CN114760101A - Product and supply chain cooperative evolution system compensation method and system under network attack - Google Patents

Product and supply chain cooperative evolution system compensation method and system under network attack Download PDF

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CN114760101A
CN114760101A CN202210271701.3A CN202210271701A CN114760101A CN 114760101 A CN114760101 A CN 114760101A CN 202210271701 A CN202210271701 A CN 202210271701A CN 114760101 A CN114760101 A CN 114760101A
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李庆奎
高雪峰
易军凯
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Beijing Information Science and Technology University
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Abstract

The invention relates to a product and supply chain collaborative evolution system compensation method and system under network attack, aiming at the problem that a data packet of a distributed information physical system is lost under network attack, firstly, a prediction model based on a recurrent neural network is designed by utilizing historical data of each subchain, and the current inventory state data of the subchain is predicted by utilizing the prediction model so as to make up for the inventory data loss caused by network attack; secondly, the consistency problem of the product and supply chain collaborative evolution system after the change and the change under uncertain market demands is solved by using the thought of the zero sum game; and finally, calculating a game solution to determine the optimal productivity and uncertain market demand. The method can ensure that the product and the supply chain cooperative evolution system reach the leader following H infinity consistency under the condition that the design of the system is changed due to DoS attack, and inhibit the ox penis effect brought by uncertain requirements and design change.

Description

Product and supply chain cooperative evolution system compensation method and system under network attack
Technical Field
The present invention relates to the field of product and supply chain systems, and in particular, to a product and supply chain cooperative evolution system compensation method and system under network attack.
Background
The product and supply chain collaborative evolution System is a distributed Network Control System (NCS) which is composed of various node enterprises such as suppliers, manufacturers, distributors and retailers serving for product production design and circulation, and realizes the production of raw materials into products and delivers the products to users by controlling information flow, logistics and fund flow. With the rapid development of artificial intelligence technology, manufacturing is gradually changing from manufacturing automation to collaborative intelligent manufacturing. As a support of major projects of national intelligent manufacturing, the product and supply chain collaborative evolution system has wide application prospects in the fields of power supply, intelligent manufacturing, biological medicine, food processing and the like.
The traditional product and supply chain collaborative evolution system is mainly used for meeting production requirements, a dedicated channel is adopted for data transmission, the problems that logistics is slow, information transmission is not timely, customized production cannot be realized, warehouse storage and warehousing are caused by inaccurate production rate design and the like generally occur in the operation process, and the resource utilization rate is extremely low. Thanks to the rapid development of big data technology and artificial intelligence technology, the product and supply chain collaborative evolution system starts to be digitalized, intelligentized and organized, and becomes a cyber-physical system (CPS) integrating data drive, comprehensive computation and network communication. Based on the cyber-physical system and the multi-agent technology, the product and supply chain collaborative evolution system can realize customized production guided by user requirements, and simultaneously monitor the production process in real time and carry out intelligent warehousing, thereby greatly reducing the phenomenon of excessive commodity inventory, simplifying the production flow and improving the operating benefits of enterprises.
The product based on the cyber-physical system and the supply chain collaborative evolution system provide great convenience for the production and the sale of complex products with the advantages of reliability, high efficiency and real-time collaboration, but the cyber-physical system is more vulnerable to malicious network attacks due to the introduction of a large number of network devices. In recent years, network attack events are frequent, and serious economic losses are caused to enterprises. The product and supply chain collaborative evolution system has become a main target of network attack, and frequent network attacks can cause node enterprises in the product and supply chain collaborative evolution system to suffer serious economic loss and even harm social stability and national development. Therefore, how to improve the emergency capacity and stability of the product and the supply chain collaborative evolution system under the sudden network attack event has important practical significance.
Disclosure of Invention
The invention aims to provide a method and a system for compensating change of a product and supply chain collaborative evolution system under network attack, which solve the problem of system emergency change control under the network attack situation.
In order to achieve the purpose, the invention provides the following scheme:
a product and supply chain cooperative evolution system compensation method under network attack comprises the following steps:
Obtaining historical inventory state data of each sub-chain in a product and supply chain collaborative evolution system, wherein the historical inventory state data comprises the historical inventory state data of the sub-chain before being attacked by a network and the historical inventory state data of the sub-chain after being attacked by the network;
training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the subchain subjected to the network attack as input and taking the historical inventory state data of the subchain subjected to the network attack as a label to obtain a trained prediction model;
for each sub-chain, inputting the latest inventory state data of the sub-chain, which is obtained after the sub-chain is subjected to network attack, into the trained prediction model, and predicting the current inventory state data of the sub-chain;
obtaining a local neighborhood inventory tracking error of the sub-chain according to the current inventory state data of the sub-chain;
according to the performance index function of the sub-chain, the minimum local neighborhood inventory tracking error of the sub-chain is taken as a target, and the optimal productivity and uncertain market requirements of the sub-chain are designed by utilizing a zero sum game method; the performance indicator function is a function of the local neighborhood inventory tracking error, the production rate, and the uncertain demand for the child chain.
