CN110611927B - Wireless sensor network guaranteed cost synchronous control method under given budget value condition - Google Patents
Wireless sensor network guaranteed cost synchronous control method under given budget value condition Download PDFInfo
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- H—ELECTRICITY
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention discloses a wireless sensor network cost-guaranteeing synchronous control method under the condition of a given precalculation value, a second-order isomorphic wireless sensor network based on the method is composed of a leader node and N-1 follower nodes, the interaction relation between the wireless sensors based on the method is described by a directed graph G, wherein the sensors are represented by the jth node, the action channels between the nodes are represented by edges, and the edge weight w ij Represents the interaction weight; and finally, obtaining a system state differential mechanical model according to the wireless sensor network system (1), the control protocol (2) and the state difference between the follower sensor node and the leader sensor node. The invention solves the network protection cost synchronous control criterion by designing the wireless sensing network protection cost synchronous control protocol under the condition of a given budget value, and finally designs the network protection cost synchronous control method under the condition of the given budget value.
Description
Technical Field
The invention belongs to the technical field of application of a distributed optimization control method of a multi-agent system, and particularly relates to a wireless sensor network guaranteed cost synchronous control method under the condition of a given budget value.
Background
In recent years, due to the decrease of network performance caused by network congestion and higher requirements for network transmission speed and transmission performance, the problem of wireless sensor network synchronization has received attention from a large number of researchers. As an information transmission communication medium, a wireless sensor network usually includes a destination node and a plurality of resource nodes, wherein the resource nodes collect environment information and transmit the environment information to the destination node. During the transmission process, the resource node transmits the collected information to the destination node directly or indirectly, and based on the structure, the network can be set to be a leader and follower structure. Under the structural model, the network congestion is easily caused by the one-to-many alternating current mode due to limited bandwidth and storage space, so in practical application, certain performances of the wireless sensor nodes need to be synchronized so as to inhibit the generation of the network congestion.
In an actual wireless sensor network, a network node is usually equipped with a certain battery energy, and due to the limitation of outdoor space, battery replacement has certain difficulty. Therefore, how to prolong the life of the battery and achieve the compromise design of energy consumption and synchronous management performance is an important research direction. There are many papers that study how to optimize energy consumption. In these studies, different cost equations were modeled as optimization or sub-optimization problems. Meanwhile, these control strategies usually only consider the synchronization performance or only consider the synchronization control consumption, and it is rare that the synchronization control strategies incorporate both of them into the evaluation range. In addition, setting the limited battery energy as the limited energy budget value is a relatively new research idea.
In the existing research on the aspect of wireless sensor network synchronization control methods, most of the existing researches are based on a linear matrix inequality technology, a feasibility solver in an MATLAB toolkit is utilized to judge whether a control gain value for enabling a wireless sensor network to realize network synchronization exists, and when the number of wireless network nodes is too large, the calculation complexity is increased due to too complex data processing. In addition, from the research results in the prior art, there are many methods for realizing optimization control, but the synchronization performance optimization and the control input optimization problem, namely the cost-guaranteed synchronization control problem, are rarely considered comprehensively. Meanwhile, due to the fact that the network node has limited energy of the battery and the battery equipment is difficult to replace due to site reasons, the problem of network protection cost synchronization control under the limited energy condition needs to be considered urgently.
Disclosure of Invention
The invention aims to solve the problems, and provides a wireless sensor network guaranteed cost synchronous control method under the condition of a given precalculated value.
