CN110611927B - Wireless sensor network guaranteed cost synchronous control method under given budget value condition - Google Patents

Abstract

Translated fromChinese

本发明公开了一种给定预算值条件下无线传感网络保成本同步控制方法，该方法基于的二阶同构无线传感器网络由一个领导者节点和N‑1个跟随者节点组成的，该方法基于的无线传感器之间的相互作用关系由一个有向图G描述，其中传感器由第j个节点表示，节点之间的作用通道由边表示，边权重w_ij代表相互作用权重；最后，根据无线传感器网络系统(1)和控制协议(2)，以及跟随者传感器节点和领导者传感器节点之间的状态差，得到系统状态差动力学模型。本发明通过设计给定预算值条件下无线传感网络保成本同步控制协议，求解出网络保成本同步控制判据，最后设计出给定预算值条件下网络保成本同步控制方法。

The invention discloses a guaranteed cost synchronization control method for a wireless sensor network under the condition of a given budget value. The second-order isomorphic wireless sensor network based on the method is composed of a leader node and N-1 follower nodes. The interaction relationship between the wireless sensors on which the method is based is described by a directed graph G, in which the sensor is represented by the jth node, the action channel between the nodes is represented by an edge, and the edge weight w_ij represents the interaction weight; finally, 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, obtain the dynamic model of the system state difference. The invention solves the network guaranteed cost synchronization control criterion by designing the wireless sensor network guaranteed cost synchronization control protocol under the given budget value condition, and finally designs the network guaranteed cost synchronization control method under the given budget value condition.

Description

Translated fromChinese

一种给定预算值条件下无线传感网络保成本同步控制方法A synchronous control method for guaranteed cost of wireless sensor network under the condition of given budget value

技术领域technical field

本发明属于多智能体系统分布式优化控制方法应用技术领域，具体涉及一种给定预算值条件下无线传感网络保成本同步控制方法。The invention belongs to the application technical field of a distributed optimization control method for a multi-agent system, and in particular relates to a synchronous control method for guaranteed cost of a wireless sensor network under the condition of a given budget value.

背景技术Background technique

近年来，由于网络拥塞引起的网络性能的下降以及对于网络传输速度和传输性能的更高要求，无线传感器网络同步问题受到了广大研究者的关注。作为信息传输交流媒介，无线传感器网络通常包含有一个目的节点和许多资源节点，其中，资源节点在对环境信息进行收集后并将其传送到目的节点。在传输的过程中，资源节点将搜集到的信息直接或者间接的传送到目的节点，基于此结构，将该网络可设为领导者、跟随者结构。在此结构模型下，一对多的交流模式由于有限的带宽和存储空间容易导致网络拥塞的发生，因此在实际应用中，无线传感器节点的某些性能需要达到同步从而抑制网络拥塞的产生。In recent years, due to the decline of network performance caused by network congestion and the higher requirements for network transmission speed and transmission performance, the synchronization problem of wireless sensor networks has attracted the attention of many researchers. As an information transmission and exchange medium, a wireless sensor network usually includes a destination node and many resource nodes, wherein the resource nodes collect environmental information and transmit it to the destination node. In the process of transmission, the resource node will directly or indirectly transmit the collected information to the destination node. Based on this structure, the network can be set as a leader and follower structure. Under this structural model, the one-to-many communication mode is easy to cause network congestion due to limited bandwidth and storage space. Therefore, in practical applications, some performances of wireless sensor nodes need to be synchronized to suppress network congestion.

在实际的无线传感器网络中，通常网络节点配备一定的电池能量，由于室外空间的限制，更换电池存在一定的难度。因此，如何延长电池的寿命，实现能量消耗和同步管理性能的折中设计是一个重要的研究方向。目前已经有诸多研究如何优化能量消耗的文章。在这些研究中，不同的成本方程被建模成优化或者次优化问题。同时，这些控制策略通常只考虑了同步性能表现或者只考虑同步控制消耗，将两者都纳入评价范围的同步控制策略比较少见。另外，将有限的电池能量设定为有限能量预算值也是一个比较新的研究思路。In the actual wireless sensor network, usually the network node is equipped with a certain amount of battery energy. Due to the limitation of outdoor space, it is difficult to replace the battery. Therefore, how to prolong the battery life and achieve a compromise design between energy consumption and synchronization management performance is an important research direction. There have been many articles on how to optimize energy consumption. In these studies, different cost equations are modeled as optimization or suboptimization problems. At the same time, these control strategies usually only consider the synchronization performance or only the synchronization control consumption, and the synchronization control strategies that both are included in the evaluation scope are relatively rare. In addition, it is also a relatively new research idea to set the limited battery energy as the limited energy budget value.

