A study on user-input dissemination for wireless sensor networking systems

Abstract

Wireless sensor network (WSN) is a group of spatially dispersed sensors for monitoring the physical conditions of the environment and organizing the collected data at a central location. Since WSNs typically have no infrastructure, one of the challenges in WSNs is the lack of appropriate method for an operator to interact with the WSN. Practical tasks for WSNs require sensor node adaptive to changes in WSN configuration, user input, and commands hence, monitoring and interaction with the WSN is needed. In this paper, a new scheme for configuration dissemination with monitoring of sensor state is proposed to control dynamically sensor node operation in real time. Moreover, a method is provided for the operator to observe the state of the sensor node, which helps the operator provide an appropriate control input to the WSN. We prove the stability properties of the proposed algorithm and show the simulation results.

Keywords

Wireless sensor networks dissemination monitoring of sensor state

1. Introduction

Wireless sensor networks (WSNs) consist of sink nodes and a large number of sensor nodes that coordinate autonomously. These networks are used to monitor physical or environmental conditions like sound, pressure, temperature, and propagate data through the network to a main location. However, sensor nodes are not yet capable of autonomously performing various tasks, and many tasks require coordination between an operator and the WSN. Therefore, the operator needs to recognize the state of WSN and convey parameter adjustments or configuration to the WSN.

One of the prominent works of configuration propagation modeled is SPIN [1]. These researchers focused on the efficient propagation of individual sensor observations to all the sensors and proposed data descriptors to eliminate the chance of redundant transmission in WSNs. Other authors proposed a TDMA-based data dissemination protocol for WSN to offer a degree of reliability [2]. The Firecracker protocol [3] used a combination of routing and broadcast principles to rapidly propagate data throughout WSNs. Trickle [4] was proposed for propagating and maintaining code updates as fast as possible from the operator to all nodes in the network. This protocol used suppression and dynamic adjustment of the broadcast rate to limit transmissions among neighboring nodes. It only provided a mechanism by which a node might decide when to propagate the code. Deluge [5] added a feature that supports transfer of large data objects based on Trickle principles. Still other authors proposed a gossip-based approach where each node decides to forward a message to another node based on some probability [6]. The problem with gossip is that, if a source has very few neighbors, then the nodes will not gossip and the information dies out. Middle-ware has been proposed [7] to provide controlled propagation to tune the process according to the desired reliability. In another case [8], a multi-rumor overwriting (MRO) model was proposed. The model described propagation and interaction of periodically sensed data, which were distributed by gossiping, without increasing the traffic on the network. Walker et al. [9,10] focused on two methods of data propagation (flooding and consensus methods) and compared the ability of operators to manage the system to the desired goals. In the flooding method, each node explicitly matches the value of operator command, and in the consensus method, each node matches the average value of operator command of all the neighbors it senses. In [11], a simple data propagation method with operator intent delivery was proposed, which allows users to interact with the WSNs to convey desired parameter values for the operations.

However, existing works have focused on the conveying the data between each node, but WSN requires an operator to be able to observe the WSN states in response to user input and the effects of control input. This paper proposes an autonomous real-time algorithm for data dissemination. In Sect. 2, we propose a method to properly propagate WSN configuration or user input by indirectly setting parameter within the framework of local rules in a decentralized manner. Based on stability analysis, we show that the proposed algorithm allows the user to observe effectively the state of the sensor node by understanding WSN dynamics. In Sect. 3, we show the superior performance of the proposed method to the consensus approach. Conclusions and future works are discussed in Sect. 4.

2. Proposed algorithm

2.1. Model

We consider a WSN system consisting of $(N - 1)$ sensor nodes, a sink node (Nth node), and an operator. Let $N = {1, 2, \dots, N}$ denote the set of sensor nodes in the WSN. The set of neighboring nodes of sensor node i ( $1 ⩽ i ⩽ N$ ) is denoted as $N_{i}$ ( $\subseteq N$ ) and its cardinality is $N_{i}$ ( $⩽ N$ ). We propose a control model of the WSN system, where for the forward control loop, operator controls the WSN by directly controlling the sink node, which influences propagates to the rest of the sensor nodes based on the control laws each sensor node uses. For the backward control loop, the operator observes the state of the sensor nodes through the sink node that provides feedback regarding the node state. No control can be exerted over individual sensor nodes, only over the WSN as a whole.