The invention realizes the purpose through the following technical scheme:
a wireless sensor network cost-guaranteeing synchronous control method under the condition of a given precalculated value is based on a second-order isomorphic wireless sensor network which is composed of a leader node and N-1 follower nodes, wherein a kinetic model of a jth sensor can be described as follows through a linearization modeling method:
where j ∈ {1,2, …, N }, x j (t) is the network node storage, v j (t) is the packet transmission speed, u j (t) is a control input;
the interaction relation between wireless sensors based on the method is described by a directed graph G, wherein the sensors are represented by jth nodes, action channels between the nodes are represented by edges, and the weight w of the edges ij The laplace matrix of fig. G is defined as L ═ L, representing the interaction weights ji ]Wherein l is jj ＝∑ i∈Nj w ji ，l ji ＝-w ji And j ≠ i;
the method is based on the control theory, and the wireless sensor network cost-guaranteed synchronous control protocol is expressed as follows:
wherein the content of the first and second substances,
in the formula, eta, gamma 1 And gamma 2 Positive definite parameter, J u (t) is a control input energy consumption function, J x (t) is a synchronization performance optimization function, N j A neighbor set for agent j; w is a ij For the interaction weight between network nodes, k 1 And k 2 Is the control gain value; according to the wireless sensor network system (1) and the control protocol (2), and the state difference between the follower sensor node and the leader sensor node, a system state difference mechanical model is obtained as follows:
the invention has the further improvement that the method specifically comprises the following implementation steps:
step one, establishing a leader-follower model based on structural characteristics of a wireless sensor network;
setting system parameters under the condition of giving a precalculated value;
step three, solving a control gain value;
step four, judging the network synchronization feasibility, if feasible, continuing to perform the step five, and if not feasible, returning to the step two to perform parameter setting again;
solving the cost protection value, and finishing the design of related parameters of network synchronous control;
step six, verifying the cost-guaranteed synchronization effect under the condition of given budget value, and verifying the solved k 1 And k 2 And substituting the result into the system to verify the synchronization effect, the cost-saving effect and the given budget value effect under the condition of the given budget value.
The invention is further improved in that, in a first step, a leader-follower model is created for the wireless sensor network system (1) on the basis of the structural characteristics of the wireless sensor network.
The invention is further improved in that in the second step, the system parameters are set based on the wireless sensor network cost-guaranteed synchronous control protocol (2) under the condition of a given precalculated value.
A further improvement of the invention is that the definition of the achievable guaranteed cost synchronization is as follows:
for a given budget value
If there is any bounded initial state x j (0) And v j (0) (j-2, 3, …, N), all with k 1 And k 2 So that lim t→∞ (x j (t)-x 1 (t)) -0 and lim t→∞ (v j (t)-v 1 (t)) -0 (j-2, 3, …, N), the wireless sensor network (1) is said to achieve cost synchronization for a given budget value under the action of the protocol (2).
The invention is further improved in that for a given eta, gamma 1 And gamma 2 Positive definite parameter, if k exists 1 And k 2 Then, the wireless sensor network (1) realizes the guarantee cost synchronization under the action of the protocol (2), and in this case, the guarantee cost value satisfies the following conditions:
wherein the content of the first and second substances,
the invention is further improved in that for a given eta, gamma 1 And gamma 2 Positive definite parameter sum
If k exists 1 And k 2 Then, the wireless sensor network (1) achieves the guaranteed cost synchronization under the condition of a given precalculated value under the action of the protocol (2), and in this case, the guaranteed cost value meets the following conditions:
wherein the content of the first and second substances,
the invention has the following beneficial technical effects:
1. the invention solves the analytic solution of the display of the synchronous control gain of the wireless sensor network, namely the wireless sensor network can be synchronized by selecting the control gain based on the value range of the control gain, the display expression effectively solves the problem that the control gain value does not exist, and the solution is not needed by means of the linear matrix inequality technology.
2. The invention considers the limit of outdoor space of the actual wireless sensor network, and the battery replacement has certain difficulty, so the limited battery energy allocated to the nodes is considered as the limited energy budget. Therefore, the design of compromising energy consumption and synchronous management performance is realized, and the service life of the wireless sensor network battery is effectively prolonged.
Drawings
FIG. 1 is a summary of a wireless sensor network security cost synchronization control graph;
FIG. 2 is a flow chart of a wireless sensor network security cost synchronization control algorithm;
FIG. 3 is a diagram of a wireless sensor network communication topology;
FIG. 4 is a diagram of a wireless sensor network node storage capacity and transmission speed state difference trace; where fig. 4(a) is a storage amount state difference, and fig. 4(b) is a transmission speed state difference;
FIG. 5 is a state trace diagram of a cost function of a wireless sensor network node.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with 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.