The invention also provides a product and supply chain cooperative evolution system compensation system under network attack, which comprises:
the system comprises a historical inventory state data acquisition module, a supply chain cooperative evolution system and a database management module, wherein the historical inventory state data acquisition module is used for acquiring historical inventory state data of each sub-chain in the product and supply chain cooperative evolution system, and the historical inventory state data comprises the historical inventory state data of the sub-chain before being subjected to network attack and the historical inventory state data of the sub-chain after being subjected to network attack;
the model training module is used for training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the subchain subjected to the network attack as input and taking the historical inventory state data of the subchain before the network attack as a label to obtain a trained prediction model;
the prediction module is used for inputting the latest inventory state data of the sub-chains, which are obtained after the sub-chains are subjected to network attack, into the trained prediction model aiming at each sub-chain, and predicting the current inventory state data of the sub-chains;
the partial neighborhood inventory tracking error calculation module of the sub chain is used for obtaining the partial neighborhood inventory tracking error of the sub chain according to the current inventory state data of the sub chain;
the optimal productivity and uncertain market demand calculation module is used for designing the optimal productivity and uncertain market demand of the sub-chain by using a zero sum game method according to the performance index function of the sub-chain and taking the minimum local neighborhood inventory tracking error of the sub-chain as a target; the performance indicator function is a function of the local neighborhood inventory tracking error, the production rate, and the uncertain demand for the child chain.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
aiming at the problem of data packet loss of a distributed information physical system under network attack, the product and supply chain collaborative evolution system compensation method and system provided by the invention firstly utilize historical data of each subchain to design a prediction model based on a recurrent neural network, and utilize the prediction model to predict the current inventory state data of the subchain so as to make up for the inventory data loss caused by network attack; secondly, the consistency problem of the product and supply chain collaborative evolution system after the change and the change under uncertain market demands is solved by using the thought of the zero sum game; and finally, calculating a game solution to determine the optimal productivity and uncertain market demand. The method can ensure that the product and the supply chain cooperative evolution system reach the leader following H infinity consistency under the condition that the design of the system is changed due to DoS attack, and inhibit the ox penis effect brought by uncertain requirements and design change.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a schematic diagram of a change mechanism under network attack according to the present invention;
fig. 2 is a flowchart of a compensation method for a product and supply chain cooperative evolution system under network attack according to embodiment 1 of the present invention;
fig. 3 is a topological relation diagram of a product and a supply chain cooperative evolution system according to embodiment 1 of the present invention;
fig. 4 is a schematic diagram of a packet loss situation of an S-C channel according to embodiment 1 of the present invention;
fig. 5 is a first device inventory prediction diagram provided in embodiment 1 of the present invention;
fig. 6 is a diagram for predicting inventory of a second device according to embodiment 1 of the present invention;
fig. 7 is a graph illustrating a change in the stock state of the first device before and after the change according to embodiment 1 of the present invention;
fig. 8 is a graph showing a change in the stock state of the second device before and after the change according to embodiment 1 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for compensating change of a product and supply chain collaborative evolution system under network attack, and solve the problem of emergency change control of the system under the network attack situation.
For a class of security issues of product and supply chain cooperative evolution systems caused by DoS attacks, researchers have performed a great deal of effective work, which mainly includes: (1) researching the optimal DoS attack moment from the perspective of an attacker; (2) researching an effective control strategy from the aspect of defenders; (3) the method is based on a game theory method for researching the confrontation relationship between a defender and a denial of service attacker. Although CPS-based security control problem research has achieved abundant results, DoS attack defense strategy research is still insufficient in a product and supply chain collaborative evolution system based on distributed CPS and with unknown models. A product based on DoS attack and a supply chain cooperative evolution system emergency change defense strategy is a main contribution of the technology.
