CN109683477A - A kind of design method and system of random multi-agent system finite-time control device - Google Patents

A kind of design method and system of random multi-agent system finite-time control device Download PDF

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CN109683477A
CN109683477A CN201811519068.5A CN201811519068A CN109683477A CN 109683477 A CN109683477 A CN 109683477A CN 201811519068 A CN201811519068 A CN 201811519068A CN 109683477 A CN109683477 A CN 109683477A
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郑世祺
杨自超
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China University of Geosciences
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Abstract

The invention discloses the design methods and system of a kind of random multi-agent system finite-time control device, what the present invention studied is non-Strict-feedback model, and establish novel stochastic finite time stability criterion, success constructs finite-time control device using Backstepping, using radial base neural net approximation theory, solves in system model unknown function to difficulty brought by controller design.By experimental result, it can be concluded that, the output of total system model can be good at following given value y in finite timerVariation.

Description

A kind of design method and system of random multi-agent system finite-time control device
Technical field
The present invention relates to intelligent body fields, more specifically to a kind of random multi-agent system finite-time control The design method and system of device.
Background technique
In recent years, random multi-agent system uniform stability control problem is standby due to its extensive civil and military Concerned, application field is related to traffic control, sensor network control, mobile robot, community network etc..Needle first The various problems of single random multiagent system are unfolded to discuss, single stochastic system is finally expanded into random multiple agent System is unfolded to discuss for various situations existing for the system.
The case where in system containing switching, scholars are designed using different methods.Some scholars explore containing not The switching stochastic non-linear system for knowing parameter and time delay is devised a kind of adaptive by introducing power integrator technology, Backstepping Answer output feedback controller.Then, how some scholars design control for the Nonlinear Stochastic switching system containing unknown parameter Device discusses.By combining mean residence time scheme and adaptive Backstepping design, an efficient adaptive mind is proposed Through state feedback controller algorithm for design.For the lower triangular structure single-input single-output non-linear stochastic with output constraint Switching system proposes a kind of controller design method based on radial basis function neural network.In addition, some scholars will be anti- Footwork and radial base neural net combine, and have studied stochastic non-linear system follows problem.Some investigators will in Lyapunov function method, contragradience technology and neural network approximatioss be applied to asymmetric input saturation switching it is non-thread at random In property system.Same part researcher also utilizes fuzzy system other than using Lyapunov function method, contragradience technology Architectural characteristic and Robust Adaptive Control technical research nonaffine Nonlinear Stochastic switching system.
Event triggers the hot topic also studied.A part of scholar considers the interconnection Nonlinear Stochastic based on event System is designed adaptively using the unknown function in the approximation theory estimating system of fuzzy logic system, and using Backstepping Controller.A part of researcher has studied the adaptive event triggering control problem of a kind of uncertain stochastic non-linear system, examines The stochastic non-linear system with actuator failures is considered, for uncertain system parameter and random perturbation, using adaptive mode Control technology is pasted, adaptive Reverse Step Control is quoted and designs reasonable controller.Then, other researchers are for random non- Linear system has studied increasingly complex problem, including unknown state variable, actuator failures and input quantization.Due to not Know the presence of state variable, the nonlinear function author in system uses the method approximation for setting up fuzzy logic system.In order to Processing input quantization and actuator failures affect, and introduce damping term estimate with Unknown Bound and with positive time-varying integral letter Number.Finally adaptive controller is had devised also with Backstepping.
Due to the limitation of single stochastic non-linear system, some scholars turn to grinding for random multi-agent system gradually Study carefully.The stability analysis conclusion of stochastic time-delay system is applied in multi-agent system by part author, when author not only considers Prolong and be also added into random perturbation, by introducing improved comparison principle, several stability for establishing random delay system are quasi- Then, the consistency problem of the multi-agent system using obtained result treatment with transmission time lag and time-varying topology.Portion Divide scholar to trigger control strategy using distributed event, has studied leader and the side of random multi-agent system is followed unanimously to ask Topic.The leader that some scholars have studied the random multi-agent system of nonlinear kinetics containing isomery and unknown disturbance follows control Problem processed, and fuzzy logic system is applied to unknown nonlinear dynamics approximation, an auto-adaptive parameter is devised to decline The influence for subtracting external disturbance designs adaptive controller using Backstepping thought.