现有的关于无线传感网络同步控制方法方面的研究，大多数基于线性矩阵不等式技术，通过利用MATLAB工具包中的可行性求解器，进行判断是否存在使得无线传感网实现网络同步的控制增益值的存在，当无线网节点数量过于强大时，会因为数据处理过于复杂而增加计算复杂度。此外，从目前已有的研究成果来看，存在诸多用于实现优化控制的方法，然而很少综合考虑同步性能优化和控制输入优化问题，即保成本同步控制问题。同时，由于存在着网络节点携带电池能量有限以及由于场地原因难于更换电池设备的现实问题，有限能量条件下的网络保成本同步控制问题亟待考虑。Most of the existing researches on synchronization control methods for wireless sensor networks are based on linear matrix inequality technology. By using the feasibility solver in the MATLAB toolkit, it is judged whether there is a control gain that enables wireless sensor networks to achieve network synchronization. The existence of the value, when the number of wireless network nodes is too powerful, will increase the computational complexity because the data processing is too complicated. In addition, according to the existing research results, there are many methods for realizing optimal control, however, the synchronization performance optimization and control input optimization problems are rarely considered comprehensively, that is, the guaranteed cost synchronization control problem. At the same time, due to the fact that the battery energy carried by network nodes is limited and it is difficult to replace battery equipment due to site reasons, the problem of synchronization control of network guarantee costs under the condition of limited energy needs to be considered urgently.

发明内容SUMMARY OF THE INVENTION

本发明的目的就在于为了解决上述问题而提供一种给定预算值条件下无线传感网络保成本同步控制方法，设计给定预算值条件下无线传感网络保成本同步控制协议，求解出网络保成本同步控制判据，最后设计出给定预算值条件下网络保成本同步控制方法。The purpose of the present invention is to provide a synchronous control method for guaranteed cost of wireless sensor network under the condition of given budget value in order to solve the above problem, to design the synchronous control protocol of guaranteed cost of wireless sensor network under the condition of given budget value, and to solve the network Based on the guaranteed cost synchronization control criterion, a network guaranteed cost synchronization control method under the given budget value is designed.

本发明通过以下技术方案来实现上述目的：The present invention realizes above-mentioned purpose through following technical scheme:

一种给定预算值条件下无线传感网络保成本同步控制方法，该方法基于的二阶同构无线传感器网络由一个领导者节点和N-1个跟随者节点组成的，其中第j个传感器的动力学模型可通过线性化建模方法描述如下：A guaranteed cost synchronization control method for wireless sensor networks under a given budget The kinetic model of can be described by a linearized modeling approach as follows:

其中，j∈{1,2,…,N}，x_j(t)是网络节点存储量，v_j(t)是数据包传输速度，u_j(t)是控制输入；Among them, j∈{1,2,…,N}, x_j (t) is the storage capacity of the network node, v_j (t) is the data packet transmission speed, and u_j (t) is the control input;

该方法基于的无线传感器之间的相互作用关系由一个有向图G描述，其中传感器由第j个节点表示，节点之间的作用通道由边表示，边权重w_ij代表相互作用权重，将图G的拉普拉斯矩阵定义为L＝[l_ji]，其中l_jj＝∑_i∈Njw_ji，l_ji＝-w_ji，且j≠i；The interaction relationship between the wireless sensors on which the method is based is described by a directed graph G, in which the sensor is represented by the jth node, the action channel between the nodes is represented by an edge, and the edge weight w_ij represents the interaction weight. The Laplace matrix of G is defined as L=[l_ji ], where l_jj =∑_i∈Nj w_ji , l_ji =-w_ji , and j≠i;

该方法基于的控制理论的无线传感网络保成本同步控制协议表示如下：The guaranteed cost synchronization control protocol of wireless sensor network based on the control theory of this method is expressed as follows:

其中，in,

式中，η、γ₁和γ₂正定参数，J_u(t)为控制输入能量消耗函数，J_x(t)为同步性能优化函数，N_j为智能体j的邻居集；w_ij为网络节点之间相互作用权重，k₁和k₂是控制增益值；根据无线传感器网络系统(1)和控制协议(2)，以及跟随者传感器节点和领导者传感器节点之间的状态差，得到系统状态差动力学模型如下：In the formula, η, γ₁ and γ₂ are positive definite parameters,_Ju (t) is the control input energy consumption function, J_x (t) is the synchronization performance optimization function, N_j is the neighbor set of the agent j; w_ij is the network The interaction weight between nodes, k₁ and k₂ are the control gain values; according to the wireless sensor network system (1) and control protocol (2), and the state difference between the follower sensor node and the leader sensor node, the system is obtained The state difference dynamic model is as follows:

本发明进一步的改进在于，该方法具体包括如下实现步骤：A further improvement of the present invention is that the method specifically includes the following implementation steps:

步骤一、基于无线传感网络的结构特征建立领导者-跟随者模型；Step 1. Establish a leader-follower model based on the structural characteristics of the wireless sensor network;

步骤二、给定预算值条件下系统参数设定；Step 2. System parameter setting under the condition of given budget value;

步骤三、求解控制增益数值；Step 3, solve the control gain value;

步骤四、网络同步可行性判断，若可行，继续进行步骤五，若不可行，返回步骤二重新进行参数设定；Step 4: Judging the feasibility of network synchronization, if feasible, continue to step 5, if not, return tostep 2 to re-set parameters;

步骤五、保成本值求解，网络同步控制相关参数设计完毕；Step 5. The guaranteed cost value is solved, and the design of the relevant parameters of the network synchronization control is completed;

步骤六、给定预算值条件下保成本同步效果验证，将求得的k₁和k₂代入系统中，验证给定预算值条件下同步效果、保成本效果及给定预算值效果。Step 6: Verify the synchronization effect of guaranteed cost under the condition of a given budget value. Substitute the obtained k₁ and k₂ into the system to verify the synchronization effect, the effect of guaranteed cost and the effect of a given budget value under the condition of a given budget value.

本发明进一步的改进在于，在第一步中，基于无线传感网络的结构特征建立领导者-跟随者模型为无线传感器网络系统(1)。A further improvement of the present invention is that, in the first step, a leader-follower model is established based on the structural features of the wireless sensor network as the wireless sensor network system (1).

本发明进一步的改进在于，在第二步中，基于给定预算值条件下无线传感网络保成本同步控制协议(2)，对系统参数设定。A further improvement of the present invention is that, in the second step, the system parameters are set based on the wireless sensor network guaranteed cost synchronization control protocol (2) under the condition of a given budget value.

本发明进一步的改进在于，可实现保成本同步的定义如下：A further improvement of the present invention is that the definition of the synchronization of guaranteed costs that can be realized is as follows:

对于给定的预算值

如果对任意有界初始状态x_j(0)和v_j(0)(j＝2,3,…,N)，都存在k₁和k₂，使得lim_t→∞(x_j(t)-x₁(t))＝0和lim_t→∞(v_j(t)-v₁(t))＝0(j＝2,3,…,N)，那么称无线传感网络(1)在协议(2)的作用下实现了给定预算值条件下保成本同步。for a given budget value

If for any bounded initial state x_j (0) and v_j (0) (j=2,3,...,N), k₁ and k₂ exist such that lim_t→∞ (x_j (t)- x₁ (t))=0 and lim_t→∞ (v_j (t)-v₁ (t))=0 (j=2,3,...,N), then the wireless sensor network (1) is said to be in Under the action of protocol (2), the guaranteed cost synchronization is realized under the condition of given budget value.

本发明进一步的改进在于，对于给定的η、γ₁和γ₂正定参数，如果存在k₁和k₂，那么无线传感网络(1)在协议(2)的作用下实现了保成本同步，在此情况下，保成本值满足：A further improvement of the present invention is that, for given positive definite parameters of η, γ₁ and γ₂ , if k₁ and k₂ exist, then the wireless sensor network (1) realizes guaranteed cost synchronization under the action of protocol (2). , in this case, the guaranteed cost value satisfies:

其中，in,

本发明进一步的改进在于，对于给定的η、γ₁和γ₂正定参数和

如果存在k₁和k₂，那么无线传感网络(1)在协议(2)的作用下实现了给定预算值条件下保成本同步，在此情况下，保成本值满足：A further improvement of the present invention is that for given η, γ₁ and γ₂ positive definite parameters and