As an important distributed CPS, a large number of unmodeled dynamic, uncertain and severe demand fluctuations and sudden network events exist in a product and supply chain cooperative evolution system, so that the structure and parameters of the system are easy to change, and product design change is an important means for maintaining the stability of the product and supply chain cooperative evolution system, meeting user demands and ensuring economic benefits. Such as system design changes that may result from network attacks. The design of an emergency change compensation mechanism by using a data-driven technology to solve the problem of product and supply chain system change control under DoS attack is another important contribution of the technology.
A product and supply chain collaborative evolution system is taken as a complex distributed information physical system (CPS), which contains a large amount of unmodeled dynamics, uncertainty, severe demand fluctuation and sudden network events, so that structural parameters of the system are easy to change, and product design change is an important means for maintaining the stability of the system, meeting user demands and ensuring economic benefits. The technology solves the problem of emergency change control of the PSCSES based on the distributed CPS under the DoS attack of the Denial-of-Service (DOS). Firstly, aiming at the problem that data packets are lost under network attack in PSCSES, a predictor based on a Recurrent Neural Network (RNN) is designed by utilizing historical data of each subchain to make up for the loss of inventory data caused by the network attack; secondly, converting the H infinity consistency control problem into a multi-person zero-sum graph game problem by utilizing the game theory idea, and providing an emergency change compensation mechanism; and then a controller online solving algorithm under the condition that a model is unknown is designed based on a Q-learning method of strategy iteration, and H-infinity consistency of the inventory state of the system is realized.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
In order to make the technical scheme of the present invention clearer, a detailed description will now be given of a generation process of the problems to be solved by the present invention.
The product and supply chain collaborative evolution system based on the invention is a distributed information physical system with unknown model. Considering that a supply chain for configuring a certain product production is composed of N sub-chains and is produced cooperatively, the kinetic equation of the ith sub-chain is assumed to be
Figure BDA0003553633910000051
Wherein x isi(t),ui(t),
Figure BDA0003553633910000052
And yi(t) production inventory status, production rate, customer demand and current product output in the ith sub-chain, respectively. From the viewpoint of control theory, xi(t),ui(t),
Figure BDA0003553633910000053
And yiAnd (t) respectively representing the state variables of the ith subchain at the moment t, control input, external disturbance and system output.
Figure BDA0003553633910000054
Is xi(t) derivative of (t). A, B and D are system matrices and are unknown. Without loss of generality, the practical experience can lead to uncertain user requirements
Figure BDA0003553633910000055
Decomposition into a constant demand d and an energy-limited demand ωi(t), i.e. ωi(t)∈L2[0,∞]。
Considering that a chain owner exists in a product and supply chain cooperative evolution system, the sub-chain needs to adjust the inventory state of the sub-chain according to the inventory state change of the chain owner and the neighbor supply chain, and the kinetic equation of the chain owner is assumed to be
Figure BDA0003553633910000056
Wherein x0And (t) is an actual inventory demand target, namely a tracking target of the inventory state of the sub-chain. Considering some limiting factors such as capacity in the actual production process, the following 2 assumptions are given:
1. Production rate ui(t) has a certain upper bound umaxI.e. 0. ltoreq. ui(t)≤umax。
2. In a practical warehousing environment, inventory capacity is limited. Therefore, let the stock level satisfy 0 ≦ xi(t)≤xmax. Here, xmaxRepresents the maximum value of the warehousing capacity of the ith sub-supply chain.
In the supply chain system, when the ith sub-chain is in stock state xi(t) when transmitted to the distributed control center via the network, if a sensor-to-controller (S-C) channel is subjected to a DoS attack, a packet loss may occur, as shown in fig. 1. In fig. 1, T is a very small sampling instant,
Figure BDA0003553633910000058
in order to change the compensated inventory state of the ith sub-chain, the inventory state of the ith sub-chain can be obtained by the distributed control center
Figure BDA0003553633910000057
Can be expressed as
Figure BDA0003553633910000061
Wherein α (t) ∈ {0,1}, where α (t) ═ 0 represents that a network attack event occurs, that is, the S-C channel is under DoS attack, and α (t) ═ 1 represents that no network attack event occurs, that is, the S-C channel is capable of normal data transmission. Without loss of generality, there are two assumptions for DoS attacks, 3 and 4 below;
3. the number of continuous attacks by the network attacker is limited, i.e. the maximum number of continuous packet losses caused by the network attack is bounded and is recorded as
