CN103869698A - Sampling control method of multi-intellectual body system consistency - Google Patents

Abstract

The invention belongs to the field of intelligent control and provides a sampling control method of multi-intellectual body system consistency. By using delay decomposition technology, the invention provides a novel consistency algorithm, i.e. a sampling control protocol of first-order multi-intellectual body system consistency with delay state derivative feedback. Based on the study on sampling data control, an appropriate sampling period is searched by using a stability theory and an algebraic graph theory of a linear system, and the necessary and sufficient conditions of gradually realizing average consistency of the first-order multi-intellectual body system consistency with the delay state derivative feedback are respectively discussed. The method has the advantages that the original protocol of a delay state derivative which is approximately calculated by using numerical differentiation is substituted, the appropriate sampling period is selected to ensure the realization of the consistency, and the necessary and sufficient conditions of gradually realizing the average consistency of the first-order multi-intellectual body system consistency with the delay state derivative feedback are respectively discussed, so that the stability of the system is improved.

Description

The conforming sampling control method of multi-agent system

One, technical field

The present invention is the conforming sampling control method of multi-agent system, belongs to field of intelligent control.

Two, background technology

Multi-agent system is the emerging complication system science that development in recent years is got up, and it is also a comprehensive cross discipline that relates to biology, mathematics, physics, control, computing machine, communication and artificial intelligence simultaneously.The Harmonic Control of multi-agent system has obtained the extensive concern from the researcher in these fields at present.

We study the distributed collaboration control of multi-agent system, it is not only the inherent law in order to disclose the many physical phenomenons of occurring in nature, that the more important thing is that utilization obtains instructs our activity better to the understanding of its inherent law, serves better human society.Nowadays, the distributed collaboration control of multi-agent system has been applied to many fields, as troop, assemble, swarm, the Collaborative Control of the congestion control of formation control, distributed sensor networks, communication network, push-button aircraft and attitude harmony etc.

In practice, replace current manual system with multi-agent system and can save significantly production cost, and safer; In addition, colony has also stimulated the application of multi-agent system in engineering by the part feature that obtains community superiority that cooperates.In military field, adopt aerial unmanned machine system fight and scout, can reduce personnel's injures and deaths, can also there is the maneuverability of superelevation overload, be conducive to attack and break away from threat; At civil area, multi-agent system can complete the task that resource exploration, the condition of a disaster scouting, communication repeating, environmental monitoring etc. are heavy, repeat or have certain risk, for example autonomous travelling car system, automatic high speed highway system, space development and detection, seafari, sensor network etc.And, infer according to brainstrust, " 21 century may become the unmanned war epoch ", that is to say, on future battlefield, automatic technology will be used on a large scale, to link together by multi-agent system with semi-autonomous ground, aerial and marine optimal in structure of various autonomies, finishes the work jointly with combatant, and this will be a kind of incontrovertible development trend.

Three, summary of the invention

The object of the invention is to propose the conforming sampling control method of multi-agent system.Specific implementation comprises following content:

In actual applications, the interference of communication delay (being mainly to carry out communication by sensor or communication facilities between individuality to produce) and input delay (individual self generation for the processing of external action or signal) is inevitably, and may cause dispersing or shaking of network system.Therefore be, very necessary to the research of time-delay.

Due to restriction and the total cost constraint of communication condition, information almost can not be transmitted continuously, or can only periodical exchange information. on the other hand, under a lot of situations, although system itself be one continuous time process, due to the application of digital sensor and controller, in many cases, although system itself is a continuous process, the comprehensive information that only uses sampling instant of controller, only effectively synthetic to controlling in the sampled data of discrete sampling moment.So, consider that intermittent transmission information is more practical, thereby be modeled as discrete-time system or commingled system.With with continuous time controller continuous time system or self be exactly compared with the system of discrete time, have many advantages by the continuous time system of controlling of sampling.On the one hand, the digitial controller based on sampled data design has clear superiority aspect control accuracy, control rate, control performance and regulate expenditure.On the other hand, in engineering application, continuous signal is higher to the requirement of communication bandwidth, and this is in most of the cases unavailable.Therefore, the controlling of sampling of continuous time system more can meet the needs of actual conditions.