If there are k₁ and k₂ , then the wireless sensor network (1) realizes the guaranteed cost synchronization under the condition of the given budget value under the action of the protocol (2). In this case, the guaranteed cost value satisfies:

其中，in,

本发明具有如下有益的技术效果：The present invention has following beneficial technical effect:

1、本发明求取了无线传感器网络同步控制增益的显示的解析解，即基于控制增益的值范围，通过选取控制增益可以使得无线传感器网络达到同步，该显示表达式有效解决了可能存在控制增益值不存在的问题，并且无需借助于线性矩阵不等式技术进行求解。1. The present invention obtains an analytical solution for the display of the synchronization control gain of the wireless sensor network, that is, based on the value range of the control gain, the wireless sensor network can be synchronized by selecting the control gain. value does not exist and can be solved without resorting to linear matrix inequality techniques.

2、本发明考虑了实际的无线传感器网络由于室外空间的限制，更换电池存在一定的难度，故将节点配备有限的电池能量考虑为有限的能量预算。从而实现能量消耗和同步管理性能的折中设计，并且有效延长无线传感器网络电池的使用寿命。2. The present invention considers that the actual wireless sensor network has a certain difficulty in replacing the battery due to the limitation of outdoor space, so the limited battery energy equipped with nodes is considered as a limited energy budget. Thus, the compromise design of energy consumption and synchronization management performance is realized, and the service life of the wireless sensor network battery is effectively extended.

附图说明Description of drawings

图1是无线传感网络保成本同步控制图形摘要；Figure 1 is a graphical summary of the guaranteed cost synchronization control of wireless sensor networks;

图2是无线传感网络保成本同步控制算法流程图；Fig. 2 is the flow chart of the wireless sensor network guaranteed cost synchronization control algorithm;

图3是无线传感网络通信拓扑图；Fig. 3 is a wireless sensor network communication topology diagram;

图4是无线传感网络节点存储量和传输速度状态差轨迹图；其中图4(a)是存储量状态差，图4(b)是传输速度状态差；Figure 4 is a trajectory diagram of the state difference between storage capacity and transmission speed of wireless sensor network nodes; Figure 4(a) is the state difference in storage capacity, and Figure 4(b) is the state difference in transmission speed;

图5是无线传感网络节点成本函数状态轨迹图。Figure 5 is the state trajectory diagram of the cost function of the wireless sensor network node.

具体实施方式Detailed ways

下面将结合本发明实施例中，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

1、系统动力学模型和控制协议1. System dynamics model and control protocol

该方法基于的二阶同构无线传感器网络由一个领导者节点和N-1个跟随者节点组成的，其中第j(j∈{1,2,…,N})个传感器的动力学模型可通过线性化建模方法描述如下：The second-order isomorphic wireless sensor network based on this method consists of a leader node and N-1 follower nodes, where the dynamic model of the j(j∈{1,2,…,N})th sensor can be The linearization modeling method is described as follows:

其中，x_j(t)是网络节点存储量，v_j(t)是数据包传输速度，u_j(t)是控制输入。w_ij为网络节点之间相互作用权重，k₁和k₂是控制增益值。Among them, x_j (t) is the storage capacity of the network node, v_j (t) is the data packet transmission speed, and u_j (t) is the control input. w_ij is the interaction weight between network nodes, and k₁ and k₂ are the control gain values.

该方法基于的无线传感器之间的相互作用关系由一个有向图G描述，其中传感器由第j个节点表示，节点之间的作用通道由边表示，边权重w_ij代表相互作用权重，将图G的拉普拉斯矩阵定义为L＝[l_ji]，其中l

l_ji＝-w_ji(j≠i).The interaction relationship between the wireless sensors on which the method is based is described by a directed graph G, in which the sensor is represented by the jth node, the action channel between the nodes is represented by an edge, and the edge weight w_ij represents the interaction weight. The Laplace matrix of G is defined as L=[l_ji ], where l

l_ji =-w_ji (j≠i).

