CN113420864B - Controller generation method of multi-agent system containing mutually exclusive resources - Google Patents

Abstract

The invention discloses a controller generation method of a multi-agent system containing mutually exclusive resources. The method comprises the following steps: firstly, processing the control requirement related to the mutually exclusive resource constraint condition by a mutex function of the SCT; then, taking the calculation result of the mutex function as a simplified controlled object; and finally, calculating the controller of the simplified controlled object relative to other control requirements. The method can effectively relieve the state explosion problem generated when the intelligent agent and each sub-requirement are subjected to parallel combination operation by preferentially processing the control requirement of the mutually exclusive resource and then processing other control requirements to generate the controller.

Description

Controller generation method of multi-agent system containing mutually exclusive resources

Technical Field

The invention relates to the field of automatic control and a discrete event system, in particular to a controller generation method of a multi-agent system containing mutually exclusive resources.

Background

In recent years, with the rapid development of artificial intelligence and communication technology, a multi-agent system MAS (MAS) has been widely and deeply applied in the fields of aerospace, unmanned driving, robots, and the like, and has become a hot research direction in the subjects of control engineering, computer science, robotics, economics, mathematics, physics, and the like. The multi-agent system consists of a plurality of individuals with certain sensing, calculating and executing capabilities, and the individuals are communicated with other agents through a network and cooperate with each other to jointly complete tasks. The intelligent degree of individual behaviors can be greatly improved by the cooperation of the multiple intelligent agents, so that the complex work which cannot be performed by a single individual can be completed better. Generally, information among the agents is affected by communication bandwidth, distance and various noises in the sensing, transmission and receiving processes, so that each agent is difficult to obtain accurate state information of its neighbors, and a coordinated multi-agent system cannot completely meet all requirements. Therefore, on the basis of autonomous calculation and planning negotiation of each intelligent agent, overall coordination control is carried out on the behavior of each intelligent agent, and the method is one of effective solutions for ensuring that the intelligent agents can effectively and safely complete tasks.

Generally, a resource that cannot be shared by a plurality of agents at the same time, i.e., a mutex resource, exists in a MAS. The problem of resource mutual exclusion is a common problem existing in MAS, in a Supervisory Control Theory SCT (SCT) of a Discrete Event System DES (DES), a controlled System and a Control requirement are generally described by a Deterministic Finite state Automaton (Finite state Automaton), and the SCT may generate a Supervisory controller having a maximum allowable behavior described by the Finite state Automaton for the controlled System. In SCT, constraints on mutually exclusive resources are described by control requirements, so that a controller can be generated to make system behavior meet mutual exclusivity. In MAS, the model of the whole system consists of the synchronous product of all the single agent models, the state number of the system model grows exponentially along with the increase of the number of agents, and the state explosion problem is a big obstacle to solving the control problem of the multi-agent system by using SCT.

The related theories of automata in the prior art generally include:

the alphabet sigma is a non-empty finite set of characters, the string s defined on sigma is made up of a series of symbols, the empty character e and all finite strings defined on sigma form the set sigma^*，∑^*Two character strings s in₁，s₂∈∑^*Is defined as s ═ s₁.s₂In general, s can be abbreviated as s ═ s₁s₂A finite state automaton is a quintuple consisting of (Q, sigma, delta, Q)₀，Q_m) Where Q is the state set, Σ is the alphabet, δ: q × ∑ → Q is the state transfer function, Q₀E.g. Q is the initial state,

to mark a state set, for states Q, Q ' ∈ Q and σ ∈ Σ, the transfer function δ (Q, σ) ═ Q ' denotes the transfer of state Q to state Q ' via event σ, if δ (Q, σ) is defined, with δ (Q, σ)! Meaning, in general, that the transfer function δ extends in a recursive manner from the domain Q × Σ to the domain Q × Σ^*：

(1)δ(q，ε)＝q；

(2) For σ ∈ Σ, Q, Q' ∈ Q, s ∈ Σ^*If δ (q, s) ═ q ', and δ (q', σ)! Then δ (q, s σ)! And δ (q, s σ) is δ (δ (q, s), σ), in which the automatons are all referred to as finite state automatons,

if there is a string s ∈ Σ^*Let δ (q, s) ═ q ', then state q' is said to be reachable from state q (reachable);

if q is from the initial state q₀If the value is reachable, the value q is called reachable;

if there is a string s ∈ Σ^*Let δ (q, s) be q ', then state q is said to reach (recoverable) state q';

if Q'. epsilon.Q_mThen q is said to be reachable;

if all states are reachable and reachable, automaton A is non-blocking, defining operation A_c(A) Delete all unreachable states:

A_c(A)＝(Q_ac，∑，δ_ac，q₀，Q_ac，m)，

wherein the content of the first and second substances,

Q_ac，m＝Q_m∩Q_ac，δ_ac：Q_ac×∑→Q_ac；

the language L defined over the alphabet sigma is sigma^*A generated language (l) (a) is denoted as l (s e Σ)^*|δ(q₀S)! }; a generated markup language (marked language) is marked as L_m(A)＝{s∈L(A)|δ(q₀，s)∈Q_m}；

Let A be₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Respectively representing two finite state automata, each of which,

definition 1: a. the₁And A₂The parallel combination of (a) is an automaton a,

A＝A₁||A₂＝A_c(Q₁×Q₂，∑₁∪∑₂，δ，(q_1，0，q_2，0)，Q_1，m×Q_2，m)，

wherein the content of the first and second substances,

if it is not

A₁And A₂Is called shuffle, for three automata A₁，A₂And A₃The parallel combining operation satisfies the combination law: (A)₁||A₂)||A₃＝A₁||(A₂||A₃) The combination law is also suitable for the parallel combination operation of n (n is more than or equal to 3) automata; TCT is a piece of software developed by the university of Toronto for generating supervisory controllers for systems in which n automata A₁，…，A_nBy sync (A)₁，…，A_n) Realizing a function;

the related knowledge of the Supervision Control Theory (SCT) in the prior art is generally:

SCT is a branch of the system's control theory for which the controller is designed by studying the logical behavior of DES (i.e. the controlled system) described by an automaton G on an alphabet sigma divided into two disjoint subsets sigma_uSum Σ_cWherein, sigma_uIs a collection of uncontrolled (uncontrolled) events, Σ_cIs a controllable (controllab1e) event set, the control requirement is described by automaton R on Σ, SCT is represented by V: l (G) → Γ realizes a control function, wherein

Is a set of control modes.

Definition 2: if the following conditions are satisfied, the language

Controllable with respect to the controlled system G:

given language

All subsets of H controllable with respect to G, denoted

The upper limit of C (H, l (g)) is supC (H, l (g)) U_{k∈C(H，L(G))}K, if

Then there is one non-blocking controller V for K and G, such that L_m(V)∩L_m(G) Is equal to K and

suppose A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Respectively represent two agents, when

When it comes to scale A₁And A₂The (a) is not crossed with each other,

representing agent A_iJ (th) state of (A)₁And A₂Is recorded as a mutually exclusive state set

Is shown in A₁||A₂Middle state

And

i-1, …, k cannot occur simultaneously; in TCT, the function a ═ mutex (a)₁，A₂List) is used to generate information about A₁||A₂And a controller of the exclusive constraint list, wherein the implementation of the "mutex" function is shown as an algorithm 1:

algorithm 1: procedure to implement the "mutex" function:

inputting: mutually disjoint agents A₁And A₂The set of mutually exclusive state pairs list,

and (3) outputting: with respect to A₁||A₂And a controller of list, specifically:

1) execution A₁₂＝A₁||A₂；

2) In A₁₂Deleting the state pairs in the list, wherein all the state pairs in the list can be reached along a path formed by the uncontrollable events;

3)A₁₂＝AC(A₁₂)；

4) output A₁₂。

Output A of Algorithm 1₁₂Are reachable and controllable, but need not be reachable; let A be A₁||A₂If A is₁₂Is reachable, A₁₂Is a controller with the maximum allowable behavior with respect to a and mutual exclusion requirements; otherwise, the function supcon of the calculation controller provided in TCT is used to obtain the controller S — supcon (a, a)₁₂)。

Disclosure of Invention

The invention aims to provide a controller generation method of a multi-agent system containing mutually exclusive resources aiming at the problem of state explosion in the prior art. The method can effectively relieve the state explosion problem generated when the intelligent agent and the sub-control demand are subjected to parallel combined operation, thereby being capable of processing the actual problem in a larger scale.