For most of existing consistency protocols, major part proposes under current state or time lag existence.But in some cases, being introduced in of time lag state derivative feedback guarantees that system realizes consistance aspect and is necessary.The people such as Cao in 2011 have studied and while having, have become the single order of reference state and the consistance tracking problem of Second Order Continuous time multi-agent system and proved in the time that virtual leader only exists part intelligent body, and the consistance without time lag state derivative feedback of proposition is followed the tracks of agreement can not guarantee to realize conforming tracking.Simultaneously, the people such as 2012 Nian Wu are in the continuous time with communication delay in multi-agent system, by introducing suitable time lag state derivative feedback gain, improved conforming performance, the robustness (be system patient maximum time lag) that its performance mainly comprises communication delay with realize consistent speed of convergence.But Cao and Wu's research in actual applications, is difficult to the time lag state derivative feedback information of the neighbours' intelligent body that obtains it for certain intelligent body, the consistance in other words with time lag state derivative feedback is difficult to realize.In order to overcome this problem, the people such as 2012 Nian Wu have proposed to come by numerical differentiation under sampled data controlled condition the strategy of approximate treatment time lag state derivative, but this approximate treatment may destroy the stability of system.And, in document, choose the suitable sampling period and guarantee that conforming realization is not also cited at present.

Comprehensive above analysis, mainly study from the following aspects:

(1) application time lag decomposition technique, has proposed a kind of new consistency algorithm and has had the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback;

(2) research based on sampled data control, stability theory and the algebraic graph theory of application linear system, find the suitable sampling period, the single order multi-agent system with time lag state derivative feedback has been discussed respectively and has been realized conforming sufficient and necessary condition;

(3) numerical simulation figure has proved the validity of notional result.

The invention has the advantages that and replace original agreement of carrying out approximate treatment time lag state derivative by numerical differentiation, choose the suitable sampling period and guarantee conforming realization, thereby improved the stability of system.

Brief description of the drawings

Fig. 1 is the network topology structure figure of the undirected connection of weighting being made up of four intelligent bodies that uses in the present invention;

The constitutional diagram that Fig. 2 multi-agent system is stable;

Fig. 3 multi-agent system unsure state figure.

Embodiment:

Below in conjunction with accompanying drawing and instantiation, the present invention will be further described:

A) problem is described:

By reference to the accompanying drawings 1, consider following single order multi-agent system

i ∈ I (1)

Wherein, x _i(t) ∈ R and u _i(t) ∈ R represents respectively state and the corresponding control inputs of intelligent body i.

Define 1 multi-agent system (1) and be called as the asymptotic average homogeneity that realizes, if the state of each intelligent body meets gradation:

for the robustness that simultaneously improves communication delay with realize consistent speed of convergence, Wu and side have proposed the following consistency protocol based on time lag state derivative feedback:

${\mathrm{\μ}}_i\left(t\right)=\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}\left\{\right[x_j(t-\mathrm{\τ})+\mathrm{\β}{\stackrel{\·}{x}}_j(t-\mathrm{\τ})]-[x_i(t-\mathrm{\τ})+\mathrm{\β}{\stackrel{\·}{x}}_i(t-\mathrm{\τ})\left]\right\}---\left(2\right)$

Wherein, τ > 0 represents that communication delay and β represent the intensity of time lag state derivative feedback and meet β ∈ (0, min{ τ, 1/ λ _n(L) }).

For application protocol (2) makes multi-agent system realize consistance, we proposed a kind of new method, uses (x _i(t-τ)-x _i(t-τ-h))/h and (x _j(t-τ)-x _j(t-τ-h))/h, j ∈ N _ireplace respectively

and x _j(t-τ), j ∈ N _i.Wherein, h > 0 represents the sampling period.So we have just proposed the agreement of the conforming numerical differentiation of single order multi-agent system with time lag state derivative feedback:

$u_i\left(t\right)=\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}\left\{\right[x_j(t-\mathrm{\τ})+\mathrm{\β}(x_j(t-\mathrm{\τ})-x_j(t-\mathrm{\τ}-h))/h]-[x_i(t-\mathrm{\τ})+\mathrm{\β}(x_i(t-\mathrm{\τ})-x_i(t-\mathrm{\τ}-h))/h\left]\right\}.---\left(3\right)$

Communication delay τ is carried out to time lag about sampling period h to be divided and solves: τ=mh+ ε (4)

Wherein, and m nonnegative integer and ε ∈ [0, h).

