CN-115293322-B - Optimal control input track determination method under multilayer complex network

Abstract

The invention discloses an optimal control input track determining method under a multi-layer complex network, which is characterized in that a control signal is input into a shallow layer to control a control input track computing method which can not directly access deep layers under the condition of controlling energy minimization for an information physical system characterized by a multi-layer complex network model. In the calculation of the control track, the calculation of complex coupling relation between characteristic values of the system adjacency matrix is not needed. In the system, when the condition that any two layers are connected is met, the control of the inaccessible deep layer to reach a given target state can be realized by controlling the surface layer.

Inventors

• Zhang Bozhu
• SUN JIAN
• WANG GANG
• CHEN JIE

Assignees

• 北京理工大学

Dates

Publication Date

20260505

Application Date

20220601

Claims (1)

1. 1. The optimal control input track determining method under the multi-layer complex network is characterized in that an appropriate multi-layer complex network model is built according to known information aiming at an information physical system which can be characterized as a multi-layer complex network model, and the optimal control input calculating method with small calculated amount and minimum control energy is provided from the whole on the premise that full rank full connection exists between any two layers of networks, and comprises the following steps: For an information physical system entity, modeling the information physical system entity as a mathematical model of a multi-layer complex network, presetting parameters of the complex network model, and establishing a super adjacency matrix of the multi-layer complex network model; the parameters of the predetermined complex network model comprise: Specifying the number of layers of a complex network model Number of network nodes per layer ; Dimension unit array Zero matrix ; First, the Layer to the first Interlayer connection weight of layer , Should satisfy ; ; Intra-layer real symmetric matrix for each layer of network ; ; First, the Layer to the first Interlayer connection matrix of layers ; Control target time Control input matrix Time step of discrete value solution Given an initial state Target state ; Establishing a multi-layer complex network model super-adjacency matrix according to the parameters of the pre-given complex network model, and establishing the multi-layer complex network model super-adjacency matrix according to the pre-given complex network model super-adjacency matrix : ; Constructing an augmentation matrix consisting of a super-adjacent matrix and an input matrix, calculating matrix index expression of the augmentation matrix at given control target time, and partitioning, wherein the augmentation matrix consisting of the super-adjacent matrix and the input matrix is constructed, and the augmentation matrix is: ; A transposed matrix of B; is the transposed matrix of O; The matrix index expression and the block of the calculation augmentation matrix under the given control target time are specifically as follows: Wherein, the The first block matrix to the fourth block matrix are respectively; initializing a common-state vector initial value and an augmentation matrix state vector, and initializing a state track matrix of the augmentation matrix, wherein the state track matrix specifically comprises the following components: Initial value of common-mode vector ; Is the generalized inverse of E 12 ; Establishing a time sequence In total Sampling points; initializing an augmented matrix initial state vector Initializing an augmented matrix state track matrix and assigning an initial value: wherein, the first Is listed as ; Calculating a discrete interval matrix index by using the augmentation matrix, iteratively calculating a state track matrix of the augmentation matrix by using the discrete interval matrix index, and after the iteration is ended, completing the track matrix calculation of the augmentation matrix, wherein the obtained track matrix is a block track matrix, and specifically comprises the following steps: calculating a discrete interval matrix index: iterative computation from Iterate to Each iteration calculation And assigning values into the track matrix After iteration is terminated, track matrix calculation is completed; The track matrix after the block calculation is as follows: ; obtaining a system state track by utilizing the block track matrix, and finally calculating the obtained control input track, wherein the finally given system state track is as follows: the final calculated control input track is ; The control input trajectory is expressed as: In the form of (a), wherein Namely, in the whole control flow, the purpose of enabling the deep network to reach the target state only through the control input layer is realized.

Description

Optimal control input track determination method under multilayer complex network Technical Field The invention relates to the technical field of information physical system control, in particular to an optimal control input track determination method under a multi-layer complex network. Background In recent years, with the rapid development of computing level and network technology, information physical systems (CPSs) are widely used by various industries, such as intelligent home appliances, unmanned vehicles, and the like. Many studies of complex information physical systems can be conducted with a ubiquitous and efficient analysis in the framework provided by complex network science. In the past researches, for the control problem of the system, most students establish a mathematical model of an actual complex information physical system as a single-layer complex network model, determine the control characteristics of the system according to the response of the system under the framework of a linear system theory by establishing a system dynamic equation, then design a control scheme and solve the optimal control input. In most real information physical systems, system components are not isolated, different types of interactions between the system components can coexist and influence each other, a single-layer complex network model is built to be researched to meet a part of control requirements, but the system components still have larger deviation from an actual system in practice, and the control scheme designed through the single-layer network model is not excellent in practical application when the model complexity is improved and the model is enlarged. Individual system components are not isolated, but are affected and affected by other surrounding components by various forces, effects, and causal interactions. For example, in smart manufacturing systems, one can selectively use different system components to achieve one and the same goal. Therefore, mathematical modeling of multi-layer networks to study control problems of complex information physical systems is a reliable development direction. In recent years, the control problem for the multilayer network has also attracted the eyes of most scholars. In 2016, giulia Menichetti et al in the literature (Control of Multilayer networks. Sci Rep 6,20706 (2016)) proposed a mathematical model to study the problem of control of a two-layer network, but under this model they considered it as a macroscopic background, not considering the influence of two-layer networks on each other, only placing two-layer networks in a super-adjacency matrix for consideration, still requiring calculation and design of control schemes for the two-layer networks separately. Then PRAGYA SRIVASTAVA et al in literature (Structural underpinnings of control in multiplex networks) established a fully connected two-layer network, more approaching a real system. In practical systems, the control of the system appears to be such that the overall system control can be met by controlling only one component, and according to this they have limited the input of control signals only into the input layer network under this model to bring the deep layer network to the target state, under which conditions the optimal control input problem has been studied. In the fully-connected double-layer network model, the relation and influence among different systems in a complex system are considered, but in the process of solving the control input track, a large amount of calculation based on diagonalization, euclidean included angles and the like is needed, and in practical application, the model precision requirement on the system is high, meanwhile, the time consumption is long, and the cost is high. Meanwhile, the real system is more close to a network model with more layers and higher complexity, and the system model only for establishing a double-layer network is different from the real system, so that the control problem under the network model with strong multi-layer universality is urgently researched. The scale of the current industrial control system is continuously increased, the calculation amount is high, the difficulty is high, and the calculation method with high precision requirement can meet great challenges. Meanwhile, the basic double-layer network model cannot well replace a control system with continuously-increased complexity. In order to solve the difficulties, considering that the deep layer which can not be directly accessed can reach the target state through the control surface layer in the actual system, the research of the optimal control input track calculation method under the minimum control energy based on the whole model of the multi-layer complex network is necessary, the calculation problem of the optimal control input track under the requirements of the minimum control energy, the limitation of the control input and the constraint of the standard state space e