The technical scheme for realizing the purpose of the invention is as follows:

a controller generation method for a multi-agent system including mutually exclusive resources, comprising the steps of:

1) defining a model: the multi-agent system consists of n single agents with sensing, calculating and executing capabilities, and the ith agent uses A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is represented by i ∈ N _n1, …, n, for any agent a_iAnd A_j，i，j∈N_nAnd i ≠ j, alphabet

Let r be_iDenotes the ith mutually exclusive resource, where i ∈ N _m1, …, m if resource r_kBy two different agents a_iAnd A_jMutually exclusive sharing, then A_iAnd A_jResource r cannot be used simultaneously_kTo r to_kCan be implemented by a finite state automaton R_kDescribing other control requirements by an automaton H, and obtaining the control requirement R of the whole system by using a supervision control theory₁，...，R_mAnd H, calculating by adopting the following process in TCT software:

1-1) calculating A ═ sync (A)₁，…，A_n)；

2-1) calculation of H' ═ sync (R)₁，…，R_m，H)；

3-1) calculating S ═ supcon (a, H);

in step 1-1), the scale of the controlled system A grows exponentially with the number n of agents, and in step 2-1), the scale of the finite state automaton H describing the global control demand also grows exponentially with the number m of sub-demands; in step 3-1), generating a global controller of the controlled system about all control requirements, and expressing the global controller by using a finite state automaton S;

2) in order to alleviate the problem of state explosion possibly generated in the step 1-1) and the step 2-1), the intelligent agent is divided into the following four different scenes for processing according to different conditions of the intelligent agent using the mutual exclusion resource:

1-2) scenario 1 uses one mutually exclusive resource for two agents: let A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Respectively represent two agents, and

let r be A₁And A₂The mutually exclusive resource used, H is a finite state automaton, alphabet, describing all other control requirements except r

And

respectively representing agents A₁And A₂Set of events, alphabet, starting to use resource r

And

respectively representing agents A₁And A₂The set of events for the resource r is released,

the process of generating the controller in scenario 1 is as follows:

1-1-2) establishing a deterministic finite state automaton (R ═ Q, Σ, δ, Q) describing the mutually exclusive control requirements of the resource R₀，Q_m) Where Q is {0, 1, 2},

q₀＝0，Q_m＝{0，1，2}；

2-1-2) order q₁∈Q₁And q is₂∈Q₂To a

If delta₁(q_1，0，σ₁)！，δ₂(q_2，0，σ₂) | A And delta₁(q_1，0，σ₁)＝q′₁，δ₂(q_2，0，σ₂)＝q′₂Then (q)₁，q₂) Is A₁And A₂For a mutex state pair of R, A is calculated according to Algorithm 2₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) All mutually exclusive state pairs for R:

and 2, algorithm: calculation of A₁And A₂Mutex status pair for R:

inputting: inputting: a. the₁，A₂，

R；

And (3) outputting: agent A₁And A₂All the exclusive state pairs of R are specifically:

1) order to

2) Order to

3)while(q₁∈Q₁)；

4)while

5)if(δ₁(q₁，σ₁) | A And delta₁(q₁，σ₁)＝q′₁)；

6)

7)end if；

8)end while；

9)end while；

10)while(q₂∈Q₂)；

11)while

12)if(δ₂(q₂，σ₂) | A And delta₂(q₂，σ₂)＝q′₂)；

13)

14)end if；

15)end while；

16)end while；

17)

3-1-2)A＝mutex(A₁，A₂，list)；

4-1-2)S＝supcon(A，H)，

Step 4-1-2) to obtain controllers S and S' ═ supcon (a)₁||A₂R H) is isostructural;

2-2) scenario 2 uses multiple mutually exclusive resources for two agents: let r₁，r₂，...，r_nAs agent A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Mutually exclusive shared resources, event sets

And

respectively represent agent a₁Starting to occupy and release resource r_iEvent set

And

respectively represent agent a₂Starting to occupy and release resource r_iLet us order

The process of generating the controller in scenario 2 is as follows:

1-2-2) establishing a description resource r_iDFA R of mutual exclusivity control requirement_i: r for automatic machine_i(i∈{1，2，…，n})＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is shown in which Q_i＝{0，1，2}，

q_i，0＝0，Q_i，m＝{0，1，2}；

2-2-2)A₁And A₂With respect to a plurality of resources r₁，r₂Control demand R of …, rn₁，R₂，...，R_nThe mutual exclusion state pair is calculated by adopting the following process:

(1) using Algorithm 2 at R₁Get list₁；

(2) Using Algorithm 2 at R₂Get list₂；

(n) at R using Algorithm 2_nGet list_n；

Exclusive status pair list₁∪list₂∪…∪list_n；

Wherein, list_iIs shown as A₁And A₂Obtaining list by using algorithm 2 about the set of the mutually exclusive state pairs of Ri_i，A₁And A₂Exclusive status list for all resources₁∪…∪list_n；

3-2-2) controller of computing system with respect to all control requirements:

if R is R ═ R₁||R₂||…||R_nAssuming that the other control requirements, other than R, are represented by the automaton H, the steps of calculating the controller are as follows:

(1)A＝mutex(A₁，A₂，list)；

(2) s is Supcon (A, H), let K be L_m((A₁||A₂) Andgate (R | | H)), under scene 2, supC (L)_m(A)∩L(H)，L(A))＝supC(K，L(A₁||A₂))；

Under scene 2, the result obtained by the technical scheme is isomorphic with a global controller obtained by directly using SCT calculation;

3-2) scenario 3 uses one mutually exclusive resource for multiple agents: let A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) For the ith agent, where i ∈ R_nAnd n is>2, for any two agents A_iAnd A_j，

And i ≠ j, and r is set as a mutually exclusive resource and an event set used by all the agents

And

respectively represent the intelligence ofEnergy body A_iStart to occupy and release resource r, order

And sigma ═ sigma₁∪...∪∑_n-∑^O-∑^RThe process of generating the controller in scene 3 is as follows:

1-3-2) establishing a finite state automaton (RR ═ Q, sigma, delta, Q) describing the mutual exclusion control requirement of a resource r₀，Q_m) Where Q is {0, 1, 2, …, n },

q₀＝0，Q_m＝{0，1，2，…，n}；

2-3-2) calculate A according to Algorithm 3₁，…，A_n-₁And A_nAll mutex status pairs for RR:

algorithm 3: calculating a mutual exclusion state pair when n agents share a mutual exclusion resource RR:

inputting: a. the₁，…，A_n，RR，

And (3) outputting: all the mutex state pairs of the n agents with respect to the RR are specifically:

inputting: a. the₁，…，A_n，RR，

And (3) outputting: all the mutex state pairs of the n agents with respect to the RR are specifically:

1)i＝1；

2)while(i≤n)；

3)

4)while(q_i∈Q_i)；

5)while

6)if(δ_i(q_i，σ_i) | A And delta_i(q_i，σ_i)＝q′_i)；

7)

8)end if；

9)end while；

10)end while；

11)i++；

12)end while；

13)j＝1；

14)while(j≤n)；

15)k＝j+1；

16)while(k≤n)；

17)while(q_i∈Q_i)；

18)while(q_k∈Q_k)；

19)list＝list∪{(q_i，q_k)}；

20)end while；

21)end while；

22)k++；

23)end while

24)i++；

25)end while；

26) Outputting a list;

wherein steps 2) to 12) are calculating agent A_iThe state of the resource r, from step 13) to step 25) is calculated, and n is set_q＝max(|Q₁|，…，|Q_nL) and n_e＝max(|∑₁|，…，|∑_n|), the computational complexity of algorithm 3 is O (max (n.n)_q.n_e，n².n_q))；