To this end, we define the state of the WSN system as $x (t)$ and denote $u (t)$ as the desired configuration set that operator wants to achieve with the WSN system at time t. In specific, $x (t)$ represents the vector of the states of all sensor nodes at time t and can be indicated as vector $x (t) = {[x_{1} (t) x_{2} (t) \dots x_{N} (t)]}^{T}$ , where $x_{i} (t) = {[x_{i}^{1} (t) x_{i}^{2} (t) \dots x_{i}^{n} (t)]}^{T} \in R^{n}$ is the state vector of node i at time t and individual node has n-dimensional state space. The state dynamics of WSN can be defined as: $\begin{matrix} (1) & \dot{x} (t) = f (x (t), u (t)) . \end{matrix}$ The operator interacts with the WSN by applying control input to the sink node, while the other nodes interact with each other following the local control law of each node in the WSN: $\begin{array}{rcl} (2) & {\dot{x}}_{i} (t) & = & \sum_{j \in N_{i}} (x_{j} (t) - x_{i} (t)), \forall i, i \neq N . \end{array}$ The operator gives commands or informs the sink node of parameter change with $u (t) \in R^{n}$ , after which information propagates according to the underlying control law sensor node members use. Let $x_{N}$ be the state of a sink node and the user input is directly applied for the sink node by letting $x_{N} (t) = u (t)$ . Then the dynamic for the sink node is as follows: $\begin{array}{rcl} (3) & {\dot{x}}_{N} (t) & = & 0 . \end{array}$ According to (2)–(3), operator directly controls the state of the single sink node and the interactions between the sensor nodes are handled autonomously. That is, the operator’s intended command is directly conveyed to the sink node and each sensor node averages the states of all neighbors it can sense, and then sets its state vector based on that average state. In this way, the operator takes actions independent of the number of nodes and supervises the WSN as a single entity, resulting in a control complexity of $O (1)$ .

2.2. Stability analysis

In this section, we will analyze the feasibility of the proposed algorithm for an operator to achieve desired WSN configurations. We denote a steady state $x_{s}$ , which is the state where the proposed system under the local control law can asymptotically converge. Let us denote $x_{s} = {[x_{1 s} x_{2 s} \dots x_{N s}]}^{T}$ as a steady state vector $x (t)$ , where $x_{i s} \in R^{n}$ is the steady state of sensor node i. We consider that the desired WSN configuration set $u (t)$ is piecewise constant such that $u (t) ≃ u$ .

