; />Sum of communication coefficients of multi-intelligent system, a iq Representing the communication coefficient between the ith agent and the qth agent, a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i to the leader if directlyReceiving the information of the leader and then mu i =1, vice versa μ i ＝0；ξ i2 Reduced order filter parameters, ζ, for the ith agent q2 The reduced order filter parameter of the q-th agent; l (L) i Dynamic gain for the reduced order filter; pi i1 And pi i2 Simplifying the function after deriving the barrier function; pi i1 ＝π i βρ i ，/>Wherein-> Is an error conversion function designed for realizing the preset transient steady state performance of the ith intelligent agent, beta is a time-varying function which needs to be designed, and zeta is a time-varying function i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 (t) introduced transfer function, +.>Is a designed computable function, where l is a constant greater than 0, e i0 Is the consistency error of the multi-agent system; />And->Parameter vector +.f. for reduced order dynamic gain filter obtained by scaling with Young's inequality>And->A function of the correlation.
To avoid the overestimation problem, we define the adaptive parameters as follows and estimate the following adaptive parameters:
β i ＝sup‖Θ i ‖,β iq ＝sup‖Θ iq ‖
wherein Θ i For all unknown constant vectors in the ith agent system, Θ iq All unknown constant vectors in the q-th intelligent agent system; sup|theta i II is theta i An upscaling of the norm; sup|theta iq II is theta iq An upscaling of the norm;is thatIs the minimum of (2); />Is->Is the upper bound of (2); />And->Reduced order dynamic gain filter parameter vector, v for the ith agent and the jth agent i(mi-2)2 ,...,ν i02 ,Ξ i2 ,φ i1 ，/>Is a parameter in the reduced order dynamic gain filters i and q.
Preferably, the adaptation rate is designed as:
wherein the method comprises the steps ofA constant greater than zero; />Estimated value for adaptive parameter +.>Is a derivative of (2); />Andis obtained by scaling through the Young's inequalityIs +.>And->A related function; />Is greater than zero constant.
Preferably, the virtual controller of the second step is designed to:
j (j is not less than 3 and not more than ρ) i ) The virtual controller is designed as follows:
in c ij ,σ ij1 、σ ij2 、σ i(j-1)1 Is a normal number of times, and the number of times is equal to the normal number,the method is designed in the following form:
τ in ij All c and σ are constants greater than zero, no matter what the subscript is, positive constants.
Preferably, the controller of the system is:
in the middle ofδ i1 ，/>Is a positive constant; />The ith P.o. of the ith agent i A step consistency error; />Is a nonlinear term in the system, l i ,/>Is a term in the reduced order filter; />For virtual controller->Is a derivative of (2); tanh is a function.
The invention adopts Matlab software to simulate four second-order agents, wherein, a second-order agent dynamics model and a related algorithm are programmed by using M files, and a Simlink module is used for building the second-order agent model. And reasonably setting the running time length and the step length of the control system in the simulation process, and comparing and testing with corresponding simulation.
The simulation results are as follows: by observing fig. 1, it is found that the tracks of the four agents can be better consistent to track the preset track. As can be seen from an examination of fig. 2, the conformity errors of the agent can be well converged between the upper and lower bounds of the performance function. The output signal of the controller is shown in fig. 3, and the controller signal is changed from a continuous signal to an intermittent signal. The present control method is effective in summary.
The present invention is not limited to the above embodiments, but is capable of modification and variation in detail, and other modifications and variations can be made by those skilled in the art without departing from the scope of the present invention.

Claims (9)

1. A method for controlling the consistency of preset performance of multi-intelligent system with event trigger features that the unknown state in system is estimated by reduced-order filter, the controller is designed by distributed adaptive control method, and the dynamic surface control technique and event trigger technique are used in the design of controller.
2. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 1, wherein the system equation is as follows:
the system is a high-order system, the order n of the system i May be any value; wherein y is i An output track of the ith agent; x is x i2 ,x i3 ,x is Is the status of the ith agent; /> Is state x i1 ，x i2 ,x i3 ,/>Is a derivative of (2); phi (phi) i1 (y i )，φ i2 (y i )，/> Is a known smooth function vector; f (f) i22 (y i ),/> Is a known smooth nonlinear function; θ i A vector that is an unknown constant in the system; u (u) i Is a control input; b i0 ,b i1 ,/>The previous coefficients are input to the controller.
3. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 2, wherein the reduced order filter is designed as follows:
wherein the method comprises the steps ofIs a function vector; zeta type toy i ＝[ξ i2 ,ξ i3 ,...,ξ in ] T ,o i ＝[o i2 ,o i3 ,...,o in ] T ,Ξ i ＝[Ξ i2 ,Ξ i3 ,...,Ξ in ] T ,ν ik ＝[ν ik2 ,ν ik3 ,...,ν ikn ] T ,k＝0,...,m,Are all parameter vectors in the reduced order filter; />D＝diag[0,...,n-2],/>Are normal number vectors; />Is a constant vector; u (u) i Is a control input;
dynamic gainl i (0)＝1，/>l i Dynamic gain for ith reduced order filter,/->Is l i Is a derivative of (2); k (k) i Is a coefficient that can be designed, Φ i Is a designed nonlinear function; pi i1 ＝π i βρ i Wherein->The error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; beta is a time-varying function to be designed, ζ i (t)＝β(t)η i (t) is based on β (t) and the introduced transfer function;is a designed calculation function, where l is a constant greater than 0; e, e i0 Is the consistency error of the multi-agent system; sigma (sigma) i10 ，σ i14 ,σ i15 A constant greater than 0; sigma (sigma) -1 i14 ，σ -1 i15 Is sigma (sigma) i10 ，σ i14 Is the reciprocal of (2); />The sum of communication coefficients of the multi-intelligent system; a, a iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
4. The multi-agent system preset performance consistency control method with event triggering of claim 3, wherein a barrier function applicable to the multi-agent system is designed according to a time-varying limiting function β (t) to realize multi-agent preset performance control with initial state unrestricted;
if a function β (t) meets the following requirement, called a time-varying constraint function:
beta (t) is a strict one-way increasing function and needs to satisfy beta (0) =1 when time t=0; when the time t is infinityAnd 0 < b f ＝1；
B:β (k) K=1, 2,3. N is at the time the boundary segments are continuous;
constructing a preset function according to the time-varying limiting function as follows:where l is a constant greater than 0, ψ (t) is the inverse of the real variable restriction function β (t), i.e +.>
5. The method for controlling the consistency of preset performances of a multi-agent system with event triggering according to claim 4, wherein designing a barrier function of the multi-agent system according to a time-varying restriction function is as follows:
zeta in i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 The transfer function to be introduced is that,the error conversion function is designed for realizing the preset temporary steady state performance of the ith intelligent agent; e, e i0 Consistency error for multi-agent systemsa iq Representing the communication coefficient between the ith agent and the qth agent, if a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, if the information mu of the leader is directly acquired i =1, vice versa μ i ＝0。
6. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 5, wherein the following coordinate transformation is performed according to a barrier function:
wherein z is i1 ,z ij Is the error needed in the back-stepping method; s is(s) ij Filtering errors before and after the virtual controller; alpha i,(j-1) Andthe method is a virtual controller which is designed in a back-stepping method and a filtered virtual controller; v imij Is a parameter in the reduced order filter;
for z i1 The derivation designs the virtual controller of the first step as:
in the middle ofRepresents->The sign, z of i1 Error for the first step of the backstepping method, < >>Is a virtual controller alpha i1 A positive constant;β i 、β iq 、λ i 、χ i is adaptive parameter->Is self-adaptive parameter beta i 、β iq 、λ i 、χ i Is a function of the estimated value of (2); />c i1 ,σ i11 ,σ i12 ,σ i14 ,σ i15 ,a i A constant greater than zero; />Sum of communication coefficients of multi-intelligent system, a iq Representing the communication coefficient between the ith agent and the qth agent, a iq =1 means that the information of the qth agent is available to the ith agent, otherwise a iq ＝0；μ i Indicating the information acquisition condition of the intelligent agent i on the leader, and if the information of the leader is directly acquired, mu i =1, vice versa μ i ＝0；ξ i2 Reduced order filter parameters, ζ, for the ith agent q2 The reduced order filter parameter of the q-th agent; l (L) i Dynamic gain for the reduced order filter; pi i1 And pi i2 Simplifying the function after deriving the barrier function; pi i1 ＝π i βρ i ，/>Wherein-> Is an error conversion function designed for realizing the preset transient steady state performance of the ith intelligent agent, beta is a time-varying function which needs to be designed, and zeta is a time-varying function i (t)＝β(t)η i0 (t) is based on beta (t) and eta i0 (t) introduced transfer function, +.>Is a designed computable function, where l is a constant greater than 0, e i0 Is the consistency error of the multi-agent system; />Andparameter vector +.f. for reduced order dynamic gain filter obtained by scaling with Young's inequality>And->A related function;
to avoid the overestimation problem, the adaptive parameters are defined as follows, and the following adaptive parameters are estimated:
β i ＝sup‖Θ i ‖,β iq ＝sup‖Θ iq ‖
wherein Θ i For all unknown constant vectors in the ith agent system, Θ iq All unknown constant vectors in the q-th intelligent agent system; sup|theta i II is theta i An upscaling of the norm; sup|theta iq II is theta iq An upscaling of the norm;is->Is the minimum of (2); />Is->Is the upper bound of (2); />And->Reduced order dynamic gain filter parameter vector, v for the ith agent and the jth agent i(mi-2)2 ,…,ν i02 ,Ξ i2 ,φ i1 ，/>…,-ν q02 ,Ξ q2 ,φ q1 Is a parameter in the reduced order dynamic gain filters i and q.
7. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 6, wherein the self-adaptive rate is designed as follows:
wherein the method comprises the steps ofA constant greater than zero; />Estimated value for adaptive parameter +.>Is a derivative of (2); />Andparameter vector +.f. for reduced order dynamic gain filter obtained by scaling with Young's inequality>And->A function of the correlation.
8. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 7, wherein the virtual controller in the second step is designed to:
j (j is not less than 3 and not more than ρ) i ) The virtual controller is designed as follows:
in c ij ,σ ij1 、σ ij2 、σ i(j-1)1 Is a normal number of times, and the number of times is equal to the normal number,the method is designed in the following form:
τ in ij All c and σ are constants greater than zero, no matter what the subscript is, positive constants.
9. The method for controlling the consistency of preset performances of a multi-intelligent system with event triggering according to claim 8, wherein the controller of the system is:
in the middle ofδ i1 ，/>Is a positive constant; />The ith P.o. of the ith agent i A step consistency error; />Is a nonlinear term in the system, l i ,/>Is a term in the reduced order filter; />For virtual controller->Is a derivative of (2);
tanh is a function.
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CN117706913A (en) * 2023-12-01 2024-03-15 河北科技大学 Nonlinear multi-intelligent system output feedback consistency control method based on reference signal generator
CN117850433A (en) * 2024-01-15 2024-04-09 齐鲁工业大学(山东省科学院) Collision avoidance formation control method and system for disturbed communication limited mobile robot

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Publication number Priority date Publication date Assignee Title
CN117706913A (en) * 2023-12-01 2024-03-15 河北科技大学 Nonlinear multi-intelligent system output feedback consistency control method based on reference signal generator
CN117706913B (en) * 2023-12-01 2024-06-07 河北科技大学 Nonlinear multi-intelligent system output feedback consistency control method based on reference signal generator
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