1. System dynamics model and control protocol
The method is based on a second-order isomorphic wireless sensor network which is composed of a leader node and N-1 follower nodes, wherein the dynamic model of the jth (j epsilon {1,2, …, N }) sensor can be described by a linearization modeling method as follows:
wherein x is j (t) is the network node storage, v j (t) is the packet transmission speed, u j (t) is a control input. w is a ij For the interaction weights between network nodes, k 1 And k 2 Is the control gain value.
The interaction relation between wireless sensors based on the method is described by a directed graph G, wherein the sensors are represented by jth nodes, action channels between the nodes are represented by edges, and the weight w of the edges ij The laplace matrix of fig. G is defined as L ═ L, representing the interaction weights ji ]Wherein l is
l ji ＝-w ji (j≠i).
The method is based on the control theory, and the wireless sensor network cost-guaranteed synchronous control protocol is expressed as follows:
wherein the content of the first and second substances,
in the formula, eta, gamma 1 And gamma 2 Positive definite parameter, J u (t) is a control input energy consumption function, J x (t) is a synchronization performance optimization function, N j Is a neighbor set for agent j. J. the design is a square u (t) is the time integral of a quadratic function of the control input, which describes the control consumption energy function of the system from the implementation of the control to the implementation of the network synchronization; performance optimization function J x And (t) is the time integral of a quadratic function of the node state difference, which describes that an accumulated value of the quadratic function of the state difference, namely a quantized value of the control performance in the control process, realizes the performance optimization of the control in the network synchronization process from the beginning to the synchronization process of the system. From the wireless sensor network system (1) and the control protocol (2), and the state differences between the follower sensor node and the leader sensor node, a system state differential dynamics model can be derived as follows:
description 1: the wireless sensor network control protocol constructed by the invention has the following two characteristics. The first point is that the protocol is different from general state information using the whole state of the sensor nodes, and the protocol uses partial state difference information between wireless sensor nodes to construct a control protocol. The second point is that the protocol is added with a quantized value which simultaneously comprises a control energy consumption function in the network synchronization process and a synchronization performance in the control process, and the compromise design of the control energy consumption function and the synchronization performance in the network synchronization process is realized on the premise of considering the limited energy of the actual system, so that the energy optimization of the wireless sensor network is optimized.
2. Wireless sensor network cost-guaranteeing synchronous control algorithm
The method comprises the following steps:
step one, establishing a leader-follower model based on the structural characteristics of a wireless sensor network; in the first step, establishing a leader-follower model based on the structural characteristics of the wireless sensor network as follows:
where j is 1,2, …, N is a wireless sensing network node, x j (t) is the network node storage, v j (t) is the packet transmission speed, u j (t) is a control input.
Setting system parameters under the condition of giving a precalculated value; in the second step, protocol (2) is as follows:
as shown in fig. 1 and fig. 2, the guaranteed cost synchronization control protocol of the wireless sensor network under the condition of a given budget value is described as follows:
wherein the content of the first and second substances,
in the formula, eta, gamma 1 And gamma 2 Positive definite parameter, J u (t) is a control input energy consumption function, J x (t) is a synchronization performance optimization function, N j Is a neighbor set for agent j. w is a ij For the interaction weights between network nodes, k 1 And k 2 Is the control gain value. J. the design is a square u (t) is the time integral of a quadratic function of the control input, which describes the control consumption energy function of the system from the implementation of the control to the implementation of the network synchronization; performance optimization function J x And (t) is the time integral of a quadratic function of the node state difference, which describes that an accumulated value of the quadratic function of the state difference, namely a quantized value of the control performance in the control process, realizes the performance optimization of the network synchronization control from the beginning to the synchronization process of the system.
Step three, solving a control gain value;
step four, judging the network synchronization feasibility, if feasible, continuing to perform the step five, and if not feasible, returning to the step two to perform parameter setting again;
solving the cost protection value, and finishing the design of related parameters of network synchronous control;
step six, verifying the cost-guaranteeing synchronization effect under the condition of given precalculated value, and verifying the obtained k 1 And k 2 And substituting the result into the system to verify the synchronization effect, the cost-saving effect and the given budget value effect under the condition of the given budget value.