Figure BDA0003553633910000062
4. A network attacker only launches an attack against a child chain.
The invention designs a reasonable change mechanism to compensate the data packet loss caused by the attack from the perspective of actively preventing and controlling the DoS attack. Since the system is influenced by uncertainty requirement and change mechanism, which may cause bullwhip effect, further design of H based on optimal control is needed∞The controller inhibits the bullwhip effect caused by uncertain requirements and change mechanisms, so that the system is subjected to the inventory state x of the child chain under DoS attacki(t) may still beImplementing inventory status x with chain owner0(t) remain consistent. First, the local neighborhood inventory tracking error of each sub-chain can be defined as follows according to the formulas (1) and (2)
Figure BDA0003553633910000063
Wherein, aijFor inter-node connection of matrix elements, giAnd more than or equal to 0 is the traction gain of the sub-chain i. G if and only if there is a directed path between the ith child chain and the chain owneri> 0, otherwise, g i0. The global inventory tracking error vector for a child chain may be represented as
Figure BDA0003553633910000064
Wherein the global inventory tracking error vector is
Figure BDA0003553633910000065
The global inventory state vector is
Figure BDA0003553633910000066
L＝[lij]∈N×NIs a Laplace matrix of a directed topology graph, and
Figure BDA0003553633910000067
G＝[gij]∈N×Nis a traction gain as a diagonal element (g)ii＝gi) The diagonal matrix of (a) shows the link relation between the supply chain main and each sub-chain; i is nIs a n-dimensional unit matrix of which,
Figure BDA0003553633910000068
1is an N-dimensional vector with elements of 1, i.e.
Figure BDA0003553633910000069
Assuming that the topology of the cooperative evolution system of the product and supply chain includes the spanning tree, the ith sub-chain can be orderedIn synchronization with inventory errors of
Figure BDA0003553633910000071
Further, a globally synchronized inventory error of
Figure BDA0003553633910000072
Further the relationship of the global inventory tracking error vector to the global synchronization inventory error may be expressed as
Figure BDA0003553633910000073
It is further appreciated that the tracking inventory error of each child chain can be represented as a dynamic system driven by the control behavior of itself and all its neighboring child chains and with uncertain user needs. Thus, the translation of the consistency problem of the supply chain system into a reasonably designed production rate may enable local neighborhood inventory tracking error δ under uncertain customer demand and change mechanismsi(t) is minimized, thereby ensuring that the inventory between chain master and all sub-chains is synchronized and that the production rate is such that each agent, as shown in equation 1, satisfies the following definitions
For a given constant γ > 0 for the bull's whip suppression level, the product and supply chain co-evolution system is said to be able to suppress bull's whip at γ level, i.e. the alteration compensation method is valid if the following two conditions are met, and therefore 1) and 2) below can be used as the basis for determining whether the adopted alteration compensation method is valid.
1) When the market demand omega is uncertainiWhen t is 0, the production rate can be designed to satisfy the requirement of the system
Figure BDA0003553633910000074
2) Satisfying ω for a given bull's whip effect suppression level constant γ > 0 and uncertain market demandi(t) ≠ 0 and ωi(t)∈L2[0, ∞) on the basis of the total length of the chain, if each sub-chain satisfies the following bull penis effect inhibition conditions
Figure BDA0003553633910000075
The product is said to be able to suppress the bullwhip effect at gamma levels in conjunction with the evolution system of the supply chain. Wherein the content of the first and second substances,
Figure BDA0003553633910000076
outputting the performance;
Figure BDA0003553633910000077
Qii≥0,Rii＞0,Rij≥0,Tii> 0 and TijA positive definite symmetric weight matrix is more than 0; β is a bounded function and satisfies β (0) ═ 0. Let gamma beminIs the minimum value of gamma. For any gamma ≧ gammaminThe following equation 10 holds. For convenience of expression, u belowj(t),ωj(t),δj(t) when no misunderstanding is caused, it will be abbreviated as uj,ωj,δj。
Aiming at the problems described in the process, the invention specifically adopts the following technical scheme:
example 1
The present embodiment provides a method for compensating a product and supply chain cooperative evolution system under a network attack, please refer to fig. 2, where the method includes:
s1, obtaining historical inventory state data of each sub-chain in the collaborative evolution system of the product and the supply chain, wherein the historical inventory state data comprises historical inventory state data of the sub-chain before the sub-chain is attacked by the network and historical inventory state data of the sub-chain after the sub-chain is attacked by the network;
S2, training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the sub-chain subjected to the network attack as input and the historical inventory state data of the sub-chain before the network attack as a label to obtain the trained prediction model;
s3, inputting the latest inventory state data of the sub-chain, which is obtained after the sub-chain is subjected to network attack, into the trained prediction model for each sub-chain, and predicting the current inventory state data of the sub-chain;
in the modification compensation method provided in this embodiment, first, for the problem that a data packet is lost in a PSCSES under a network attack, a predictor based on a Recurrent Neural Network (RNN) is designed using historical data of each child chain to compensate for the loss of inventory data caused by the network attack.