该方法基于的控制理论的无线传感网络保成本同步控制协议表示如下：The guaranteed cost synchronization control protocol of wireless sensor network based on the control theory of this method is expressed as follows:

其中，in,

式中，η、γ₁和γ₂正定参数，J_u(t)为控制输入能量消耗函数，J_x(t)为同步性能优化函数，N_j为智能体j的邻居集。J_u(t)为控制输入的一个二次型函数的时间积分，其描述了系统从实施控制到实现网络同步过程中的控制消耗能量函数；性能优化函数J_x(t)为节点状态差的一个二次型函数的时间积分，其描述了系统从开始到同步过程中，状态差二次型函数的一个累计值，也就是控制过程中控制性能的一个量化值，实现了网络同步过程中控制的性能优化。根据无线传感器网络系统(1)和控制协议(2)，以及跟随者传感器节点和领导者传感器节点之间的状态差，可得到系统状态差动力学模型如下：In the formula, η, γ₁ and γ₂ are positive definite parameters,_Ju (t) is the control input energy consumption function, J_x (t) is the synchronization performance optimization function, and N_j is the neighbor set of agent j. Ju (t) is the time integral of a quadratic function of the control input, which describes the control energy consumption function of the system from the implementation of control to the realization of network synchronization; the performance optimization function J_x (_t ) is the node state difference. The time integral of a quadratic function, which describes a cumulative value of the quadratic function of the state difference from the start to the synchronization process of the system, that is, a quantified value of the control performance in the control process, realizes the control in the network synchronization process. performance optimization. According to the wireless sensor network system (1) and the control protocol (2), as well as the state difference between the follower sensor node and the leader sensor node, the dynamic model of the system state difference can be obtained as follows:

说明1：本发明构建的无线传感器网络控制协议有以下两个特征。第一点是区别于一般的利用传感器节点全局的状态信息，本协议利用无线传感器节点之间的部分状态差信息构建控制协议。第二点是本协议加入了同时包括实现网络同步过程中的控制消耗能量函数和控制过程中同步性能的量化值，在考虑到实际系统能量有限的前提下，实现二者的折中设计，从而优化无线传感器网络的能量优化。Description 1: The wireless sensor network control protocol constructed by the present invention has the following two characteristics. The first point is that, different from the general use of the global state information of sensor nodes, this protocol uses part of the state difference information between wireless sensor nodes to construct a control protocol. The second point is that this protocol includes both the control energy consumption function in the process of realizing network synchronization and the quantified value of synchronization performance in the control process. Considering the limited energy of the actual system, a compromise design between the two is realized, so that Optimizing energy optimization for wireless sensor networks.

2、无线传感器网络保成本同步控制算法2. Wireless sensor network guaranteed cost synchronization control algorithm

该方法包括如下步骤：The method includes the following steps:

步骤一、基于无线传感网络的结构特征建立领导者-跟随者模型；在第一步中，基于无线传感网络的结构特征建立领导者-跟随者模型为：Step 1: Establish a leader-follower model based on the structural characteristics of the wireless sensor network; in the first step, establish a leader-follower model based on the structural characteristics of the wireless sensor network as follows:

式中，j＝1,2,…,N为无线传感网络节点，x_j(t)是网络节点存储量，v_j(t)是数据包传输速度，u_j(t)是控制输入。In the formula, j=1,2,...,N is the wireless sensor network node, x_j (t) is the storage capacity of the network node, v_j (t) is the data packet transmission speed, and u_j (t) is the control input.

步骤二、给定预算值条件下系统参数设定；在第二步中，协议(2)如下：Step 2. System parameter setting under the condition of given budget value; in the second step, the protocol (2) is as follows:

如图1和图2所示，给定预算值条件下无线传感网络保成本同步控制协议描述如下：As shown in Figure 1 and Figure 2, the guaranteed cost synchronization control protocol for wireless sensor networks under the given budget value is described as follows:

其中，in,

式中，η、γ₁和γ₂正定参数，J_u(t)为控制输入能量消耗函数，J_x(t)为同步性能优化函数，N_j为智能体j的邻居集。w_ij为网络节点之间相互作用权重，k₁和k₂是控制增益值。J_u(t)为控制输入的一个二次型函数的时间积分，其描述了系统从实施控制到实现网络同步过程中的控制消耗能量函数；性能优化函数J_x(t)为节点状态差的一个二次型函数的时间积分，其描述了系统从开始到同步过程中，状态差二次型函数的一个累计值，也就是控制过程中控制性能的一个量化值，实现了网络同步控制的性能优化。In the formula, η, γ₁ and γ₂ are positive definite parameters,_Ju (t) is the control input energy consumption function, J_x (t) is the synchronization performance optimization function, and N_j is the neighbor set of agent j. w_ij is the interaction weight between network nodes, and k₁ and k₂ are the control gain values. Ju (t) is the time integral of a quadratic function of the control input, which describes the control energy consumption function of the system from the implementation of control to the realization of network synchronization; the performance optimization function J_x (_t ) is the node state difference. The time integral of a quadratic function, which describes a cumulative value of the quadratic function of the state difference from the start to the synchronization process of the system, that is, a quantitative value of the control performance in the control process, realizes the performance of network synchronization control optimization.