3-3-2) generating a controlled System A₁||…||A_nGlobal controller with respect to overall control requirements: calculate n (n) according to algorithm 4>2) In the case of agents sharing a resource, algorithm 4 calculates the "mutex" function that n agents use a mutually exclusive resource:

inputting: disjoint Agents A₁，A₂，…，A_nAnd a set list of mutually exclusive state pairs;

and (3) outputting: with respect to A₁||A₂||...||A_nAnd a controller for restricting list, specifically:

1) execution A_12…n＝A₁||A₂||…||A_n；

2) In A_12…nDelete the status in the list, and A_12…nAll states of the states in list can be reached along an uncontrollable path;

3)A_12…n＝AC(A_12…n)；

4) output A_12…n；

Output result A_12…nIs reachable and controllable, let A ═ A₁||…||A_nIf A is_12…nIs reachable, algorithm 4 is just the controller that calculates the controlled system a as to the control demand RR; otherwise, S ═ supcon (a, a) is used_12…n) Obtaining a controller, assuming that other control requirements than the RR are represented by the automaton H, the controller of the controlled system with respect to global control requirements is generated as follows:

(1)A＝mutex(A₁，…，A_n，list)；

(2)S＝supcon(A_12…nh), if K is equal to L_m(A | (R | | H)), then sucC (L)_m(A_12…n)∩L(H)，L(A_12…n) supC (K, l (a)); in a scene 3, the result obtained by the technical scheme is isomorphic with a global controller obtained by directly using a supervisory control theory for calculation;

4-2) scenario 4 shares multiple resources for multiple agents: let A₁，A₂，…，A_nN agents, r₁，r₂，…，r_mFor m resources, let set a ═ a₁，…，A_nR as a set { r }₁，…，r_mThe resource allocation function is defined as the mapping Φ: r → 2^A，Φ(r_i)＝A_iWherein r is_i∈r，

The problem in scenario 4 can be decomposed into m "multiple agents share a resource" sub-problems, A_iThe agent in (1) is related to the resource r_iThe mutual exclusion state pair of the intelligent agent-resource relation graph ARRD is calculated by adopting an algorithm 4, and the definition of the intelligent agent-resource relation graph ARRD is as follows:

agent resource relationship graph ARRD (a, r, Φ) is an undirected graph, where a is a set of mutually exclusive agents, r is a set of mutually exclusive resources shared by the agents in set a, Φ: r → 2^AIs a resource allocation function, phi (r)_i)＝A_iRepresenting mutually exclusive resources r_iFrom A_iIn the graphical representation of the ARRD, the agent is represented by a rectangle, the number of states and transitions of the finite state automaton representing the agent are given in parentheses below the rectangle, in an elliptic table, if phi (r)_i)＝A_iThen from r_iTo picture A_iIn this scenario, the problem is decomposed into m sub-problems in scenario 3, how to arrange the processing order of the m sub-problems is the key to the computational efficiency, and the priority problem of sub-problem processing is solved by adopting two greedy ideas:

greedy idea 1: the more states deleted in the mutex function, the smaller the scale of the finally obtained automaton;

greedy idea 2: the smaller the size of the agents, the more priority the control needs relating to these agents should be, for

With respect to mutually exclusive resources r_iAutomatic machine R for controlling demand_iCarrying out the description;

based on the ARRD and the two greedy ideas, the algorithm for generating the controller with respect to the control requirements of the agent and the mutually exclusive resource is shown as algorithm 5:

and algorithm 5: controller computation method for n agents and m mutually exclusive resources:

inputting: ARRD (A, r, phi), n agents A₁，A₂，…，A_nAnd m automata R describing mutually exclusive resources₁，R₂，…，R_m；

And (3) outputting: the controller for controlling the requirements of the intelligent agent and the mutual exclusion resource specifically comprises:

1)i＝1；R＝{R₁，R₂，…，R_m}；

2)while(i≤|R|)；

3)

4) computing list by Algorithm 2_i；

5)j＝i+1；

6)while(j≤|R|)；

7)if(Φ(r_i)＝Φ(r_j))；

8) Calculating list by Algorithm 4_j；

9)list＝list∪list_j；

10)R＝R-{R_j}；

11)end if；

12)j++；

13)end while；

14)if

15)list＝list∪list_i；

16)A_i＝Φ(r_i)；

17)A′_i＝mutex(A_i，list)；

18)A＝A-A_i；

19)A＝A∪{A_i}′；

20)end if；

21)i++；

22)end while；

23)k＝1，p＝0；

24)

25)while

26)for each R_k∈R，

27)A_k＝Φ(r_k)，

28)if

29)

30)p＝k；

31)end if；

32)end for each；

33) Calculating list_p；

34)A′_p＝muter(A_p，list_p)；

35)A＝A-A_p；

36)A＝A∪{A′_p}；

37)R＝R-{R_p}；

38)end while；

39) Output of A'_p；

Steps 2) to 22) describe that a plurality of mutually exclusive resources are shared by the same agent, and priorities related to control requirements of the resources are processed by adopting a first greedy idea; from step 23) to step 38), in accordance with the second greedy ideaThe computational complexity of Algorithm 5 is O (| R²) S for the output of Algorithm 5_rLet A be A, assuming that other control requirements are described by automaton H₁||…||A_nThe controller of the controlled system with respect to global control demand is calculated by:

S＝supcon(S_r，H)，

let K equal to L_m(A)∩L(R||H)，SupC(L_m(S_r)∩L(H)，L(S_r))＝SupC(K，L(A))；

In the technical scheme, a controller is generated for an MAS (Multi-agent System) with mutually exclusive resources by using a supervisory control theory, and in order to relieve the problem of state explosion when a plurality of intelligent agents perform parallel combination operation, a controller generation method for preferentially processing the control requirement of the mutually exclusive resources is adopted, namely, the supervisory control theory firstly processes the control requirement related to the mutually exclusive resources in a distributed manner, and then, the result obtained in the first step is taken as a controlled system; finally, a controller related to other control requirements is generated by using a supervision control theory; this can effectively alleviate the state explosion problem to can handle larger-scale actual problem.

The method can effectively relieve the state explosion problem generated when the intelligent agent and the sub-control demand are subjected to parallel combined operation, thereby being capable of processing the actual problem in a larger scale.

Drawings

FIG. 1 is a diagram of a finite state automaton R implementing the mutual exclusion control requirement of a resource R described in scenario 1 of an example;

FIG. 2 is a diagram illustrating resource r described in scenario 2 in an embodiment example_iFinite state automaton R for mutual exclusion control requirements_iA schematic diagram of (a);

FIG. 3 shows the calculation A in scenario 2 of the example₁And A₂A frame diagram of a mutually exclusive status pair of mutually exclusive resources;

FIG. 4 is a diagram illustrating a finite state automaton RR for implementing the mutually exclusive control requirement of resource r described in scenario 3 of example;

FIG. 5 shows an agent A in an embodiment_iWherein i is 1, 2;

FIG. 6 shows agent A in the embodiment₁And A₂A finite state automaton (R) diagram relating to the mutually exclusive resource control requirement;

FIG. 7 is a diagram illustrating fairness control requirement H in an example implementation;

FIG. 8 is a schematic diagram of a controller S in an embodiment;

FIG. 9 is a philosophical model P in an embodiment_iWherein i is 1, 2;

FIG. 10 is a diagram of an automaton R in an embodiment₁A schematic diagram of (a);

FIG. 11 is a diagram of an automaton R in an embodiment₂A schematic diagram of (a);

FIG. 12 is a diagram of an automaton S according to an exemplary embodiment;

FIG. 13 is a schematic diagram of an AGV system in an example implementation;