From (2), $x_{i s}$ is expressed as: $\begin{array}{rcl} (4) & x_{i s} & = & \frac{1}{N_{i}} (1_{(i, 1)} x_{1 s} + 1_{(i, 2)} x_{2 s} + \dots + 1_{(i, N)} x_{N s}), \forall i \in N, i \neq N, \end{array}$ where $1_{(i, j)}$ is the indication function: $1_{(i, j)} = 1$ indicating $j \in N_{i}$ , otherwise, $1_{(i, j)} = 0$ , therefore $\sum_{\forall j \in N_{i}} 1_{(i, j)} = N_{i}$ : Let ${\tilde{x}}_{s} = {[x_{1 s} x_{2 s} \dots x_{(N - 1) s}]}^{T}$ . Then, (4) is rewritten as $\begin{array}{rcl} (5) & A {\tilde{x}}_{s} = b \end{array}$ where $\begin{array}{rcl} A & = & [\begin{matrix} 1 & - \frac{1}{N_{1}} 1_{(1, 2)} & \dots & - \frac{1}{N_{1}} 1_{(1, N - 1)} \\ - \frac{1}{N_{2}} 1_{(2, 1)} & 1 & \dots & - \frac{1}{N_{2}} 1_{(2, N - 1)} \\ ⋮ & ⋱ & ⋱ & ⋮ \\ - \frac{1}{N_{N - 1}} 1_{(N - 1, 1)} & - \frac{1}{N_{N - 1}} 1_{(N - 1, 2)} & \dots & - \frac{1}{N_{N - 1}} 1_{(N - 1, N - 1)} \end{matrix}], \\ b & = & {[\begin{matrix} \frac{1}{N_{1}} 1_{(1, N)} u & \frac{1}{N_{2}} 1_{(2, N)} u & \dots & \frac{1}{N_{N - 1}} 1_{(N - 1, N)} u \end{matrix}]}^{T} . \end{array}$ Let L is a Laplacian matrix $L = D - A$ where D is the diagonal matrix and $\begin{array}{rcl} (6) & A_{i j} = \{\begin{matrix} 1 & if 1_{(i, j)} = = 1, \\ 0 & otherwise . \end{matrix} \end{array}$ Therefore, the elements of $L$ are given by $\begin{array}{rcl} (7) & L_{i j} = \{\begin{matrix} 1 & if i = = j, \\ - \frac{1}{N_{i}} & if 1_{(i, j)} = = 1, \\ 0 & otherwise . \end{matrix} \end{array}$ Consider a vector $v = {[x_{1}, x_{2}, \dots, x_{N}]}^{T}$ , then we will have the action of L as $\begin{array}{rcl} (8) & {[L v]}_{i} = x_{i} - \frac{1}{N_{i}} \sum_{j \in N_{i}, j \neq i} x_{j} . \end{array}$ We observe that $1 = {[1, \dots, 1]}^{T}$ is an eigenvector of L with eigenvalue 0, since for this vector $x_{i}$ always equals the average of its neighbors’ values.

According to (5), $A$ has a Laplacian matrix such as L and the constant $x_{s}$ are eigenvectors of eigenvalue 0. In the proposed algorithm, the user input is directly applied for the Nth agent, and then we divide two cases: $1_{(i, N)} = 1$ and $1_{(i, N)} = 0$ . In the case of $1_{(i, N)} = 1$ , obviously $x_{N s} = u$ . From (4), we obtain the following: $\begin{array}{rcl} (9) & N_{i} x_{i s} = (N_{i} - 1) x_{i s} + u . \end{array}$ It shows that $x_{i s} = u$ , $\forall i$ . That is, $\begin{array}{rcl} (10) & x_{s} = {[\begin{matrix} u & u & \dots & u \end{matrix}]}^{T} . \end{array}$ In the case of $1_{(i, N)} = 0$ , $\begin{array}{rcl} (11) & \sum_{j \in N_{i}, j \neq N} x_{j s} = N_{i} x_{i s} . \end{array}$ If there exists any j ( $\in N_{i}$ ) with $N \in N_{j}$ , we obtain $x_{i s} = x_{j s}$ . Finally, we get the following conclusion: $\begin{array}{rcl} x_{s} & = & {[\begin{matrix} x_{1 s} & x_{2 s} & \dots & x_{N s} \end{matrix}]}^{T} \\ (12) & = & {[\begin{matrix} u & u & \dots & u \end{matrix}]}^{T} . \end{array}$ Therefore, we conclude that the operator can achieve some configuration described by $u (t)$ with the proposed system.

Next, we need to prove that the proposed system ensures the stability. If the system is asymptotically stable, then the trajectory will converge to the steady state, described in (10) and (12), as time goes to infinity. In order to derive the system stability, we define the following change of coordinates $\begin{array}{rcl} (13) & e_{i} (t) = x_{i} (t) - x_{i s} . \end{array}$ Then, we obtain the following representation of the system: $\begin{array}{rcl} (14) & {\dot{e}}_{i} (t) & = & \sum_{j \in N_{i}} (e_{j} (t) - e_{i} (t)) \\ (15) & = & - N_{i} e_{i} (t) + \sum_{j \in N_{i}} e_{j} (t) . \end{array}$ Defining $e (t) = {[e_{1} (t) e_{2} (t) \dots e_{N - 1} (t)]}^{T}$ , our system can be represented in a matrix form as: $\begin{matrix} (16) & \dot{e} (t) = A_{s} e (t), \end{matrix}$ where $\begin{array}{rcl} A_{s} & = & [\begin{matrix} - N_{1} & 1_{(1, 2)} & \dots & 1_{(1, N - 1)} \\ 1_{(2, 1)} & - N_{2} & \dots & 1_{(2, N - 1)} \\ ⋮ & ⋱ & ⋱ & ⋮ \\ 1_{(N - 1, 1)} & 1_{(N - 1, 2)} & \dots & - N_{N - 1} \end{matrix}] \end{array}$ We use Lyapunov Theory to claim that the system defined by (16) will be convergent if we can find a Lyapunov function $V (e)$ that satisfies the following conditions:

$V (e)$ is positive definite;

$\dot{V} (e)$ is negative definite;

We assume that there exist positive definite matrices P and Q,

P = P^{T}

, such that

\begin{array}{rcl} (17) & P A_{s} + A_{s}^{T} P = - Q . \end{array}

Consider the Lyapunov function in the following form:

\begin{array}{rcl} (18) & V (e) = \frac{1}{2} e^{T} P e . \end{array}

Then, obviously

V (e) ⩾ 0

and we can get the time derivative

\dot{V} (e)

as follows:

\begin{array}{rcl} \dot{V} (e) & = & \frac{1}{2} ({\dot{e}}^{T} P e + e^{T} P \dot{e}) \\ = & \frac{1}{2} e^{T} (A_{s}^{T} P + P A_{s}) e \\ = & - \frac{1}{2} e^{T} Q e ⩽ 0 . \end{array}

Based on the above analysis, both conditions of the Lyapunov function

V (e)

have been satisfied, thus we can claim that the system is stable and the error dynamics will converge to zero exponentially. This result guarantees the autonomous adaptation of sensor node state according to operator-defined WSN configuration, resulting in asynchronous convergence of the WSN to the desired global behavior.

For the state monitoring, the sink node determines the difference between the states of its neighbors and control input as ${\overline{e}}_{N} = u - {\overline{x}}_{N}$ where ${\overline{x}}_{N} = \frac{1}{N_{N}} \sum_{j \in N_{N}} x_{j}$ . The sink node provides feedback the value of ${\overline{e}}_{N}$ to the operator. According to the above stability analysis, we know that the states of all sensor nodes converges to the control input in the steady state, i.e., ${\overline{e}}_{N} = 0$ . Therefore, the operator can be able to learn to understand node states and estimate the timing to give the next configuration inputs, given the feedback from the sink node only.

3. Simulation results

3.1. Configurations

To evaluate the performance of our proposed system, we develop a simulation environment using MATLAB. The simulation area is 100 m × 100 m, where the entire network is divided into equally shaped grids, and the sensor nodes are uniformly deployed. We set $N = 50$ , and the sensor nodes are arbitrary connected. The sink node is denoted as $R_{50}$ , which is chosen randomly by the operator. The channel capacity is set to 200 kbps, the transmission range and carrier sense range to 20 m and 40 m, respectively.

3.2. Results

Fig. 1.

Time trajectories of state of 10 nodes with $u = {[4, 4]}^{T}$ indicated as ∙. The initial state of each node is indicated as ×.

We compared the performance of the proposed method with the consensus method [9]. The consensus algorithm is an asynchronous distributed protocol for distributed averaging, which aims to compute the average $\bar{x} = \sum_{i = 1}^{N} x_{i} / N$ . Each member in a system averages the values of all of its neighbors, and adapts its own value toward that average.

Figure 1 shows the trajectories of states of 10 among 50 nodes ( $R_{1}, R_{2}, \dots, R_{10}$ ). The initial state of each node is set differently and indicated as ×. The configuration input is given by the operator, such as $u = {[4, 4]}^{T} \in R^{2}$ , indicated as ∙. Simulations are conducted over the interval from 0 to 40 s in 100 ms increments. Results indicate that the state of each node is autonomously adapted and converged to the configuration input given by the operator.

Fig. 2.

Time trajectories of state of $R_{1}$ , $R_{2}$ , and $R_{3}$ without error: (a) consensus method and (b) proposed method.

Fig. 3.

Time trajectories of state of $R_{1}$ , $R_{2}$ , and $R_{3}$ with error: (a) consensus method and (b) proposed method.