The inventory state predictor is designed based on RNN network, i.e. the continuous packet loss occurring before time t is defined as nα(T-T), if at time T, x (T) is successfully transmitted, then nα(T-T) ═ 0. It is clear that,
Figure BDA0003553633910000081
(
Figure BDA0003553633910000082
is a constant). Thus, at time t, the distributed control center may obtain the latest inventory status quantity of
Figure BDA0003553633910000083
If the S-C communication channel is attacked and the packet loss phenomenon occurs at the time t, predicting the current inventory state data by utilizing a predictor according to the historical inventory state data X
Figure BDA0003553633910000084
Namely that
Figure BDA0003553633910000085
Wherein h is the hidden layer, and U, V and W represent the ideal weights of the input layer, the output layer and the hidden layer, respectively; f () and g () are the activation functions of the hidden layer and the output layer, respectively.
S4, obtaining local neighborhood inventory tracking errors of the sub-chain according to the current inventory state data of the sub-chain;
according to the stepsSteps S1-S3 obtain child chain current inventory status data
Figure BDA0003553633910000086
Then, will
Figure BDA0003553633910000087
Substituting the formula (3) to obtain the stock state of the ith subchain
Figure BDA0003553633910000088
Further, according to the stock state of the ith sub-chain
Figure BDA0003553633910000089
And the formula (4) can obtain the local neighborhood inventory tracking error delta of the ith sub-chaini(t)。
S5, according to the performance index function of the sub-chain, aiming at minimizing the local neighborhood inventory tracking error of the sub-chain, and designing the optimal productivity and uncertain market demand of the sub-chain by using a zero sum game method; the performance indicator function is a function of local neighborhood inventory tracking error for the child chain, the production rate, and the uncertain demand.
The following performance index function can be specifically designed for the ith sub-chain
Figure BDA0003553633910000091
Wherein deltai(0) Is the initial error data.
Defining a value function of the sub-chain according to the index function, wherein the value function of the ith sub-chain is
Figure BDA0003553633910000092
In this embodiment, productivity and uncertain market demand can be viewed as both parties to the game, and then the consistency of the supply chain system is equivalent to solving the supply chain system zero and differential map game problem described below
Figure BDA0003553633910000093
If the above zero-sum differential game formula has saddle points
Figure BDA0003553633910000094
Then there is a unique solution to the game, i.e.
Figure BDA0003553633910000095
Which is equivalent to the following Nash equilibrium conditions
Figure BDA0003553633910000096
According to the Laibunitz formula and the Bellman equation, a Hamiltonian function (Hamiltonian function) (V) equivalent to the formula (11) can be obtainedi(0)＝0)
Figure BDA0003553633910000097
Is obtained from the stability condition
Figure BDA0003553633910000101
Figure BDA0003553633910000102
The value function of the ith partial chain can be further written in the form of a quadratic form, namely
Figure BDA0003553633910000103
Wherein, PiA positive symmetric matrix is determined for the object. According to formula (18), formulae (16) and (17) can be further represented as
Figure BDA0003553633910000104
Figure BDA0003553633910000105
It should be noted that, in the present embodiment, a change control strategy based on data-driven and game theory needs to be designed according to the following 3 points so that the product and supply chain collaborative evolution system under the zero sum game achieves inventory synchronization and has nash solution.
For a product and supply chain collaborative evolution system (1), assuming that 1-4 conditions are established, if a smooth positive solution exists in an HJI equation
Figure BDA0003553633910000106
And the production strategy and the uncertain market demand strategy of the adjacent subchains are optimal, then the production rate is high
Figure BDA0003553633910000107
Ensuring that the sub-chain i can be synchronous and consistent with the chain main inventory state and the horizontal gamma is more than or equal to gamma*(γ*Given constant) suppresses the bullwhip effect.
Secondly, for the product and supply chain collaborative evolution system (1), assuming that 1-4 conditions are established, if a smooth positive definite solution exists in the HJI equation
Figure BDA0003553633910000108
And the production strategy and the uncertain market demand strategy of the adjacent subchain are optimal, a graph game Nash equilibrium solution, namely a saddle point exists
Figure BDA0003553633910000109
Solutions exist and game values are resolved by HJI
Figure BDA00035536339100001010
It is given.