In addition to the problem that follows of the random multi-agent system of single order, some scholars are also to the random multi-agent system of high-order Produce interest.For random High Order Nonlinear System, part document completely eliminates power order limitation for the system, non-thread Property condition of growth has obtained significantly relaxing, and gives a weaker adequate condition.It is handled using Backstepping The problem of adaptive stabilizing.For the uncertain high-order stochastic nonlinear systems of the limitation containing input, some scholars utilize diameter Nonlinear function and random perturbation in system have been handled to base neural net, and has utilized Backstepping and Lyapunov function Propose the adaptive neural network tracing control method of dispersion.
Summary of the invention
The consistency problem for analyzing random multi-agent system above, includes the case where single order and high-order, comes from status It seeing, most of scholar considers situations such as quantization, export-restriction, nonlinear function containing input, but in random multiple agent system In system, do not consider under conditions of finite time, so that the output of system follows given value to change；It is non-in system model The case where including whole state variables in linear function.In addition, present invention consideration is approached using radial base neural net method and is Unknown function in system.Therefore, how to be designed by neural network function, adaptive Backstepping techniques and Lyapunov function More simple and effective controller, and the controller can allow the output of system to follow the change of given value in finite time Change, at the direction of the invention studied.
The present invention is to solve its technical problem, and a kind of random multi-agent system finite-time control device provided is set Meter method comprises the following steps:
(1) kinetics equation of the random multi-agent system of N number of follower and leader composition is obtained；
Wherein, i represents i-th of intelligent body equation group, i=1, and 2 ..., N+1, j are indicated in each intelligent body equation group J-th of equation, j=1 ..., n-1, n and N are positive integer, and n > 1；xi,jIt is the state variable of system, uiIt is i-th of intelligence The input of body, yiIt is the output of i-th of intelligent body, w is the random Brownian motion of a standard, fi,j(xi),It is not The nonlinear function known, xi=[xi,1,...,xi,n]；
(2) by the input signal y of the random multi-agent system gotr, define error varianceWherein ηi>=0, only when i-th of intelligent body receives input signal yrWhen, ηi> 0, otherwise, ηi=0, ai,mIndicate the connection weight between node i and node m；To zi,1Differentiate dzi,1, in conjunction with formula (3) first equation and error variance zi,2=xi,2-τi,1, obtain error variance zi,1Form about equation (a)；It chooses Liapunov function Vi,1, then to the V of the selectioni,1Differentiate operator LVi,1, according to equation (b), poplar inequality and lemma 2 obtain LVi,1Simplest formula, and in LVi,1Simplest formula choose the virtual controlling amount τ containing β poweri,1, obtain LVi,1Most Whole simplest formula, in zi,2When being 0, LV is obtainedi,1Final simplest formula about after the form of lemma 1 solve obtain τi,1So that system Stablize in finite time；
(3) according to error variance zi,j=xi,j-τi,j-1, wherein control signal xi,jEqual to virtual controlling amount τi,j-1, obtain Error variance zi,jAbout the form of equation (a), liapunov function V is choseni,j, then to the V of the selectioni,jIt differentiates calculation Sub- LVi,j, LV is obtained according to equation (b), poplar inequality and lemma 2i,jSimplest formula, and LVi,jSimplest formula in choose contain β The virtual controlling amount τ of poweri,j-1, obtain LVi,jFinal simplest formula, in zi,j+1When being 0, LV is obtainedi,jFinal simplest formula τ is obtained about solving after the form of lemma 1i,1So that system is stablized in finite time；Wherein, j=2 ..., n-1；
(4) according to error variance zi,n=xi,n-τi,n-1, wherein control signal xi,nEqual to virtual controlling amount τi,n-1, obtain Error variance zi,nAbout the form of equation (a), Lyapunov function V is choseni,n, then to the V of the selectioni,nIt differentiates operator LVi,n, and LV is obtained according to equation (b), poplar inequality and lemma 2i,nSimplest formula, and in LVi,nSimplest formula in, selection contains There is the self adaptive control rate u of β poweri, obtain LVi,nSelf adaptive control rate u is obtained about solving after the form of lemma 1iSo that being System is stablized in finite time.