FIG. 14 is a schematic diagram of the logic model of AGVi in an embodiment, wherein i is 1, 2, 3, 4, 5, (a) is A₁(AGV1) and (b) is A₂(AGV2), (c) is A₃(AGV3), (d) is A₄(AGV4), (e) is A₅(AGV5)；

FIG. 15 is a schematic diagram of Z1SPEC in an embodiment example;

FIG. 16 is a diagram showing Z2SPEC in an embodiment example;

FIG. 17 is a schematic view of Z3SPEC in an embodiment example;

FIG. 18 is a diagram showing Z4SPEC in an embodiment example;

FIG. 19 is a diagram illustrating IPSSPEC in an example implementation;

FIG. 20 is a diagram showing WS1SPEC in an embodiment example;

FIG. 21 is a diagram showing WS2SPEC in an example of embodiment;

FIG. 22 is a schematic diagram of WS3SPEC in an example embodiment;

FIG. 23 is a diagram of ARRD1 for each AGV in an example implementation with respect to all mutually exclusive shared area control requirements;

FIG. 24 is a diagram of ARRD2 after update of ARRD1 for each AGV for all mutually exclusive shared area control requirements in an example embodiment;

FIG. 25 is a schematic diagram of ARRD3 in an example implementation;

FIG. 26 is a schematic diagram of ARRD4 in an example embodiment.

Detailed Description

The invention is further illustrated, but not limited, by the following description of the embodiments with reference to the accompanying drawings.

Implementation example:

a controller generation method for a multi-agent system including mutually exclusive resources, comprising the steps of:

1) defining a model: the multi-agent system consists of n single agents with sensing, calculating and executing capabilities, and the ith agent uses A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is represented by i ∈ N_n1, …, n, for any agent a_iAnd A_j，i，j∈N_nAnd i ≠ j, alphabet

Let r be_iDenotes the ith mutually exclusive resource, where i ∈ N _m1, …, m if resource r_kBy two different agents a_iAnd A_jMutually exclusive sharing, then A_iAnd A_jResource r cannot be used simultaneously_kTo r to_kCan be implemented by a finite state automaton R_kDescribing other control requirements by an automaton H, and obtaining the control requirement R of the whole system by using a supervision control theory₁，…，R_mAnd H, calculating by adopting the following process in TCT software:

1-1) calculating A ═ sync (A)₁，…，A_n)；

2-1) calculation of H' ═ sync (R)₁，…，R_m，H)；

3-1) calculating S ═ supcon (a, H);

in the step 1-1), the scale of the controlled system A grows exponentially along with the number n of the intelligent agents, in the step 2-1), the scale of a finite state automaton H for describing the global control requirement also grows exponentially along with the number of the sub-requirements m, and in the step 3-1), a global controller of the controlled system for all the control requirements is generated and is represented by a finite state automaton S;

2) according to different conditions of using the mutual exclusion resource by the intelligent agent, processing is respectively carried out according to the following four scenes:

1-2) scenario 1 uses one mutually exclusive resource for two agents: let A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Respectively represent two agents, and

let r be A₁And A₂The mutually exclusive resource used, H is a finite state automaton, alphabet, describing all other control requirements except r

And

respectively representing agents A₁And A₂Set of events, alphabet, starting to use resource r

And

respectively representing agents A₁And A₂The set of events for the resource r is released,

the process of generating the controller in scenario 1 is as follows:

1-1-2) establishing a deterministic finite state automaton R ═ describing the mutual exclusion control requirements of the resource R (Q, Σ, δ, Q)₀，Q_m) Where Q is {0, 1, 2},

q₀＝0， Q _m0, 1, 2, as shown in fig. 1;

2-1-2) order q₁∈Q₁And q is₂∈Q₂To a

If delta₁(q_1，0，σ₁)！，δ₂(q_2，0，σ₂) | A And delta₁(q_1，0，σ₁)＝q′₁，δ₂(q_2，0，σ₂)＝q′₂Then (q)₁，q₂) Is A₁And A₂For a mutex state pair of R, A is calculated according to Algorithm 2₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) All mutually exclusive state pairs for R:

and 2, algorithm: calculation of A₁And A₂Mutex status pair for R:

inputting: a. the₁，A₂，

R；

And (3) outputting: agent A₁And A₂All the exclusive state pairs of R are specifically:

1) order to

2) Order to

3)while(q₁∈Q₁)；

4)while

5)if(δ₁(q₁，σ₁) | A And delta₁(q₁，σ₁)＝q′₁)；

7)

7)end if；

8)end while；

9)end while；

10)while(q₂∈Q₂)；

11)while

12)if(δ₂(q₂，σ₂) | A And delta₂(q₂，σ₂)＝q′₂)；

13)

16)end if；

17)end while；

16)end while；

17)

3-1-2)A＝mutex(A₁，A₂，list)；

4-1-2)S＝supcon(A，H)，

Step 4-1-2) to obtain controllers S and S' ═ supcon (a)₁||A₂R H) is isostructural;

the controller generated by the technical scheme and the controller directly generated by the supervisory control theory are isomorphic, and the calculation A in the supervisory control theory can be relieved to a certain extent₁||A₂||R||H-generated state explosion problems, specifically:

two agents A₁And A₂As shown in FIG. 5, events i1 and i2 represent agent A, respectively_iStarting and ending the use of resources, the control requirements for mutually exclusive resources are depicted in FIG. 6; thus, in A₁||A₂The middle state (2, 2) is A₁And A₂A mutually exclusive state pair; another control requirement of the system is fairness of resource usage, i.e. "request first use", the model of the control requirement is as shown in fig. 7, and a self-loop about events 12, 22 is added to each state in fig. 7 to obtain a finite state automaton model of the control requirement, and the TCT software is used to generate the controller according to the following steps:

1)A₁₂＝mutex(A₁，A₂，[(2，2)])；

2)S＝supcon(A₁₂h), Supcon with TCT (syn (A)₁，A₂) The result of sync (R, H)), the controller S is as shown in fig. 8;

2-2) scenario 2 uses multiple mutually exclusive resources for two agents: let r₁，r₂，…，r_nAs agent A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Mutually exclusive shared resources, event sets

And

respectively represent agent a₁Start to occupy and release resources r_iEvent set

And

respectively represent agent a₂Start ofSeizing and releasing resource r_iLet us order

The process of generating the controller in scenario 2 is as follows:

1-2-2) establishing a description resource r_iFinite state automaton R for mutual exclusion control requirements_i: r for automatic machine_i(i∈{1，2，…，n})＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is shown in which Q_i＝{0，1，2}，

q_i，0＝0， Q _i，m0, 1, 2, as shown in fig. 2;

2-2-2)A₁and A₂With respect to a plurality of resources r₁，r₂，…，r_nControl demand R of₁，R₂，...，R_nThe mutual exclusion state pair of (c) is calculated by the following process, as shown in fig. 3:

(1) using Algorithm 2 at R₁Get list₁；

(2) Using Algorithm 2 at R₂Get list₂；

……

(n) at R by Algorithm 2_nGet list_n；

Exclusive status pair list ═ list₁∪list₂∪…∪list_n；

Wherein, list_iIs represented by A₁And A₂With respect to R_iThe list is obtained by using an algorithm 2_i，A₁And A₂Exclusive status list for all resources₁∪…∪list_n；

3-2-2) controller of computing system with respect to all control requirements:

if R is R ═ R₁||R₂||…||R_nAssuming that the other control requirements are represented by automaton H, in addition to R, the steps for computing the controller are as follows:

(1)A＝mutex(A₁，A₂，list)；

(2) s is Supcon (A, H), let K be L_m((A₁||A₂) Andgate (R | | H)), under scene 2, supC (L)_m(A)∩L(H)，L(A))＝supC(K，L(A₁||A₂))；