The definition of achievable guaranteed cost synchronization is as follows:
for a given budget value
If there is any bounded initial state x j (0) And v j (0) (j-2, 3, …, N), all in the presence of k 1 And k 2 So that lim t→∞ (x j (t)-x 1 (t)) -0 and lim t→∞ (v j (t)-v 1 (t)) -0 (j-2, 3, …, N), the wireless sensor network (1) is said to achieve cost synchronization for a given budget value under the action of the protocol (2).
For a given η, γ 1 And gamma 2 Positive definite parameter, if k exists 1 And k 2 The wireless sensor network (1) then achieves guaranteed cost synchronization under the action of the protocol (2), in which case,cost guarantee value satisfies
Wherein the content of the first and second substances,
for a given η, γ 1 And gamma 2 Positive definite parameter sum
If k exists 1 And k 2 The wireless sensor network (1) then achieves the guaranteed cost synchronization under the action of the protocol (2) under the condition of a given budget value, and in this case, the guaranteed cost value meets the requirement
Wherein the content of the first and second substances,
description 2: the invention has difficulty in solving the value range of the control gain for realizing the cost-guaranteed synchronous control of the wireless sensor network under the condition of a given precalculated value. For the problem, the inventor finds out that decoupling processing is carried out on the control gain by applying the inequality property of a quadratic function and the monotonic characteristic of the function, and two control gains K are separated 1 And K 2 And separately find out the control gain K 1 And K 2 The value range of (a). In addition, the gain K is controlled 1 And K 2 Depends only on the non-zero minimum and maximum eigenvalues of the laplacian matrix. To further reduce computational complexity, non-zero minimum and maximum eigenvalues may be provided according to methods provided in the existing literatureAnd performing calculation evaluation. It is not necessary to calculate all the topology feature values. Thereby reducing computational complexity.
Description 3: the method adopted by the invention for realizing the cost-guaranteed synchronous control of the wireless sensor network under the condition of a given precalculated value is different from the common linear matrix inequality technology, namely, the value range of a feasible solution of the control gain is directly solved. The linear matrix inequality approach requires the use of a FEASP solver in the MATLAB toolbox, so that the existence of no solution is easy to occur. In order to solve the problem, the invention aims to solve the feasible solution range of the control gain, and can directly solve the control gain value according to the range of the control gain analysis solution so as to realize the cost-guaranteed synchronous control of the wireless sensor network.
The following introduces the simulation experiment:
in a wireless sensor network composed of six two-dimensional nodes, a node 1 is taken as a leader node, and the other five nodes are taken as follower nodes. The action topology can be described as a 0-1 weight directed graph, and as shown in fig. 3, the initial state information of six sensor network nodes can be set as: x is the number of 1 (0)＝[4.0,2.1] T ,x 2 (0)＝[5.6,2.1] T ,x 3 (0)＝[3.1,1.2] T ,x 4 (0)＝[5.9,2.7] T ,x 5 (0)＝[4.7,0.9] T ,x 6 (0)＝[8.0,1.7] T 。
The parameters for the cost equation are set as follows, η ═ 0.08, γ 1 ＝0.3，γ 2 0.2. From theorem 2, the control gain K can be obtained 1 And K 2 The value range of (A): k is more than 3.49 1 < 6.12 and 1.19 < k 2 Is less than 2.88. Thus can take k 1 6 and k 2 ＝1.2。
Fig. 4 mainly shows a track diagram of the transmission speed and the storage state difference between the leader and the follower node of the wireless sensor network. Figure 5 shows a linear quadratic optimization index function. From the simulation result, on the premise of giving a precalculated value, the wireless sensor network realizes cost-guaranteed synchronous control.