Further, in the design method of random multi-agent system finite-time control device of the invention, work as node When i can obtain the information of node m, ai,m> 0, otherwise, ai,m=0.
Further, in the design method of random multi-agent system finite-time control device of the invention, formula (a) and (b) it is defined as follows:
Stochastic non-linear system are as follows:
Dx=f (x) dt+g (x) dw (a)
Wherein, x indicates the state of system, and w is the random Brownian motion of a standard, and f (), g () are continuous letters Number, and meet f (0)=0, g (0)=0；
For any given V (x) in conjunction with stochastic non-linear system, it is as follows to define differential operator
Wherein, Tr { A } is the mark of matrix A, and h indicates the vector of any unknown linear function composition.
The present invention also provides a kind of designing system of random multi-agent system finite-time control device, use is above-mentioned It is limited that the design method of described in any item random multi-agent system finite-time control devices carries out random multi-agent system The design of time controller.
What the present invention studied is non-Strict-feedback model, and establishes novel stochastic finite time stability criterion, success Finite-time control device is constructed using Backstepping, using radial base neural net approximation theory, is solved in system model not Know function to difficulty brought by controller design.By experimental result, it can be concluded that, the output of total system model is limited It can be good at following given value y in timerVariation.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is Communication topology figure；
Fig. 2 is to solve for the flow chart of virtual controlling amount.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail A specific embodiment of the invention.
Algebraic graph theory plays a key role in the consistency analysis of multi-agent system.If the letter between n intelligent body Interaction topological diagram g=(i, j) is ceased, wherein fixed-point set v={ 1 ..., n }, indicates that n intelligent body, ε are the side collection of figure.G's Side (i, j) indicates that information exchange can occur between intelligent body i and intelligent body j.Scheme the adjacency matrix A=[a of gij], wherein aij>=0 indicates the connection weight between node i and node j, when node i can obtain the information of node j, aij> 0, otherwise, aij=0.The LaPlacian matrix definition for scheming g is L=D-A, wherein matrix D=diag { d1,d2,...,dn, that is, haveFor non-directed graph g, wherein Laplacian Matrix L is a symmetrical matrix.
It defines 1: considering stochastic non-linear system
Dx=f (x) dt+g (x) dw, (1)
Wherein, x indicates the state of system, and w is the random Brownian motion of a standard, and f (), g () are continuous letters Number, and meet f (0)=0, g (0)=0.For the system, definition
The referred to as Stochastic stable function of time.NoteExpression initial value is x0When system in the state of t moment, equalization point x=0 is referred to as finite time stability 's.
For any given V (x) in conjunction with stochastic non-linear system, it is as follows to define differential operator
Wherein, Tr { A } is known as the mark of matrix A.
Lemma 1: setting the stochastic non-linear system has globally unique solution, if there is the Second Order Continuous of a positive definite bounded Can 0,0 < β < 1 and ρ > 0 of micro- liapunov function V (x) and real number c >, meet
LV(x)≤-cVβ(x)+ρ
For all x ∈ Rn, the solution of stochastic non-linear system (1) is global finite time Stochastic stable.
Lemma 2: radial base neural net function is used for an approximate continuous function f (Z).The function can be with following Form description:
Wherein, W* is ideal known weight, and Z is input vector, and δ (Z) is approximate error, and is met | δ (Z) | < ε, q > 1.