Figures 2–3 illustrate time trajectories of node states when the command input remains constant during runtime. The input is given by the operator, such as $u = 4$ . Simulations are conducted over the interval from 0 to 5 s in 100 ms increments. Randomly chosen are 3 out of 49 nodes, namely, $R_{1}$ , $R_{2}$ , and $R_{3}$ . To show the performance of controlling state of each node, we set the initial state for each differently. Figure 2(a), (b) illustrates the state change with the consensus method and the proposed one in a condition without error. Both the consensus and the proposed methods converge the states of all sensor nodes to the desired state u despite the difference in initial states of each node. As for the time taken to converge to the configuration by the operator, the consensus method is a bit faster, but both methods show similar performance for the error-free condition.

Figure 3(a), (b) illustrates the state change of nodes in an error condition. The error condition is implemented so that the state value of $R_{2}$ is not updated between 0.5 and 2 s due to the malfunction of $R_{2}$ . During $[0.5, 2]$ s, $R_{2}$ exchanges the last updated state value with its neighbor sensor nodes. Both methods show that the state values of all nodes converge to the desired state after 3 s. However, for the consensus method, the malfunction of $R_{2}$ directly affects the state values of the neighboring nodes during $[0.5, 2]$ s. That is, in the consensus method, the state value of each node is sensitive to changes in its neighbor nodes’ states, so there is a large difference in state values between nodes. On the other hand, the proposed method shows that the wrong behavior of $R_{2}$ does not have a significant effect on the state control of other nodes. As can be seen from (2), each node indirectly uses the state of neighboring nodes in adjusting its state values, which leads to be less susceptible to error conditions and more robust performance.

Fig. 4.

State adaptation according to user input change during runtime: (a) consensus method and (b) proposed method.

Next, we examine the trajectories of states corresponding to control input changes during the runtime. Simulations are conducted over the interval from 0 to 20 s in 100 ms increments. The configuration input is initially set to $u = 2$ and changed to $u = 4$ at 10 s. The error condition is implemented so that the state value of $R_{2}$ is not updated during $[0.5, 2]$ s and $[10.5, 12]$ s. Figure 4(a), (b) shows the state adaptation behavior for consensus method and the proposed method according to control input changes. As shown in Fig. 4(a), the consensus method shows that the state values of $R_{1}$ and $R_{3}$ are largely affected by the state value of $R_{2}$ during the malfunction period, and the difference of the state values of each node remains large. For the proposed method, the state change between the nodes is not large despite the malfunction of $R_{2}$ and it is adapted successfully according to the desired configuration. In Fig. 4(b), the dashed trajectory ${\overline{e}}_{50}$ belongs to $R_{50}$ controlled by the operator. The operator can estimate the state of the WSN through the value of ${\overline{e}}_{50}$ of $R_{50}$ , which helps in properly determining the timing for the next configuration input. The fact that the value of ${\overline{e}}_{50}$ is close to 0 reflects the convergence of the WSN configuration to the control input. Therefore, the operator obtains the appropriate timing to tune the next configuration command to the WSN system by observing the value ${\overline{e}}_{50}$ of the sink node.

4. Conclusions

This paper presents a scheme of configuration dissemination for WSN systems. The operator interacts with the sensor nodes by applying user input to a single sink node while the other nodes interact with each other according to the proposed dynamics. The proposed scheme properly influences the WSN operation by propagating the operator input to the rest of the sensor nodes based on the control laws of each node. The operator can effectively observe the state of the WSN by understanding dynamics and estimate the timing for the next control inputs, such is based on the feedback of the sink node only. An important area for further study includes selection of a sink node which influences dissemination to the rest of the sensor nodes, and system modeling with moving nodes in the WSN. In this study, the sink node provides feedback to the operator for the state estimation in the network. Then, the operator can be able to learn to understand node states and estimate the timing to give the next configuration inputs. However, this study assumed that the state values at a particular node represent the state of the entire system, so it might be different from the actual situation. In the next study, it needs to be extended in such a way that the state of the entire system can be predicted.

Footnotes

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2017R1A2B1007779).

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