For the product and supply chain collaborative evolution system (1), assuming that 1-4 conditions are satisfied, a topological graph G formed by sub-chain nodes and connections has a strong connection relation, and the production strategy and the uncertain market demand strategy of adjacent sub-chains are optimal, the product and supply chain collaborative evolution system can realize that the inventory states of the sub-chains and the chain owner are consistent under model unknown and DoS network attack, and the system meets certain user requirements and can enable gamma to be more than or equal to gammaminThe level inhibits the bullwhip effect.
Because the theoretical process is only a theoretical derivation process and cannot directly obtain the final productivity and the numerical value of the uncertain market demand, a Q-learning algorithm needs to be designed, the Q-learning algorithm computer based on strategy iteration outputs the productivity and the uncertain market demand, and the Q-learning algorithm based on strategy iteration is as follows:
Figure BDA0003553633910000111
In the above-mentioned algorithm, the algorithm,
Figure BDA0003553633910000112
is the neutralization variable u in formula (15)i，δi，ωiThe arithmetic sign of the corresponding matrix element is multiplied.
The method provided by the invention solves the problem of emergency change control under the condition that a system model is unknown and DoS attack is performed by a product and supply chain collaborative evolution system based on the distributed CPS. By utilizing a data driving technology, an emergency defense change mechanism is designed according to historical data and reference information to deal with the situation that a system sensor-controller communication channel is subjected to DoS attack, an H-infinity consistency controller is designed through a zero-sum differential diagram game theory and an enhanced Q-learning technology, the situation that a product and a supply chain cooperative evolution system are led to lead to the H-infinity consistency is ensured under the situation that the system is subjected to design change due to DoS attack, the uncertain demand is restrained, the ox penis effect brought by design change is achieved, and meanwhile, the system is ensured to have certain product adaptability and user satisfaction.
In order to illustrate the effectiveness of the above scheme of the present embodiment, the following scheme is provided for verification:
consider a product and supply chain collaborative evolution system with an unknown model containing four child chains
Figure BDA0003553633910000121
And a chain owner
Figure BDA0003553633910000122
Wherein each sub-supply chain comprises two devices and the topology of the system is shown in figure 3.
To design a data driven controller, the following model parameters are selected to generate training data
Figure BDA0003553633910000123
And assume the initial inventory status values of the four child chains to be x respectively1＝[50,10]T,x2＝[35,40]T,x3＝[21,10]T， x4＝[20,25]TThe initial value of the stock state of the chain owner is x0＝[10,30]T。
The first step is as follows: in order to verify the effectiveness of the adopted prediction algorithm, in a simulation environment, under the condition of data packet loss caused by network attack as shown in fig. 4, the historical inventory data of the first sublink for 200 days is used for testing to predict the inventory data of the future 50 days, so as to obtain the prediction results of the two devices as shown in fig. 5 and 6.
The second step is that: and considering the change compensation design of the product supply chain collaborative evolution system, selecting a proper weight matrix, and solving the minimum production rate and the maximum uncertain demand through a strategy iteration Q-learning algorithm to further obtain the inventory state and synchronous inventory error state response curve of each sub-chain. In order to verify the effectiveness of the change compensation measures, the inventory conditions of the sub-supply chains before and after the change is introduced are compared. Fig. 7 and 8 respectively show the change of the inventory level of each sub-chain before and after the change compensation mechanism is introduced under the DoS attack.
TABLE 1 index comparison before and after Change
Figure BDA0003553633910000124
As can be seen from the simulation results in the figure, after the system introduces the change compensation mechanism, the system can effectively track the user requirements set by the collaborative evolution system around the 10 th day, that is, the user requirements are consistent.
The third step: to further verify the impact of the alteration compensation mechanism on the product fitness and the user satisfaction, consider the index values listed in table 1, i.e., the delivery time under network attack and the average tracking error of the stock. As can be seen from table 1, by introducing the alteration compensation mechanism under the network attack, the delivery time of the system (i.e. the time for the system to achieve the inventory consistency to meet the contractual provisions to deliver the product to the customer) can be effectively increased and the average inventory tracking error can be reduced.
In conclusion, the H-infinity controller based on Q-Learning under the change mechanism provided by the technology can enable the product and the supply chain cooperative evolution system to resist the DoS attack and effectively inhibit the bull penis effect and realize the leadership-following consistency.