Consider that the random multi-agent system being made of N number of follower and a leader, random multi intelligent agent move Mechanical equation is described as follows:
Wherein, i represents i-th of intelligent body equation group, i=1, and 2 ..., N+1, j are indicated in each intelligent body equation group J-th of equation, j=1 ..., n-1, n and N are positive integer, and n > 1；xi,jIt is the state variable of system, uiIt is the defeated of system Enter, yiIt is the output of system, w is the random Brownian motion of a standard, fi,j(xi),It is unknown non-linear letter Number, xi=[xi,1,...,xi,n], therefore this system model is non-Strict-feedback model.Corresponding to h, h in formula (2)i=[ψi,1 ψi,2ψi,3…ψi,n]。
Fig. 1 shows leader-follower topology diagram:
The target of design controller is to allow the output y of system model (3)iInput signal y can be followedrVariation.
By system model it is found that is studied herein is N number of intelligent body, and just occur in n-th of equation self-adaptive controlled Rate u processedi, have no idea directly to design its expression formula, therefore, be proposed for system (3) a kind of based on the adaptive of Backstepping Answer control design case method.Specific design procedure is as follows:
(1) kinetics equation of the random multi-agent system of N number of follower and leader composition is obtained, specifically See formula (3)；
(2) Fig. 2 is referred to, by the input signal y of the random multi-agent system gotr, define error varianceWherein ηi>=0, only when i-th of intelligent body receives input signal yrWhen, ηi> 0, otherwise, ηi=0, ai,mIndicate the connection weight between node i and node m；To zi,1Differentiate dzi,1, in conjunction with formula (3) first equation and error variance zi,2=xi,2-τi,1, obtain error variance zi,1Form about equation (1)；It chooses Liapunov function Vi,1, then to the V of the selectioni,1Differentiate operator LVi,1, according to equation (2), poplar inequality and lemma 2 obtain LVi,1Simplest formula, and in LVi,1Simplest formula choose the virtual controlling amount τ containing β poweri,1, obtain LVi,1Most Whole simplest formula, in zi,2When being 0, LV is obtainedi,1Final simplest formula about after the form of lemma 1 solve obtain τi,1So that system Stablize in finite time；It is wherein based on Backstepping thought, signal x will be controlledi,2Regard virtual controlling amount τ asi,1；
(3) according to error variance zi,j=xi,j-τi,j-1, wherein control signal xi,jEqual to virtual controlling amount τi,j-1, obtain Error variance zi,jAbout the form of equation (1), liapunov function V is choseni,j, then to the V of the selectioni,jIt differentiates calculation Sub- LVi,j, LV is obtained according to equation (2), poplar inequality and lemma 2i,jSimplest formula, and LVi,jSimplest formula in choose contain β The virtual controlling amount τ of poweri,j-1, obtain LVi,jFinal simplest formula, in zi,j+1When being 0, LV is obtainedi,jFinal simplest formula τ is obtained about solving after the form of lemma 1i,1So that system is stablized in finite time；Wherein, j=2 ..., n-1；
(4) according to error variance zi,n=xi,n-τi,n-1, wherein control signal xi,nEqual to virtual controlling amount τi,n-1, obtain Error variance zi,nAbout the form of equation (1), Lyapunov function V is choseni,n, then to the V of the selectioni,nIt differentiates operator LVi,n, and LV is obtained according to equation (2), poplar inequality and lemma 2i,nSimplest formula, and in LVi,nSimplest formula in, selection contains There is the self adaptive control rate u of β poweri, obtain LVi,nSelf adaptive control rate u is obtained about solving after the form of lemma 1iSo that being System is stablized in finite time.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned tools Body embodiment, the above mentioned embodiment is only schematical, rather than restrictive, the ordinary skill of this field Personnel under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, can also make Many forms, all of these belong to the protection of the present invention.