In scene 2, the result obtained by the technical scheme is isomorphic with a global controller obtained by directly using a supervisory control theory, specifically:

two philosophies in two philosophies share a dish of spaghetti, each philosophile needs two forks to eat the spaghetti, but cannot take them up at the same time, one philosophere can take up the forks in any order and put them back on the table at the same time after eating the spaghetti; the control requirement is that each fork cannot be picked up by two philosophers at the same time and there is no deadlock, the behavior of each philosopher is described as automaton P_i(i e1, 2) as shown in FIG. 9, controllable event i1 represents philosopher i to take fork 1, controllable event i3 represents philosopher i to take fork 3, and uncontrollable event i0 represents philosopher i to put two forks back on the desktop, as shown in FIGS. 10 and 11, R of FIG. 10₁And R of FIG. 11₂Describing the control demand models of fork 1 and fork 2, respectively, the philosopher dining problem can be generated into a system global controller by the following steps:

(1) calculating list { (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3) } according to algorithm 3;

(2) calculating S ═ mutex (A)₁，A₂List), the automaton S is shown in fig. 12;

3-2) scenario 3 uses one mutually exclusive resource for multiple agents: let A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is the ith agent, where i ∈ R_nAnd n is>2, for any two agents A_iAnd A_j，

And i ≠ j, providedr is a mutually exclusive resource, set of events, used by all agents

And

respectively represent agent a_iStart to occupy and release resource r, order

And sigma ═ sigma₁∪...∪∑_n-∑^O-∑^RThe process of generating the controller under scene 3 is as follows:

1-3-2) establishing a finite state automaton (RR ═ Q, sigma, delta, Q) describing the mutual exclusion control requirement of a resource r₀，Q_m) Where Q is {0, 1, 2, …, n },

q₀＝0， Q _m0, 1, 2, …, n, as shown in fig. 4;

2-3-2) calculate A according to Algorithm 3₁，…，A_n-1And A_nAll mutex status pairs for RR:

algorithm 3: calculating a mutual exclusion state pair when n agents share a mutual exclusion resource RR:

inputting: a. the₁，…，A_n，RR，

And (3) outputting: all the mutex state pairs of the n agents with respect to the RR are specifically:

1)i＝1；

2)while(i≤n)；

4)

4)while(q_i∈Q_i)；

5)while

6)if(δ_i(q_i，σ_i) ! And delta_i(q_i，σ_i)＝q′_i)；

7)

8)end if；

9)end while；

10)end while；

11)i++；

12)end while；

13)j＝1；

14)while(j≤n)；

15)k＝j+1；

16)while(k≤n)；

17)while(q_i∈Q_i)；

18)while(q_k∈Q_k)；

19)list＝list ∪{(q_i，q_k)}；

20)end while；

21)end while；

22)k++；

23)end while

24)i++；

25)end while；

26) Outputting a list;

wherein steps 2) to 12) are calculating agent A_iThe state of the resource r, from step 13) to step 25) is calculated, and n is set_q＝max(|Q₁|，…，|Q_nL) and n_e＝max(|∑₁|，…，|∑_n|), the computational complexity of algorithm 3 is O (max (n.n)_q·n_e，n².n_q))；

3-3-2) generating a controlled System A₁||…||A_nGlobal controller with respect to overall control requirements: calculate n (n) according to algorithm 4>2) In the case of agents sharing a resource, algorithm 4 calculates the "mutex" function that n agents use a mutually exclusive resource:

inputting: disjoint Agents A₁，A₂，…，A_nAnd a set list of mutually exclusive state pairs;

and (3) outputting: with respect to A₁||A₂||…||A_nAnd a controller for restricting list, specifically:

1) execution A_12…n＝A₁||A₂||…||A_n；

2) In A_12…nDelete the status in the list, and A_12…nAll states of the states in list can be reached along an uncontrollable path;

3)A_12…n＝AC(A_12…n)；

4) output A_12…n；

Output result A_12…nIs reachable and controllable, let A ═ A₁||…||A_nIf A is_12…nIs reachable, algorithm 4 is just the controller that calculates the controlled system a as to the control demand RR; otherwise, S ═ supcon (a, a) is used_12…n) Obtaining a controller, and assuming that other control requirements except RR are represented by the automaton H, generating the controller of the controlled system relative to the global control requirement according to the following steps:

(1)A＝mutex(A₁，…，A_n，list)；

(2)S＝supcon(A_12…nh), let K be L_m(A | (R | | H)), then sucC (L)_m(A_12…n)∩L(H)，L(A_12…n))＝supC(K，L(A))；

4-2) scenario 4 shares multiple resources for multiple agents: let A₁，A₂，…，A_nN agents, r₁，r₂，…，r_mFor m resources, let set A ═ A₁，…，A_nAre collectedr＝{r₁，…，r_m}. the resource allocation function is defined as the mapping Φ: r → 2^A，Φ(r_i)＝A_iWherein r is_i∈r，

The problem in scenario 4 can be decomposed into m "multiple agents share a resource" sub-problems, A_iThe agent in (1) is related to the resource r_iThe mutual exclusion state pair is calculated by adopting an algorithm 4, and the definition of an agent-resource relation graph ARRD is as follows:

agent resource relationship graph ARRD (a, r, Φ) is an undirected graph, where a is a set of mutually exclusive agents, r is a set of mutually exclusive resources shared by the agents in set a, Φ: r → 2^AIs a resource allocation function, phi (r)_i)＝A_iRepresenting mutually exclusive resources r_iFrom A_iIn the graphical representation of the ARRD, the agent is represented by a rectangle, the number of states and transitions of the finite state automata describing the agent are given in parentheses below the rectangle, the volunteers are represented by ovals, if phi (r)_i)＝A_iThen from r_iTo A_iEach agent in (1) draws a straight line, as in the example of ARRD in fig. 23, in which the problem is decomposed into m sub-problems for scenario 3, and two greedy ideas are used to solve the priority problem of sub-problem processing:

greedy idea 1: the more states deleted in the mutex function, the smaller the scale of the obtained automaton;

greedy idea 2: the combined size of the agents should be as small as possible, and the smaller the size of the agents, the more control needs relating to these agents should be handled with priority, for

With respect to mutually exclusive resources r_iControl demand automaton R_iThe description is that:

based on the ARRD and the two greedy ideas, the algorithm for generating the controller with respect to the control requirements of the agent and the mutually exclusive resource is shown as algorithm 5:

and algorithm 5: controller computation method for n agents and m mutually exclusive resources:

inputting: ARRD (A, r, phi), n agents A₁，A₂，…，A_nAnd m automata R describing mutually exclusive resources₁，R₂，…，R_m；

And (3) outputting: the controller for controlling the requirements of the intelligent agent and the mutual exclusion resource specifically comprises:

1)i＝1；R＝{R₁，R₂，…，R_m}；

2)while(i≤|R|)；

3)

4) computing list by Algorithm 2_i；

5)j＝i+1；

6)while(j≤|R|)；

7)if(Φ(r_i)＝Φ(r_j))；

8) Calculating list by Algorithm 4_j；

9)list＝list∪list_j；

10)R＝R-{R_j}；

11)end if；

12)j++；

13)end while；

14)if

15)list＝list∪list_i；

16)A_i＝Φ(r_i)；

17)A′_i＝mutex(A_i，list)；

18)A＝A-A_i；

19)A＝A∪{A_i}′；

20)end if；

21)i++：

22)end while；

23)k＝1，p＝0；

24)

25)while

26)for each R_k∈R，

27)A_k＝Φ(r_k)，

28)if

29)

30)p＝k；

31)end if；

32)end for each；

33) Calculating list_p；

34)A′_p＝muter(A_p，list_p)；

35)A＝A-A_p；

36)A＝A∪{A′_p}；

37)R＝R-{R_p}；

38)end while；

39) Output of A'_p；

Wherein, steps 2) to 22) describe that a plurality of mutually exclusive resources are shared by the same agent, and a first greedy idea is adopted to process the priority of the control requirements of the resources; from step 23) to step 38), the priority of the relevant control requirements is processed according to the second greedy idea, and the computational complexity of the algorithm 5 is O (| R |²) S for the output of Algorithm 5_rShow, assume other controlsThe demand is described by an automaton H, and A is equal to A₁||…||A_nThe controller of the controlled system with respect to global control demand is calculated by:

S＝supcon(S_r，H)，

let K equal to L_m(A)∩L(R||H)，SupC(L_m(S_r)∩L(H)，L(S_r))＝SupC(K，L(A))。

Specifically, the method comprises the following steps:

1) automatic Guided Vehicle (AGV): a plurality of AGVs run on a fixed route to load or unload parts, and an abstract working scenario is shown in fig. 13; in the distributed supervision control of the AGV, the generated control logics of the sub-controllers conflict, so that a coordinator needs to be designed to solve the conflict; according to the method, the global controller of the whole controlled system can be generated without generating any coordinator; the system in fig. 13 consists of five AGVs (AGV1, AGV2, AGV3, AGV4 and AGV5), three workstations (WS1, WS2 and WS3), two loading stations (IPS1 and IPS2) for type I and type II components, and one station CPS for unloading finished products, the AGVs transporting the components on a fixed circular path in which there are four mutually exclusive shared areas: AGVl and AGV2 share Zone 1; AGV2 and AGV3 share Zone 2; AGV2 and AGV4 share Zone 3; AGV4 and AGV5 share Zone 4; the endless transport route of the AGV is as follows:

arrows → and

representing the direction of travel of the AGV when loading and unloading parts, respectively, the sequence of processing for the two types of input parts is as follows:

IPS1→AGV1→WS2→AGV3→WS1；

IPS2→AGV2→WS3→AGV4→WS1，

type I and type II parts are assembled into a complete product in WS1, the AGV5 transports the assembled product from WS1 to CPS, and an automaton model describing the behavior of AGVi uses A_i(i ═ 1, 2, 3, 4, 5), as shown in fig. 14, the event representations of the automaton model were even for uncontrollable events and odd for controllable events, and the physical meanings of the events in the model shown in fig. 14 are listed in table 1:

table 1: physical significance of events in AGV model

2) Description of the control requirements: for safety reasons, Zone1, Zone2, Zone3 and Zone4 cannot be occupied simultaneously by two AGVs simultaneously, all events are contained in the alphabet Σ, the control requirements of mutually exclusive and common work areas IPS1 and IPS2 are as follows:

z1 SPEC: for Zone1, the AGV1 and AGV2 cannot enter the Zone1 together,

z2 SPEC: for Zone2, the AGV2 and AGV3 cannot enter the Zone2 together,

z3 SPEC: for Zone3, the AGV2 and AGV4 cannot enter the Zone3 together,

z4 SPEC: for Zone4, the AGV4 and AGV5 cannot enter the Zone4 together,

IPSPEC: AGVs 1 and AGVs 2 cannot simultaneously enter the common work area of IPS1 and IPS2,

is ∑'₁The robot model of Z1SPEC is shown in fig. 15, and Σ — {10, 11, 12, 13, 20, 22, 23, 24}, and Σ 'is omitted from all states in fig. 15 for simplicity'₁Self-loopa of (1);

is ∑'₂An automaton model of Z2SPEC is shown in fig. 16, and Σ - {18, 20, 24, 26, 31, 32, 33, 34}, and Σ 'is omitted from all states in fig. 16 for simplicity'₂Self-loopa of (1);

is ∑'₃The machine model for Z3SPEC is shown in fig. 17, with sigma- (18, 21, 26, 28, 40, 41, 44, 46), and for simplicity, sigma 'is omitted from all states in fig. 17'₃Self-loopa of (1);

is ∑'₄The robot model of Z4SPEC is shown in fig. 18, and Σ - {40, 42, 43, 44, 50, 51, 52, 53}, and Σ 'is omitted from all states in fig. 18 for simplicity'₄Self-circulation;

is sigma'₅The machine model of IPSSPEC is shown in fig. 19, and for simplicity, the machine model for Σ — 10, 13, 22, 23 is omitted from fig. 19 for all states'₁Self-loopa of (1);

other control requirements besides the mutually exclusive shared region are described below:

WS1 SPEC: type I and type II parts are assembled into a complete product in the workstation WS1, the workstation WS1 can only accommodate one of the two types, which can be shipped to the WS1 in any order, before shipping the entire product to the CPS;

WS2 SPEC: the AGV1 transports a type I part to the workstation WS2, and the AGV3 unloads a type I part from the WS2, the station accommodating only one part at a time;

WS3 SPEC: AGVs 2 transport type II parts to the workstation WS3, AGVs 4 unload type II parts to WS3, which can only accommodate one part at a time;

is ∑'₆The automaton model for WS1SPEC is shown in fig. 20, and for simplicity, the model for Σ ″, which is omitted from all states in fig. 20'₆Self-loopa of (1);

is ∑'₇The automaton model for WS2SPEC is shown in fig. 21, and for simplicity, the model for Σ ″ 'is omitted in all states in fig. 21'₇Self-loopa of (1);

is ∑'₈The automaton model for WS3SPEC is shown in fig. 22, and for simplicity, # is omitted from all states in fig. 22'₈Self-loopa of (1);

3) the controller is generated by adopting the method of the embodiment: ARRD for each AGV for all mutually exclusive shared area control requirements is shown in FIG. 23; according to algorithm 5, Z1SPEC and IPSPEC involving AGV1 and AGV2 are processed first, A for clarity₁，A₂The connection between Z1SPEC and IPSPEC is plotted using a dashed line in FIG. 23; for Z1SPEC, A₁And A₂The mutually exclusive state pairs of (1, 3), (3, 3), (1, 5); for IPSPEC, A₁And A₂Is (2, 4), thus, a list is obtained₁＝{(1，3)，(3，3)，(1，5)，(2，4)}，A₁₂Z₁IP＝mutex(A₁，A₂，list₁) (17, 26); the state of the automaton and the number of transitions are marked in parentheses after the equation, the same notation is used below, and then A is₁，A₂Z1SPEC and IPSPEC are deleted and A is deleted₁₂Z₁IP is added to ARRD1, and the updated ARRD is shown in FIG. 24, A₄And A₅The number of states of the synchronization product is less than A₃And A₁₂Z₁IP synchronous product, A₄And A₁₂Z₁The number of states of the automaton obtained by the IP Sync product, therefore, the second step should be done with priority to the Z4SPEC, A₄And A₅The mutually exclusive state pairs for Z4SPEC are (2, 1), (2, 3), (4, 1), (4, 3),

A₄₅Z₄＝mutex(A₄，A₅，{(2，1)，(2，3)，(4，1)，(4，3)})(18，26)；

after this step, A in ARRD2 is added₄，A₅And Z4SPEC is deleted and A is removed₄₅Z₄Added to ARRD2 to give ARRD3, shown in fig. 25, and the third step is to process the Z2SPEC related to AGVs 2 and AGVs 3 by algorithm 5; for Z2SPEC, automaton A₁₂Z₁IP and A₃In the set list₂Of { (4, 1), (4, 3), (9, 1), (9, 3), (10, 1), (10, 3), (12, 1), (12, 3), (14, 1), (14, 3) },

A₁₂₃Z₁₂IP＝mutex(A₁₂Z₁IP，A₃，list₂)(54，118).

