## 1 Introduction
A secondary feedback control loop was added to extend the node battery lifetime by managing the node targeted optimal number of neighbors considering the battery level. Whenever the node battery level drops below a critical value, the targeted number of neighbors is decreased, whereby the node transmission power is reduced and, thus, the node energy consumption. Figure 1: Control system design for self-adapting the Wireless Sensor and Actuator Networks’ (WSAN) nodes transmission power considering the number of neighbors and the battery level. In some of the above-mentioned related works, improvements in the WSAN energy consumption are carried out by means of new routing protocols, entailing an overload for the network. In others, the node must run algorithms for either making predictions or estimating node locations or distance to other nodes, which might not be accurate in real deployments and involve stressing node computational resources. However, the solution proposed in Figure 1, deeply described in the following sections, has no significant impact on the performance of existing WSANs, because it requires few extra computational resources in a node, as it implies running very simple algorithms, and does not require data interchange among nodes over the network, whereas the built-in routing protocol in the node provides accurate information about the number of neighbors, no matter the distance. The rationale for the system in Figure 1 is available in [11; 12; 13]. Briefly, the probability of a WSAN being k-connected is the same as the probability of all WSAN nodes having a minimum number of neighbors equals to \(k\) and depends on the number of deployed nodes \(n\), the node density \(\rho\), defined as \(n/A\), where \(A\) is the deployment area, and the nodes' radio range \(r\), as shown in Equation (1). \[P(k)=\left(1-\sum_{N=0}^{k-1}\frac{\left(\rho\pi r^{2}\right)^{N}}{N!}e^{-\rho \pi r^{2}}\right)^{n} \tag{1}\]  
Thus, for a concrete set of deployment parameters, an optimal number of neighbors for all network nodes can be estimated for guaranteeing that all of them have a good connectivity probability. At this juncture, the node target must be to manage its power transmission accordingly to keep the minimum number of neighbors estimated for its network always, as depicted in Figure 1, which also considers decreasing a node's desired number of neighbors to extend its battery lifetime, though the probability of good network connectivity also decreases. In addition, in [14], [PERSON] _et al._ compare the fuzzy logic controller against other techniques for WSAN topology control, and the results from simulation highlight the fuzzy logic controller benefits. Additionally, in [15], [PERSON] _et al._ compare fuzzy logic controllers obtained through a training dataset and fuzzy logic controllers based on heuristic if-then rules and membership functions. The former are preferred for WSAN deployments that can be accurately described by a mathematical model, and the latter is preferred when no mathematical model is available or accurate enough. For the approach analyzed in this paper, the latter kind of controller has been carried out. This paper shows the results concerning the WSAN nodes' connectivity and energy consumption from a real deployment, accomplishing the system in Figure 1. This paper's novelty lies in the system simplicity. The approach is very easy to carry out and does not impose significant burdens to being deployed in existing WSANs. However, it includes some uncertainty, as a high probability of getting a k-connected network does not guarantee it is. Besides, the results in this paper come from a real deployment, not from simulations, like in most of the related previous works. In the following sections, the implemented system's inner details and its software design are discussed in Sections 2 and 3, respectively. Section 4 describes the deployed experiments, and Section 5 analyzes and compares the results from those experiments. Finally, Section 6 presents the conclusions and depicts future works.