Claims (6)
1. A wireless sensor network cost-guaranteeing synchronous control method under the condition of a given precalculated value is characterized in that a second-order isomorphic wireless sensor network based on the method is composed of a leader node and N-1 follower nodes, wherein a kinetic model of a jth sensor can be described as follows through a linearization modeling method:
where j ∈ {1,2, …, N }, x j (t) is the network node storage, v j (t) is the packet transmission speed, u j (t) is a control input;
the interaction relation between wireless sensors based on the method is described by a directed graph G, wherein the sensors are represented by jth nodes, action channels between the nodes are represented by edges, and the weight w of the edges ij The laplace matrix of fig. G is defined as L ═ L, representing the interaction weights ji ]In which
l ji ＝-w ji And j is not equal to i;
the method is based on the control theory, and the wireless sensor network cost-guaranteed synchronous control protocol is expressed as follows:
wherein, the first and the second end of the pipe are connected with each other,
in the formula, eta, gamma 1 And gamma 2 To positive definite parameters, J u (t) is a control input energy consumption function, J x (t) is a synchronization performance optimization function, N j A neighbor set for agent j; w is a ij For the interaction weights between network nodes, k 1 And k 2 Is the control gain value; according to the wireless sensor network system (1) and the control protocol (2), and the state difference between the follower sensor node and the leader sensor node, a system state difference mechanical model is obtained as follows:
the method specifically comprises the following implementation steps:
firstly, establishing a sensor network node dynamic model described in a formula (1) based on the structural characteristics of a wireless sensor network;
step two, system parameters eta and gamma under the constraint condition of giving a precalculated value 1 And gamma 2 Setting;
step three, solving the control gain value k in the control protocol (2) 1 And k 2 ；
Step four, judging the network synchronization feasibility, if feasible, continuing to perform the step five, and if not feasible, returning to the step two to perform parameter setting again;
step five, controlling cost keeping value J in the protocol (2) s Solving, and finishing the design of related parameters of network synchronization control;
step six, giving a precalculated value
Verifying the cost synchronization effect under the condition, and obtaining k 1 And k 2 And substituting the result into the system to verify the synchronization effect, the cost-saving effect and the given budget value effect under the condition of the given budget value.
2. The method for controlling synchronization of wireless sensor networks under the condition of a given budget value according to claim 1, wherein in step one, a leader-follower model is built as the wireless sensor network system (1) based on the structural characteristics of the wireless sensor networks.
3. The method for controlling synchronization of guaranteed cost of wireless sensor network under the condition of the given budget value according to claim 2, wherein in the second step, the system parameters are set based on the protocol (2) for controlling synchronization of guaranteed cost of wireless sensor network under the condition of the given budget value.
4. The method for controlling the guaranteed cost synchronization of the wireless sensor network under the condition of the given budget value according to claim 3, wherein the guaranteed cost synchronization can be achieved by the following definition:
for a given budget value
If there is any bounded initial state x j (0) And v j (0) (j-2, 3, …, N), all with k 1 And k 2 So that lim t→∞ (x j (t)-x 1 (t)) -0 and lim t→∞ (v j (t)-v 1 And (t)) -0 (j-2, 3, …, N), the wireless sensor network (1) is said to achieve cost synchronization under the action of the protocol (2) under the condition of a given budget value.
5. The method for controlling synchronization of security cost of wireless sensor network under the condition of given precalculated value according to claim 4, wherein for given η, γ 1 And gamma 2 Positive definite parameter, if k exists 1 And k 2 Then, the wireless sensor network (1) realizes the guaranteed cost synchronization under the action of the protocol (2), and in this case, the guaranteed cost value satisfies the following conditions:
wherein the content of the first and second substances,
6. the method for controlling the cost-guaranteed synchronization of the wireless sensor network under the condition of the given budget value according to claim 4, wherein the given eta and gamma are used for controlling the synchronization 1 And gamma 2 Positive definite parameter sum
If k exists 1 And k 2 Then, the wireless sensing network (1) achieves the guaranteed cost synchronization under the condition of a given precalculated value under the action of the protocol (2), and in this case, the guaranteed cost value meets the following conditions:
wherein, the first and the second end of the pipe are connected with each other,
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