步骤三、求解控制增益数值；Step 3, solve the control gain value;

步骤四、网络同步可行性判断，若可行，继续进行步骤五，若不可行，返回步骤二重新进行参数设定；Step 4: Judging the feasibility of network synchronization, if feasible, continue to step 5, if not, return tostep 2 to re-set parameters;

步骤五、保成本值求解，网络同步控制相关参数设计完毕；Step 5. The guaranteed cost value is solved, and the design of the relevant parameters of the network synchronization control is completed;

步骤六、给定预算值条件下保成本同步效果验证，将求得的k₁和k₂代入系统中，验证给定预算值条件下同步效果、保成本效果及给定预算值效果。Step 6: Verify the synchronization effect of guaranteed cost under the condition of a given budget value. Substitute the obtained k₁ and k₂ into the system to verify the synchronization effect, the effect of guaranteed cost and the effect of a given budget value under the condition of a given budget value.

可实现保成本同步的定义如下：The definition of achievable guaranteed cost synchronization is as follows:

对于给定的预算值

如果对任意有界初始状态x_j(0)和v_j(0)(j＝2,3,…,N)，都存在k₁和k₂，使得lim_t→∞(x_j(t)-x₁(t))＝0和lim_t→∞(v_j(t)-v₁(t))＝0(j＝2,3,…,N)，那么称无线传感网络(1)在协议(2)的作用下实现了给定预算值条件下保成本同步。for a given budget value

If for any bounded initial state x_j (0) and v_j (0) (j=2,3,...,N), k₁ and k₂ exist such that lim_t→∞ (x_j (t)- x₁ (t))=0 and lim_t→∞ (v_j (t)-v₁ (t))=0 (j=2,3,...,N), then the wireless sensor network (1) is said to be in Under the action of protocol (2), the guaranteed cost synchronization is realized under the condition of given budget value.

对于给定的η、γ₁和γ₂正定参数，如果存在k₁和k₂，那么无线传感网络(1)在协议(2)的作用下实现了保成本同步，在此情况下，保成本值满足For the given positive definite parameters of η, γ₁ and γ₂ , if k₁ and k₂ exist, then the wireless sensor network (1) achieves guaranteed-cost synchronization under the action of protocol (2). The cost value is satisfied

其中，in,

对于给定的η、γ₁和γ₂正定参数和

如果存在k₁和k₂，那么无线传感网络(1)在协议(2)的作用下实现了给定预算值条件下保成本同步，在此情况下，保成本值满足For given η, γ₁ and γ₂ positive definite parameters and

If there are k₁ and k₂ , then the wireless sensor network (1) realizes the guaranteed cost synchronization under the condition of the given budget value under the action of the protocol (2). In this case, the guaranteed cost value satisfies

其中，in,

说明2：本发明对于实现给定预算值条件下无线传感器网络的保成本同步控制，在求解控制增益的值范围过程中存在困难。控制增益之间存在耦合关系，因此针对此问题，本发现运用二次型函数不等式性质以及函数的单调特性，将控制增益进行解耦处理，分离两个控制增益K₁和K₂，并分别求出控制增益K₁和K₂的取值范围。此外，控制增益K₁和K₂的取值范围仅仅依赖于拉普拉斯矩阵的非零最小特征值和最大特征值。为了进一步降低计算复杂度，非零最小特征值和最大特征值可以根据现有文献提供的方法进行计算评估。因此没有必要算出所有的拓扑图特征值。从而降低计算复杂度。Description 2: The present invention has difficulties in solving the value range of the control gain for realizing the guaranteed cost synchronization control of the wireless sensor network under the condition of a given budget value. There is a coupling relationship between the control gains. Therefore, in order to solve this problem, we use the quadratic function inequality property and the monotonic characteristic of the function to decouple the control gains, separate the two control gains K₁ and K₂ , and find them respectively. out the value range_of the control gains K1 and_K2 . In addition, the value range_of the control gains K1 and K2 only depends_on the non-zero minimum and maximum eigenvalues of the Laplacian matrix. To further reduce the computational complexity, the non-zero minimum and maximum eigenvalues can be evaluated computationally according to the methods provided in the existing literature. Therefore, it is not necessary to calculate all the topological map eigenvalues. Thereby reducing the computational complexity.