Life cycle Sampling techniques and zero-order holder technology, by consistency protocol (3), we have proposed to have the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback:

$u_i\left(t\right)=\left\{\begin{array}{c}{u}_i(\mathrm{kh}-\mathrm{mh}-h)=\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}\left\{\right[x_j(\mathrm{kh}-\mathrm{mh}-h)+\mathrm{\β}(x_j(\mathrm{kh}-\mathrm{mh}-h)-x_j(\mathrm{kh}-\mathrm{mh}-2h))/h]\\ -[x_i(\mathrm{kh}-\mathrm{mh}-h)+\mathrm{\β}(x_i(\mathrm{kh}-\mathrm{mh}-h)-x_i(\mathrm{kh}-\mathrm{mh}-2h))/h]\},t\∈[\mathrm{kh},\mathrm{kh}+\mathrm{\ϵ});\\ u_i(\mathrm{kh}-\mathrm{mh})=\underset{j\∈N_i}{\mathrm{\Σ}}{a}_{\mathrm{ij}}\left\{\right[x_j(\mathrm{kh}-\mathrm{mh})+\mathrm{\β}(x_j(\mathrm{kh}-\mathrm{mh})-x_j(\mathrm{kh}-\mathrm{mh}-h))/h]\\ -[x_i(\mathrm{kh}-\mathrm{mh})+\mathrm{\β}(x_j(\mathrm{kh}-\mathrm{mh})-x_j(\mathrm{kh}-\mathrm{mh}-h))/h]\},t\∈[\mathrm{kh}+\mathrm{\ϵ},\mathrm{kh}+h).\end{array}\right.---\left(5\right)$

We say the asymptotic average homogeneity that realized of system (1), when

Lemma 1 equation s ³+ a ₂s ²+ a ₁s+a ₀=0 all in unit circle, wherein a ₂, a ₁, a ₀∈ R, four inequality 1+a below and if only if ₂+ a ₁+ a ₀> 0 ,-1+a ₂-a ₁+ a ₀< 0, | a ₀| < 1 He | a ₀ ²-1| > | a ₀a ₂-a ₁| set up simultaneously.

B) convergence

In this section, the knowledge such as stability theory and algebraic graph theory of application linear system, we have obtained guaranteeing that multi-agent system (1) application consistency protocol (5) realizes the sufficient and necessary condition of average homogeneity, i.e. equation

z ^m+3-z ^m+2+(h-ε)(1+β/h)λ _i(L)z ²+(ε-β+2εβ/h)λ _i(L)z-ε(β/h)λ _i(L)＝0，i∈I\{1}(6)

All all in unit circle.

Although all of equation (6) is all sufficient and necessary condition in unit circle, but for large sampling time lag, be difficult to obtain guaranteeing that multi-agent system (1) application consistency protocol (5) realizes the span in the accurately sampling period of average homogeneity.Therefore, the notional result of equation (6) is mainly used to test the validity of guaranteeing to realize the conforming sampling period.

Can be drawn by time lag decomposition technique equation (4), in the time of m=0 and ε ≠ 0,0 < ε=τ < h, that is to say that communication delay is less than the sampling period.In this case, deteriorate to the consistency protocol with little sampling time lag with the consistency protocol (5) of large sampling time lag: $u_i\left(t\right)=\left\{\begin{array}{c}{u}_i(\mathrm{kh}-h)=\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}\left\{\right[x_j(\mathrm{kh}-h)+\mathrm{\&beta;}(x_j(\mathrm{kh}-h)-x_j(\mathrm{kh}-2h))/h]\\ -[x_i(\mathrm{kh}-h)+\mathrm{\&beta;}(x_i(\mathrm{kh}-h)-x_i(\mathrm{kh}-2h))/h]\},t\&Element;[\mathrm{kh},\mathrm{kh}+\mathrm{\&tau;});\\ u_i\left(\mathrm{kh}\right)=\underset{j\&Element;N_i}{\mathrm{\&Sigma;}}{a}_{\mathrm{ij}}\left\{\right[x_j\left(\mathrm{kh}\right)+\mathrm{\&beta;}(x_j\left(\mathrm{kh}\right)-x_j(\mathrm{kh}-h))/h]\\ -[x_i\left(\mathrm{kh}\right)+\mathrm{\&beta;}(x_j\left(\mathrm{kh}\right)-x_j(\mathrm{kh}-h))/h]\},t\&Element;[\mathrm{kh}+\mathrm{\&tau;},\mathrm{kh}+h).\end{array}\right.---\left(7\right)$