deletion of A in ARRD3₁₂Z₁IP，A₃And Z2SPEC, and adding A₁₂₃Z₁₂IP, ARRD4 Final processing Z3SPEC, A relating to AGV2 and AGV4 is shown in FIG. 26₁₂₃Z₁₂IP and A₄₅Z₄Is contained in list₃＝{(2，1)，(2，6)，(2，11)，(2，13)，(2，16)，(2，17)，(12，1)，(12，6)，(12，11)，(12，13)，(12，16)，(12，17)，(30，1)，(30，6)，(30，11)，(30，13)，(30，16)，(30，17)，(34，1)，(34，6)，(34，11)，(34，13)，(34，16)，(34，17)，(35，1)，(35，6)，(35，11)，(35，13)，(35，16)，(35，17)，(38，1)，(38，6)，(38，11)，(38，13)，(38，16)，(38，17)，(39，1)，(39，6)，(39，11)，(39，13)，(39，16)，(39，17)，(4l，1)，(41，6)，(41，11)，(41，13)，(41，16)，(41，17)，(42，1)，(42，6)，(42，11)，(42，13)，(42，16)，(42，17)，(43，1)，(43，6)，(43，11)，(43，13)，(43，16)，(43，17)，(45，1)，(45，6)，(45，11)，(45，13)，(45，16)，(45，17)，(46，1)，(46，6)，(46，11)，(46，13)，(46，16)，(46，17)，(47，1)，(47，6)，(47，11)，(47，13)，(47，16)，(47，17)，(49，1)，(49，6)，(49，11)，(49，13)，(49，16)，(49，17)，(50，1)，(50，6)，(50，11)，(50，13)，(50，16)，(50，17)，(51，1)，(51，6) Of (51, 11), (51, 13), (51, 16), (51, 17), (52, 1), (52, 6), (52, 11), (52, 13), (52, 16), (52, 17), (53, 1), (53, 6), (53, 11), (53, 13), (53, 16), (53, 17) },

A₁₂₃₄₅2₁₂₃₄IP＝mutex(A₁₂₃2₁₂IP，A₄₅2₄，list₃)(748，2504).

after handling the control demand of the mutually exclusive shared resource, the other control demands WS1SPEC, WS2SPEC and WS3SPEC are subsequently handled,

WSPEC＝sync(WS1SPEC，WS2SPEC，WS3SPEC)(16，356)；

S₁＝supcon(A₁₂₃₄₅Z₁₂₃₄IP，WSPEC)(4406，11338).

automatic machine S₁Is the controller of the controlled system for global control requirements generated by this example;

4) by using a supervisory control theory, a global controller of the whole system about control requirements can be obtained, and the calculation can be carried out in TCT software through the following steps:

A＝sync(A₁，A₂，A₃，A₄，A₅)(3072，15360)；

SPEC＝sync(Z1SPEC，Z2SPEC，Z3SPEC，Z4SPEC，IPSPEC，WSlSPEC，WS2SPEC，WS3SPEC)(3888，20196).

S₂＝supcon(A，SPEC)(4406，11338).

automatic machine S₂The controller is calculated by a supervisory control theory global controller and is used for controlling the global control requirement of the controlled system;

5) the results obtained by the two methods were compared: the results generated by the method and the global controller are tested by TCT, and the automaton S₁And S₂Is isomorphic, and the automaton S obtained by the method of the embodiment₁Is a controller of the controlled system for the global control requirement, table 2 lists the sizes of the automata involved in the two methods, and the conclusion can be drawn from the data in table 2: the automaton adopting the method of the embodiment has a much smaller scale than the automaton generated during the calculation of the global controllerScale:

table 2: comparison of results of the two methods

Claims (1)

1. A controller generation method for a multi-agent system including mutually exclusive resources, comprising the steps of:

1) defining a model: the multi-agent system consists of n single agents with sensing, calculating and executing capabilities, and the ith agent uses A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is represented by i ∈ N_n1, …, n, for any agent a_iAnd A_j，i，j∈N_nAnd i ≠ j, alphabet

Let r be_iDenotes the ith mutually exclusive resource, where i ∈ N_m1, …, m if resource r_kBy two different agents a_iAnd A_jMutually exclusive sharing, then A_iAnd A_jResource r cannot be used simultaneously_kTo r_kCan be implemented by a finite state automaton R_kDescribing other control requirements by an automaton H, and obtaining the control requirement R of the whole system by using a supervision control theory₁，...，R_mAnd H, calculating by adopting the following process in TCT software:

1-1) calculating a ═ sync { a ═ sync }₁，…，A_n)；

2-1) calculating H' ═ sync { R₁，…，R_m，H)；

3-1) calculating S ═ supcon (a, H);

in step 1-1), the scale of the controlled system a grows exponentially with the number n of agents; in step 2-1), generating a global controller of the controlled system about all control requirements, and expressing the global controller by using the finite state automata S;

2) according to different conditions of using the mutual exclusion resource by the intelligent agent, processing is respectively carried out according to the following four scenes:

1-2) scenario 1 uses one mutually exclusive resource for two agents: let A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Respectively represent two agents, and

let r be A₁And A₂The mutually exclusive resource used, H is a finite state automaton, alphabet, describing all other control requirements except r

And

respectively representing agents A₁And A₂Set of events, alphabet, starting to use resource r

And

respectively representing agents A₁And A₂The set of events for the resource r is released,

the process of generating the controller in scenario 1 is as follows:

1-1-2) establishing a deterministic finite state automaton (R ═ Q, Σ, δ, Q) describing the mutually exclusive control requirements of the resource R₀，Q_m) Where Q is {0, 1, 2},

q₀＝0，Q_m＝{0，1，2}；

2-1-2) order q₁∈Q₁And q is₂∈Q₂To for

If delta₁(q_1，0，σ₁)！，δ₂(q_2，0，σ₂) | A And delta₁(q_1，0，σ₁)＝q′₁，δ₂(q_2，0，σ₂)＝q′₂Then (q)₁，q₂) Is A₁And A₂For a mutex state pair of R, A is calculated according to Algorithm 2₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) All mutually exclusive state pairs for R:

and 2, algorithm: calculation of A₁And A₂Mutex status pair for R:

inputting: a. the₁，A₂，

R；

And (3) outputting: agent A₁And A₂All the exclusive state pairs of R are specifically:

1) order to

2) Order to

3)while(q₁∈Q₁)；

4)

5)if(δ₁(q₁，σ₁) | A And delta₁(q₁，σ₁)＝q′₁)；

6)

7)end if；

8)end while；

9)end while；

10)while(q₂∈Q₂)；

11)

12)if(δ₂(q₂，σ₂) | A And delta₂(q₂，σ₂)＝q′₂)；

13)

14)end if；

15)end while；

16)end while；

17)

And is

3-1-2)A＝mutex(A₁，A₂，list)；

4-1-2)S＝supcon(A，H)，

Step 4-1-2) to obtain controllers S and S' ═ supcon (a)₁||A₂R H) is isostructural;

2-2) scenario 2 uses multiple mutually exclusive resources for two agents: let r₁，r₂，…，r_nAs agent A₁＝(Q₁，∑₁，δ₁，q_1，0，Q_1，m) And A₂＝(Q₂，∑₂，δ₂，q_2，0，Q_2，m) Mutually exclusive shared resources, event sets

And

respectively represent agent a₁Starting to occupy and release resource r_iEvent set

And

respectively represent agent a₂Start to occupy and release resources r_iLet us order

The process of generating the controller in scenario 2 is as follows:

1-2-2) establishing a description resource r_iFinite state automaton R for mutual exclusion control requirements_i: r for automatic machine_i(i∈{1，2，…，n})＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is shown in which Q_i＝{0，1，2}，

q_i，0＝0，Q_i，m＝{0，1，2}；

2-2-2)A₁And A₂With respect to a plurality of resources r₁，r₂，…，r_nControl demand R of₁，R₂，...，R_nThe mutual exclusion state pair is calculated by adopting the following process:

(1) using Algorithm 2 at R₁Get list₁；

(2) Using Algorithm 2 at R₂Get list₂；

……

(n) at R by Algorithm 2_nGet list_n；

Exclusive status pair list ═ list₁∪list₂∪…∪list_n；

Wherein, list_iIs represented by A₁And A₂With respect to R_iThe list is obtained by using an algorithm 2_i，A₁And A₂Exclusive status list for all resources₁∪…∪list_n；

3-2-2) controller of computing system with respect to all control requirements:

if R is R ═ R₁||R₂||…||R_nAssuming that the other control requirements, other than R, are represented by the automaton H, the steps of calculating the controller are as follows:

(1)A＝mutex(A₁，A₂，list)；

(2) s is Supcon (A, H), let K be L_m((A₁||A₂) Andgate (R | | H)), under scene 2, supC (L)_m(A)∩L(H)，L(A))＝supC(K，L(A₁||A₂))；

3-2) scenario 3 uses one mutually exclusive resource for multiple agents: let A_i＝(Q_i，∑_i，δ_i，q_i，0，Q_i，m) Is the ith agent, where i ∈ R_nAnd n > 2, for any two agents A_iAnd A_j，

And i ≠ j, and r is set as a mutually exclusive resource and an event set used by all the agents

And

respectively represent agent a_iBegin to occupy and release resource r, order

And sigma' ═ sigma₁∪...∪∑_n-∑^O-∑^RThe process of generating the controller in scene 3 is as follows:

1-3-2) establishing a finite state automaton (RR ═ Q, sigma, delta, Q) describing the mutual exclusion control requirement of a resource r₀，Q_m) Where Q is {0, 1, 2, …, n },

q₀＝0，Q_m＝{0，1，2，…，n}；

2-3-2) calculate A according to Algorithm 3₁，…，A_n-1And A_nAll mutex status pairs for RR:

algorithm 3: calculating a mutual exclusion state pair when n agents share a mutual exclusion resource RR:

inputting: a. the₁，…，A_n，RR，

…，

And (3) outputting: all the mutex state pairs of the n agents with respect to the RR are specifically:

1)i＝1；

2)while(i≤n)；

3)

4)while(q_i∈Q_i)；

5)

6)if(δ_i(q_i，σ_i) | A And delta_i(q_i，σ_i)＝q′_i)；

7)

8)end if；

9)end while；

10)end while；

11)i++；

12)end while；

13)j＝1；

14)while(j≤n)；

15)k＝j+1：

16)while(k≤n)；

17)while(q_i∈Q_i)；

18)while(q_k∈Q_k)；

19)list＝list∪{(q_i，q_k)}；

20)end while；

21)end while；

22)k++；

23)end while

24)i++；

25)endwhile；

26) Outputting a list;

wherein steps 2) to 12) are calculating agent A_iThe state of use of resource r, step 13) to step 25)Setting n for mutual exclusion state pair of each agent_q＝max(|Q₁|，…，|Q_nI) and n_e＝max(|∑₁|，…，|∑_n|), the computational complexity of algorithm 3 is O (max (n.n)_q.n_e，n².n_q))；

3-3-2) generating a controlled System A₁||…||A_nGlobal controller with respect to overall control requirements: according to the algorithm 4, the condition that n (n is more than 2) agents share one resource is calculated, and the algorithm 4 calculates a 'mutex' function of the n agents using one mutually exclusive resource:

inputting: disjoint Agents A₁，A₂，…，A_nAnd a set list of mutually exclusive state pairs;

and (3) outputting: with respect to A₁||A₂||...||A_nAnd a controller for restricting list, specifically:

1) execution A_12…n＝A₁||A₂||…||A_n；

2) At A_12…nDelete the status in the list, and A_12…nAll states of the states in list can be reached along an uncontrollable path;

3)A_12…n＝AC(A_12…n)；

4) output A_12…n；

Output result A_12…nIs reachable and controllable, let A ═ A₁||…||A_nIf A is_12…nIs reachable, algorithm 4 is just the controller that calculates the controlled system a as to the control demand RR; otherwise, S ═ supcon (a, a) is used_12…n) Obtaining a controller, assuming that other control requirements than the RR are represented by the automaton H, the controller of the controlled system with respect to global control requirements is generated as follows:

(1)A＝mutex(A₁，…，A_n，list)；

(2)S＝supcon(A_12…nh), if K is equal to L_m(A | (R | | H)), then sucC (L)_m(A_12…n)∩L(H)，L(A_12…n))＝supC(K，L(A))；

4-2) Scenario 4 shares multiple resources for multiple agents: let A₁，A₂，…，A_nN agents, r₁，r₂，…，r_mFor m resources, let set a ═ a₁，…，A_nR as a set { r }₁，…，r_mThe resource allocation function is defined as the mapping Φ: r → 2^A，Φ(r_i)＝A_iWherein r is_i∈r，

The problem in scenario 4 can be decomposed into m "multiple agents share a resource" sub-problems, A_iThe agent in (1) is related to the resource r_iThe mutual exclusion state pair of the intelligent agent-resource relation graph ARRD is calculated by adopting an algorithm 4, and the definition of the intelligent agent-resource relation graph ARRD is as follows:

agent resource relationship graph ARRD (a, r, Φ) is an undirected graph, where a is a set of mutually exclusive agents, r is a set of mutually exclusive resources shared by the agents in set a, Φ: r → 2^AIs a resource allocation function, phi (r)_i)＝A_iRepresenting mutually exclusive resources r_iFrom A_iIn the graphical representation of the ARRD, the agent is represented by a rectangle, the number of states and transitions of the finite state automata describing the agent are given in parentheses below the rectangle, the resource is represented by an ellipse, if phi (r)_i)＝A_iThen from r_iTo A_iEach agent in (1) draws a straight line, in this scenario, the problem is decomposed into m scenario 3 sub-problems, and two greedy ideas are used to solve the priority problem of sub-problem processing:

greedy idea 1: the more states deleted in the mutex function, the smaller the scale of the finally obtained automaton;

greedy idea 2: the smaller the size of the agents, the more priority the control requirements relating to these agents are to be handled, for

With respect to mutually exclusive resources r_iAutomatic machine R for controlling demand_iThe description is carried out;

based on the ARRD and the two greedy ideas, the algorithm for generating the controller with respect to the control requirements of the agent and the mutually exclusive resource is shown as algorithm 5:

and algorithm 5: controller computation method for n agents and m mutually exclusive resources:

inputting: ARRD (A, r, phi), n agents A₁，A₂，…，A_nAnd m automata R describing mutually exclusive resources₁，R₂，…，R_m；

And (3) outputting: the controller related to the requirements of controlling the intelligent agent and the mutual exclusion resource specifically comprises the following components:

1)i＝1；R＝{R₁，R₂，…，R_m}；

2)while(i≤|R|)；

3)

4) computing list by Algorithm 2_i；

5)j＝i+1；

6)while(j≤|R|)；

7)if(Φ(r_i)＝Φ(r_j))；

8) Calculating list by Algorithm 4_j；

9)list＝list∪list_j；

10)R＝R-{R_j}；

11)end if；

12)j++；

13)end while；

14)

15)list＝list∪list_i；

16)A_i＝Φ(r_i)；

17)A′_i＝mutex(A_i，list)；

18)A＝A-A_i；

19)A＝A∪{A_i}′；

20)end if；

21)i++；

22)end while；

23)k＝1，p＝0；

24)l_min＝+∞；

25)

26)for each R_k∈R；

27)

28)if(l_min＞l)；

29)l_min＝l；

30)p＝k；

31)endif；

32)end while；

33) Calculating list_p；

34)A′_p＝muter(A_p，list_p)；

35)A＝A-A_p；

36)A＝A∪{A′_p}；

37)R＝R-{R_p}；

38)end while；

39) Output of A'_p；

Wherein, steps 2) to 22) describe that a plurality of mutually exclusive resources are shared by the same agent, and a first greedy idea is adopted to process the priority of the control requirements of the resources; from step 23) to step 38), the priority of the relevant control requirements is processed according to the second greedy idea, and the computational complexity of the algorithm 5 is O (| R |²) The output of algorithm 5 is S_rIt is shown that assuming that the other control requirements are described by automaton H, let a be a₁||…||A_nThe controller of the controlled system with respect to global control demand is calculated by:

S＝supcon(S_r，H)，

let K equal to L_m(A)∩L(R||H)，SupC(L_m(S_r)∩L(H)，L(Sr))＝SupC(K，L(A))。

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