说明3：本发明对于实现给定预算值条件下无线传感器网络的保成本同步控制采用的方法与一般线性矩阵不等式技术不同，即直接求解出了控制增益的可行解的值范围。线性矩阵不等式方法需要借助于MATLAB工具箱中FEASP求解器，从而容易出现存在无解的情况。针对该问题，本发明致力于求解出控制增益的可行解范围，根据控制增益解析解的范围，可以直接求出控制增益值实现无线传感器网络的保成本同步控制。Description 3: The method adopted by the present invention for realizing the guaranteed cost synchronization control of wireless sensor network under the condition of a given budget value is different from the general linear matrix inequality technology, that is, the value range of the feasible solution of the control gain is directly solved. The linear matrix inequality method requires the help of the FEASP solver in the MATLAB toolbox, so it is easy to have no solution. Aiming at this problem, the present invention is devoted to solving the feasible solution range of the control gain. According to the range of the analytical solution of the control gain, the control gain value can be directly obtained to realize the guaranteed cost synchronization control of the wireless sensor network.

下面对仿真实验进行介绍：The simulation experiment is introduced as follows:

在一个的由六个二维节点构成的无线传感器网络中，设节点1为领导者节点，其他五个节点为跟随者节点。其作用拓扑可描述为0-1权重有向图，如图3所示，六个传感器网络节点的初始状态信息可设置为：x₁(0)＝[4.0,2.1]^T,x₂(0)＝[5.6,2.1]^T,x₃(0)＝[3.1,1.2]^T,x₄(0)＝[5.9,2.7]^T,x₅(0)＝[4.7,0.9]^T,x₆(0)＝[8.0,1.7]^T。In a wireless sensor network composed of six two-dimensional nodes, setnode 1 as the leader node, and the other five nodes as follower nodes. Its function topology can be described as a 0-1 weighted directed graph. As shown in Figure 3, the initial state information of the six sensor network nodes can be set as: x₁ (0)=[4.0, 2.1]^T , x₂ (0 )=[5.6,2.1]^T ,x₃ (0)=[3.1,1.2]^T ,x₄ (0)=[5.9,2.7]^T ,x₅ (0)=[4.7,0.9]^T ,x₆ (0)=[8.0,1.7]^T .

对于成本方程的参数设置如下，η＝0.08,γ₁＝0.3，γ₂＝0.2。根据定理2，可以求出控制增益K₁和K₂的取值范围：3.49＜k₁＜6.12和1.19＜k₂＜2.88。因而可以取k₁＝6和k₂＝1.2。The parameters for the cost equation are set as follows, η=0.08, γ₁ =0.3, γ₂ =0.2. According toTheorem 2, the value ranges of the control gains K₁ and K₂ can be obtained: 3.49<k₁ <6.12 and 1.19<k₂ <2.88. Thus k₁ =6 and k₂ =1.2 can be taken.

图4主要给出了无线传感器网络领导者与跟随者节点之间传输速度以及存储量状态差轨迹图。图5给出了线性二次型优化指标函数。从仿真结果来看，在给定预算值的前提下，无线传感器网络实现了保成本同步控制。Figure 4 mainly shows the trajectory diagram of the transmission speed and the state difference of the storage capacity between the leader and the follower node of the wireless sensor network. Figure 5 shows the linear quadratic optimization index function. From the simulation results, under the premise of a given budget value, the wireless sensor network realizes the guaranteed cost synchronization 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,

in the formula, eta, gamma₁ And gamma₂ 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, k₁ And k₂ 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 value₁ And gamma₂ Setting;

step three, solving the control gain value k in the control protocol (2)₁ And k₂ ；

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 k₁ And k₂ 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 k₁ And k₂ So that lim_t→∞ (x_j (t)-x₁ (t)) -0 and lim_t→∞ (v_j (t)-v₁ 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, γ₁ And gamma₂ Positive definite parameter, if k exists₁ And k₂ 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,

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 synchronization₁ And gamma₂ Positive definite parameter sum

If k exists₁ And k₂ 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,

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