Example 2
The embodiment provides a product and supply chain collaborative evolution system compensation system under network attack, and the system comprises:
a historical inventory status data obtaining module M1, configured to obtain historical inventory status data of each child chain in the collaborative evolution system of the product and the supply chain, where the historical inventory status data includes historical inventory status data of the child chain before the child chain is subjected to the network attack and historical inventory status data of the child chain after the child chain is subjected to the network attack;
The model training module M2 is used for training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the sub-chain subjected to the network attack as input and the historical inventory state data of the sub-chain subjected to the network attack as a label to obtain a trained prediction model;
the prediction module M3 is used for inputting the latest inventory state data of the sub-chains, which are obtained after the sub-chains are subjected to network attacks, into the trained prediction model for each sub-chain, and predicting the current inventory state data of the sub-chains;
the partial neighborhood inventory tracking error calculation module M4 of the sub chain is used for obtaining the partial neighborhood inventory tracking error of the sub chain according to the current inventory state data of the sub chain;
the optimal productivity and uncertain market demand calculation module M5 is used for designing the optimal productivity and uncertain market demand of the sub-chain by utilizing a zero sum game method according to the performance index function of the sub-chain and aiming at the minimum local neighborhood inventory tracking error of the sub-chain; the performance indicator function is a function of local neighborhood inventory tracking error for the child chain, the production rate, and the uncertain demand.
As an optional implementation, the system further comprises:
The first judging module M6 is configured to judge whether the uncertain market demand is zero, and obtain a first judgment result;
the second determination module M7 is configured to verify, according to the first determination result, whether the inventory status of the chain master in the product and supply chain collaborative evolution system is consistent with the inventory status of all the sub-chains to obtain a second determination result, or verify, according to the first determination result, whether the product and supply chain collaborative evolution system can suppress the bull penis effect, to obtain a third determination result;
a third determining module M8, configured to determine whether the modification compensation method is valid according to the second determination result and/or the third determination result.
For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.
The principle and the embodiment of the present invention are explained by applying specific examples, and the above description of the embodiments is only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the foregoing, the description is not to be taken in a limiting sense.

Claims (10)

1. A product and supply chain cooperative evolution system compensation method under network attack is characterized by comprising the following steps:
obtaining historical inventory state data of each sub-chain in a product and supply chain collaborative evolution system, wherein the historical inventory state data comprises historical inventory state data of the sub-chain before network attack and historical inventory state data of the sub-chain after network attack;
training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the child chain subjected to the network attack as input and the historical inventory state data of the child chain before the network attack as a label to obtain a trained prediction model;
for each subchain, inputting the latest inventory state data of the subchain, which is obtained after the subchain is subjected to network attack, into the trained prediction model, and predicting the current inventory state data of the subchain;
obtaining a local neighborhood inventory tracking error of the sub-chain according to the current inventory state data of the sub-chain;
according to the performance index function of the sub-chain, the minimum local neighborhood inventory tracking error of the sub-chain is taken as a target, and the optimal productivity and uncertain market demand of the sub-chain are designed by utilizing a zero sum game method; the performance indicator function is a function of local neighborhood inventory tracking error for the child chain, the production rate, and the uncertain demand.
2. The compensation method according to claim 1, wherein the designing of the best productivity and uncertain market demand of the sub-chain by using a zero-sum game method with the goal of minimizing the local neighborhood inventory tracking error of the sub-chain according to the performance index function of the sub-chain specifically comprises:
defining a value function of the subchain according to the index function;
calculating the optimal value of the value function by adopting a zero sum game method;
and obtaining the optimal productivity and the uncertain market demand of the subchain according to the optimal value of the value function.
3. The compensation method of claim 2, wherein the computing the optimal value of the value function using a zero-sum game method comprises:
establishing a zero and differential game formula according to the value function;
obtaining a Hamiltonian equivalent to the value function according to the zero and differential game formulas;
and solving the solution of the Hamiltonian through a Q-learning algorithm, wherein the solution of the Hamiltonian is the optimal value of the value function.
4. A compensation method according to claim 3, characterized in that the calculation formula of the hamiltonian is:
Figure FDA0003553633900000021
wherein, deltaiLocal neighborhood inventory tracking error, u, for a child chain iAnd ujThe production rate of the ith sub-chain and the production rate of the jth sub-chain, ωiAs uncertain market demand of the ith subchain, ωjThe uncertain market demand of the jth sub-chain is; A. b and D are both system matrixes; d is a radical ofiThe constant demand of the ith subchain; g is a radical of formulaiThe drag gain of the sub-chain i; a is aijConnecting matrix elements among nodes; qii≥0,Rii＞0,Rij≥0,Tii> 0 and TijMore than 0 is a positive definite symmetric weight matrix; gamma is the constant of the inhibition level of the bullwhip effect.