By reference to the accompanying drawings 1, consider multi-agent system (1) have one fixing, undirected, the network topology structure of connection.Suppose τ < 1/ λ _n, so much multiagent system (1) application consistency protocol (7) has been realized average homogeneity, and and if only if

$\max \{\mathrm{\&tau;},\frac{\mathrm{\&beta;\&tau;}{\mathrm{\&lambda;}}_N(1-\mathrm{\&tau;}{\mathrm{\&lambda;}}_N+\mathrm{\&beta;}{\mathrm{\&lambda;}}_N)}{(1+\mathrm{\&beta;}{\mathrm{\&lambda;}}_N)(1-\mathrm{\&tau;}{\mathrm{\&lambda;}}_N)}\}<h<\sqrt{{(\mathrm{\&beta;}-\mathrm{\&tau;}-1/{\mathrm{\&lambda;}}_N)}^2+4\mathrm{\&beta;\&tau;}}+\mathrm{\&tau;}+1/{\mathrm{\&lambda;}}_N-\mathrm{\&beta;}.---\left(8\right)$

Prove: as 0 < ε=τ < h, equation (6) deteriorates to

z ³+[(h-τ)(1+β/h)λ _i(L)-1]z ²+(τ-β+2τβ/h)λ _i(L)z-τ(β/h)λ _i(L)＝0，i?∈I\{1}.(9)

By lemma 1, all in unit circle, and if only if for all of equation (9)

$\left\{\begin{array}{c}h{\mathrm{\&lambda;}}_i\left(L\right)>0;\\ (h+2\mathrm{\&beta;}-2\mathrm{\&tau;}-4\mathrm{\&tau;\&beta;}/h){\mathrm{\&lambda;}}_i\left(L\right)<2;\\ \mathrm{\&tau;}(\mathrm{\&beta;}/h){\mathrm{\&lambda;}}_i\left(L\right)<1;\\ |{\mathrm{\&tau;}}^2({\mathrm{\&beta;}}^2/h^2){{\mathrm{\&lambda;}}_i}^2\left(L\right)-1|>\\ \left|\right[(h-\mathrm{\&tau;})(1+\mathrm{\&beta;}/h){\mathrm{\&lambda;}}_i\left(L\right)-1]\mathrm{\&tau;}(\mathrm{\&beta;}/h){\mathrm{\&lambda;}}_i\left(L\right)\\ -(\mathrm{\&tau;}-\mathrm{\&beta;}+2\mathrm{\&tau;\&beta;}/h){\mathrm{\&lambda;}}_i\left(L\right)|\end{array}\right.,i\&Element;I\backslash \left\{1\right].---\left(10\right)$

Proof completes.

C) Simulation results

By reference to the accompanying drawings 1, be easy to obtain the eigenvalue of maximum λ of L ₄be 4.This algorithm does emulation experiment as an example of the sampling period example, now suppose τ=0.2 and β=0.1, draw and guaranteed that it is (0.2,0.8) that multi-agent system (1) application consistency protocol (7) is realized the span in the sampling period of average homogeneity by (8).

By reference to the accompanying drawings 2, we find in the time of h=0.3, meet the condition of (8), and given multi-agent system (1) application consistency protocol (7) has been realized average homogeneity.

By reference to the accompanying drawings 3, we find in the time of h=0.9, meet the condition of (8), and given multi-agent system (1) application consistency protocol (7) can not be realized average homogeneity.

Claims (3)

1. the conforming sampling control method of multi-agent system, the method is mainly studied from the following aspects:

(1) application time lag decomposition technique, has proposed a kind of new consistency algorithm and has had the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback;

(2) research based on sampled data control, stability theory and the algebraic graph theory of application linear system, find the suitable sampling period, the progressive sufficient and necessary condition of realizing average homogeneity of single order multi-agent system with time lag state derivative feedback has been discussed respectively;

(3) numerical simulation figure has proved the validity of notional result.

2. the conforming sampling control method of multi-agent system according to claim 1, is characterized in that: the time lag decomposition technique theory in described content (1) proposition and a kind of new consistency algorithm proposed had the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback.

3. the conforming sampling control method of multi-agent system according to claim 1, it is characterized in that: described step (2) is being utilized stability theory and the algebraic graph theory of linear system, find the suitable sampling period, the progressive sufficient and necessary condition of realizing average homogeneity of single order multi-agent system with time lag state derivative feedback has been discussed respectively.

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