Claims (4)

1. a kind of design method of random multi-agent system finite-time control device, which is characterized in that comprise the following steps:
(1) kinetics equation of the random multi-agent system of N number of follower and leader composition is obtained；
Wherein, i represents i-th of intelligent body equation group, i=1, and 2 ..., N+1, j indicate j-th in each intelligent body equation group Equation, j=1 ..., n-1, n and N are positive integer, and n > 1；xi,jIt is the state variable of system, uiIt is the defeated of i-th of intelligent body Enter, yiIt is the output of i-th of intelligent body, w is the random Brownian motion of a standard, fi,j(xi),It is unknown non-thread Property function, xi=[xi,1,...,xi,n]；
(2) by the input signal y of the random multi-agent system gotr, define error varianceWherein ηi>=0, only when i-th of intelligent body receives input signal yrWhen, ηi > 0, otherwise, ηi=0, ai,mIndicate the connection weight between node i and node m；To zi,1Differentiate dzi,1, in conjunction with formula (c) First equation and error variance zi,2=xi,2-τi,1, obtain error variance zi,1Form about equation (a)；Choose Li Ya Pu Nuofu function Vi,1, then to the V of the selectioni,1Differentiate operator LVi,1, obtained according to equation (b), poplar inequality and lemma 2 LVi,1Simplest formula, and in LVi,1Simplest formula choose the virtual controlling amount τ containing β poweri,1, obtain LVi,1It is final most simple Formula, in zi,2When being 0, LV is obtainedi,1Final simplest formula about after the form of lemma 1 solve obtain τi,1So that system is limited Stablize in time；
(3) according to error variance zi,j=xi,j-τi,j-1, wherein control signal xi,jEqual to virtual controlling amount τi,j-1, obtain error change Measure zi,jAbout the form of equation (a), liapunov function V is choseni,j, then to the V of the selectioni,jDifferentiate operator LVi,j, LV is obtained according to equation (b), poplar inequality and lemma 2i,jSimplest formula, and LVi,jSimplest formula in choose the void containing β power Quasi- control amount τi,j-1, obtain LVi,jFinal simplest formula, in zi,j+1When being 0, LV is obtainedi,jFinal simplest formula about lemma 1 Form after solve obtain τi,1So that system is stablized in finite time；Wherein, j=2 ..., n-1；
(4) according to error variance zi,n=xi,n-τi,n-1, wherein control signal xi,nEqual to virtual controlling amount τi,n-1, obtain error change Measure zi,nAbout the form of equation (a), Lyapunov function V is choseni,n, then to the V of the selectioni,nDifferentiate operator LVi,n, and LV is obtained according to equation (b), poplar inequality and lemma 2i,nSimplest formula, and in LVi,nSimplest formula in, choose contain β power Self adaptive control rate ui, obtain LVi,nSelf adaptive control rate u is obtained about solving after the form of lemma 1iSo that system is limited Stablize in time.
2. the design method of random multi-agent system finite-time control device according to claim 1, which is characterized in that When node i can obtain the information of node m, ai,m> 0, otherwise, ai,m=0.
3. the design method of random multi-agent system finite-time control device according to claim 1, which is characterized in that It formula (a) and (b) is defined as follows:
Stochastic non-linear system are as follows:
Dx=f (x) dt+g (x) dw (a)
Wherein, x indicates the state of system, and w is the random Brownian motion of a standard, and f (), g () they are continuous functions, and Meet f (0)=0, g (0)=0；
For any given V (x) in conjunction with stochastic non-linear system, it is as follows to define differential operator
Wherein, Tr { A } is the mark of matrix A, and h indicates the vector of any unknown linear function composition.
4. a kind of designing system of random multi-agent system finite-time control device, which is characterized in that using such as claim The design method of the described in any item random multi-agent system finite-time control devices of 1-3, which carries out random multi-agent system, to be had Limit the design of time controller.
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