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Topology control is an important technique to improve the connectivity and the reliability of Wireless Sensor Networks (WSNs) by means of adjusting the communication range of wireless sensor nodes. In this paper, a novel Fuzzy-logic Topology Control (FTC) is proposed to achieve any desired average node degree by adaptively changing communication range, thus improving the network connectivity, which is the main target of FTC. FTC is a fully localized control algorithm, and does not rely on location information of neighbors. Instead of designing membership functions and if-then rules for fuzzy-logic controller, FTC is constructed from the training data set to facilitate the design process. FTC is proved to be accurate, stable and has short settling time. In order to compare it with other representative localized algorithms (NONE, FLSS, k-Neighbor and LTRT), FTC is evaluated through extensive simulations. The simulation results show that: firstly, similar to k-Neighbor algorithm, FTC is the best to achieve the desired average node degree as node density varies; secondly, FTC is comparable to FLSS and k-Neighbor in terms of energy-efficiency, but is better than LTRT and NONE; thirdly, FTC has the lowest average maximum communication range than other algorithms, which indicates that the most energy-consuming node in the network consumes the lowest power.

Topology control has been proposed as a technique to address many problems in networks by adding or deleting nodes/links according to certain algorithms/protocols, with the aim of obtaining expected network properties. In Wireless Sensor Networks (WSNs), the topology control is usually achieved by means of changing the communication range (equivalently, transmission power), scheduling sensor nodes to active/sleep mode, placing sensor nodes in specific positions,

The node degree means the number of one-hop neighbors a node has. If all nodes in a network are still connected after removal of any

In order to obtain the desired node degree, many algorithms are proposed to adjust sensor nodes' communication range to control the desired number of nodes in neighbor list, e.g., [

In this paper, we propose a localized fuzzy-logic approach, without the assumption that location information is needed, to adaptively control the communication range of each node in order to achieve the desired node degree. It is named Fuzzy-logic Topology Control, FTC for short. Fuzzy-logic is a very powerful control algorithm. Fuzzy-logic control has been proved to be a very successful control approach to many complex nonlinear systems [

To the best of our knowledge, this paper is the first that applies the fuzzy-logic controller based on a training data set to be used in topology control for WSNs. We study the impact of the integral controller parameters on network properties, and prove that the system is stable, accurate and has short settling time. In order to compare it with other representative localized algorithms (NONE, FLSS [

The rest of this paper is organized as follows. An introduction of related works is provided in Section 2. Section 3 presents our proposed control algorithm FTC. We evaluate FTC by comparing it with other localized algorithms in Section 4. Section 5 concludes our work.

Topology control for network connectivity issues has been widely studied. Latest surveys can be found in [

Many works focus on study of the node degree _{1} log _{2} log _{1} = _{2}. It is worth mentioning that once the network is connected with high probability, it is also immediately

Previous results are asymptotical in nature, so they may not be able to be applied to real world scenarios easily. From a more practical perspective, it is necessary to propose topology control algorithms/protocols to make the network connected with high probability, while conserving as much energy as possible. However, the optimal solutions are usually not available. The problems, such as minimizing power consumption while maintaining a

Control theory has been applied to WSNs. Ref [

In this section, we first present the design of Fuzzy-logic Topology Control (FTC), and then propose a protocol that can run on sensor nodes. We utilize topology control based on fuzzy-logic to achieve the desired node degree, in turn improving the network connectivity. Because WSNs are large-scale and distributed networks, the algorithm/protocol running in a sensor node is localized, only depending on the node itself and its one-hop neighbors' information.

In general, there are two ways to design the fuzzy-logic controller. The most commonly used approach is to design the membership functions and the if-then rules on the basis of understanding the system from domain experts. However, due to the complexity and dynamic of the system (such as WSNs), the design of the membership functions and if-then rules might not be easy. Without any (or with incomplete) knowledge about a system, tuning the parameters often takes very long time, e.g., the shape of the membership functions. Another way to design fuzzy controllers is to use the training data set obtained from extensive experiments or mathematical description if it exists. By means of applying some learning algorithms, the fuzzy controller can be learnt from training data set. In this paper, our FTC leverages the second approach.

_{ref}_{ref}_{ref}_{max}_{max}

Provided a training data set from _{ref}_{ref}_{1},_{2},⋯ _{m}_{1}, _{2},⋯, _{j}_{ref},CR_{ref}, Prob, CR_{ref}

Since _{ref}_{ref}_{ref}_{ND}_{0} and _{ND}_{0} and

According to the design of FTC in Section 3.1, corresponding FTC protocol is presented in this section, as shown in FTC protocol running for a generic node. Each node broadcasts the HELLO message at the maximum communication range _{max}

On the one hand, in this paper, we only consider undirected links (that is, there is a link between two nodes if and only if they are both in each other's communication range), because in practice many routing protocols assume that the link between two nodes are undirected. On the other hand, FTC is a localized control algorithm running at each node independently. As a result, the node degree changes over time. For instance, node

FTC protocol (for a generic node

_{max}

_{ref}

_{0}; 5: Initial

_{0}; 6: Number of rounds,

_{i}

_{max}

_{0}; 10:

_{i}

_{ND}

_{ref}

_{ND}

_{0}; 17:

_{ND}

_{i}

_{ref}, Prob

_{i}

_{i}

In this section, we evaluate our proposal FTC by using Matlab, comparing FTC with three representative localized topology control algorithms (FLSS, k-Neighbor, and LTRT), together with an algorithm without any control algorithms, called NONE in this paper. We will introduce them in Section 4.3.