5. The compensation method of any one of claims 1-4, wherein after said designing the best productivity and uncertain market demand of the subchain using the zero-sum game method, the method further comprises:
judging whether the uncertain market demand is zero or not to obtain a first judgment result;
verifying whether the inventory state of the chain master in the product and supply chain cooperative evolution system is consistent with the inventory state of all the sub chains according to the first judgment result to obtain a second judgment result, or verifying whether the product and supply chain cooperative evolution system can inhibit the bullwhip effect according to the first judgment result to obtain a third judgment result;
and judging whether the change compensation method is effective or not according to the second judgment result and/or the third judgment result.
6. The compensation method according to claim 5, wherein verifying, according to the first determination result, whether the inventory status of the chain owner in the product and supply chain collaborative evolution system is consistent with the inventory status of all the sub-chains to obtain a second determination result, or verifying, according to the first determination result, whether the product and supply chain collaborative evolution system can suppress a bullwhip effect to obtain a third determination result, specifically comprising:
if the first judgment result is yes, verifying whether the inventory state of the chain master in the product and supply chain collaborative evolution system is consistent with the inventory states of all the sub-chains to obtain a second judgment result;
and when the first judgment result is negative, designing a bull's penis effect inhibition condition, and verifying whether each sub-chain meets the bull's penis effect inhibition condition so as to verify whether the product and a supply chain cooperative evolution system can inhibit the bull's penis effect.
7. The compensation method according to claim 6, wherein the determining whether the modification compensation method is effective according to the second determination result and/or the third determination result includes:
when the second determination result and/or the third determination result is yes, determining that the change compensation method is effective;
Otherwise, the change compensation method is judged to be invalid.
8. The compensation method of claim 6, wherein the bullwhip effect suppression condition is formulated as:
Figure FDA0003553633900000031
wherein gamma is a bullwhip effect inhibition level constant, and gamma is more than 0;
Figure FDA0003553633900000032
performance output
Figure FDA0003553633900000033
Qii≥0,Rii＞0,Rij≥0,Tii> 0 and TijMore than 0 is a positive definite symmetric weight matrix; β is a bounded function and satisfies β (0) ═ 0.
9. A system for compensating a product and supply chain cooperative evolution system under network attack, the system comprising:
the system comprises a historical inventory state data acquisition module, a supply chain cooperative evolution system and a control module, wherein the historical inventory state data acquisition module is used for acquiring historical inventory state data of each subchain in the product and supply chain cooperative evolution system, and the historical inventory state data comprises the historical inventory state data of the subchain before network attack and the historical inventory state data of the subchain after network attack;
the model training module is used for training a prediction model established based on a recurrent neural network by taking the historical inventory state data of the subchain after the subchain is subjected to the network attack as input and the historical inventory state data of the subchain before the subchain is subjected to the network attack as a label to obtain a trained prediction model;
the prediction module is used for inputting the latest inventory state data of the sub-chains, which are obtained after the sub-chains are subjected to network attack, into the trained prediction model aiming at each sub-chain, and predicting the current inventory state data of the sub-chains;
The partial neighborhood inventory tracking error calculation module of the sub chain is used for obtaining the partial neighborhood inventory tracking error of the sub chain according to the current inventory state data of the sub chain;
the optimal productivity and uncertain market demand calculation module is used for designing the optimal productivity and uncertain market demand of the sub-chain by using a zero sum game method according to the performance index function of the sub-chain and aiming at the minimum local neighborhood inventory tracking error of the sub-chain; the performance indicator function is a function of local neighborhood inventory tracking error for the child chain, the production rate, and the uncertain demand.
10. The compensation system of claim 9, further comprising:
the first judgment module is used for judging whether the uncertain market demand is zero or not to obtain a first judgment result;
the second judging module is used for verifying whether the inventory state of the chain master in the product and supply chain collaborative evolution system is consistent with the inventory states of all the sub-chains according to the first judging result to obtain a second judging result, or verifying whether the product and supply chain collaborative evolution system can inhibit the bullwhip effect according to the first judging result to obtain a third judging result;
And the third judging module is used for judging whether the change compensation method is effective or not according to the second judging result and/or the third judging result.
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