FTC is applicable to a network when all nodes are randomly and uniformly deployed, because the training data derived from ^{2} field. All nodes are stationary after the deployment. The maximum communication ranges, denoted as _{max}_{max}_{max}_{ref}

As we mentioned in Section 3.1, FTC is affected by two parameters (_{0} and

_{0} is higher at the beginning, the nodes are more likely to be connected than _{0} is lower. Nevertheless, the average node degree goes to stable state after 10 rounds as well. As a result, _{0} has an impact on the initial status of network.

In short, the simulation results illustrate that _{0} = 0.8 and

In this section, we briefly introduce four algorithms we have compared FTC with. More details can be found in the corresponding references.

NONE: once all sensor nodes are deployed in the field, each node configures its communication range to the maximum communication range, and the communication range does not change during the simulation. NONE generates the most connected network, thus gives the upper bound of network connectivity. NONE algorithm is used to simulate the case that there is no topology control applied to WSNs.

Fault-tolerant Local Spanning Subgraph (FLSS) [

k-Neighbor algorithm [

Local Minimum Spanning Tree (LTRT) [_{1}), and then removes all links in _{1} from _{1}). Next, the same process is conducted on _{1}). After _{1} + _{2} + ⋯ + _{k}_{1} + _{2} + ⋯ + _{k}

FLSS, k-Neighbor, and LTRT share some common features: they are all localized algorithms; they all need location information of neighbors; they all aim at finding out

First, we evaluate whether FTC is able to trace the _{ref}

Second, we compare FTC with other algorithms.

Third, we further study the average node degree.

Moreover, it is worth noting that the communication range is proportional to the energy consumption of wireless sensor nodes. Therefore, a lower average communication range implies a lower energy consumption, which is a significant performance when designing WSNs.

Finally,

In this paper, we address the connectivity problem in WSNs. More specifically, we proposed a novel localized adaptive fuzzy-logic topology control algorithm, called FTC, to control the communication range of sensor nodes in WSNs, with the purpose of achieving the desired node degree (namely the number of one-hop neighbors a node has), therefore in turn improving the network connectivity. Unlike other ways to design fuzzy-logic control system, the fuzzy-logic controller of FTC is constructed from a training data set. One of the great advantages of this approach is that it is easier to design a feasible controller without complicated parameter adjustment for the fuzzy-logic controller, especially when the network is highly dynamic.

FTC has been compared with four representative localized algorithms: NONE, FLSS, k-neighbors and LTRT. The simulation results show that FTC is able to trace the desired node degree as k-Neighbor algorithm which is based on the locations of neighbors, but FTC does not depend on location information. On the contrary, NONE, FLSS, and LTRT are unable to achieve the desired node degree. The average communicating range of FTC is very close to FLSS and k-Neighbor, but lower than NONE and LTRT. It implies that the energy consumption of FTC is lower than that of NONE and LTRT. In addition, the average maximum communication of FTC is the lowest, which means that the highest energy-consuming node in the network running FTC protocol consumes the lowest power than running other algorithms. The Energy Expended Ratio (EER) of FTC is very close to LTRT, but higher than FLSS and k-Neighbor. In summary, without knowing the neighbor location information, our localized FTC shows the capability of achieving desired node degree, maintaining network connectivity, and it is energy-efficient.

In this paper, all nodes are stationary after they are deployed. In our future works, we will take into account the mobility of sensor nodes. Furthermore, our validations are based on computer simulations. In order to validate FTC protocol, real experiments will be carried out on our Sun SPOT sensor platform in the near future. The node deployment is very unlikely to be an ideal random and uniform distribution, so we will calculate all sensor nodes' locations through computer simulation prior to deploying them in the field.

This work is supported by the European project “Design, Monitoring and Operation of Adaptive Networked Embedded Systems” (DEMANES) (project code ARTEMIS-JU:295372) and Spanish “Ministerio de Industria, Energía y Turismo” (project code ART-010000-2012-2).

Yuanjiang Huang, José-Fernán Martínez and Juana Sendra were responsible for the theoretical analysis of the control system. Yuanjiang Huang, José-Fernán Martínez and Vicente Hernández designed the simulation procedure and analyzed the simulation results. The simulation platform is being developed by the Research Group of Next-Generation Networks and Services (GRyS), where the authors belong to.

The authors declare no conflicts of interest

Fuzzy-logic topology control (FTC).

Average node degree with different K (_{0} = 0.8, n = 60, k = 3).

Average node degree with different _{0} (K = 0.02, n = 60, k = 3).

Different desired node degree k.

Example of resultant topology (n = 65, k = 3). (

Average node degree (k = 3).

Average communication range (k = 3).

Average maximum communication range (k = 3).

Energy expended ratio (