## 1 Introduction  
The Wireless Sensor and Actuator Networks (WSAN) are a well-known wireless communication technology with benefits that are becoming significantly important for solving upcoming societies challenges [1]. The WSAN reliability is strongly affected by unpredictable changes in the environment. A node transmitting always using its maximum power will show a reliability highly immunized to changes in the environment, but the node energy consumption will unnecessarily soar. Thus, a trade-off between energy consumption and communication reliability is required, as proposed in diverse strategies. For instance, in [2], [PERSON] _et al._ analyze four algorithms for a proactive transmission power control system, where the transmission power is tuned according to link quality predictions. Nodes must interchange information to measure link quality for making predictions. In [PERSON] _et al._ (2018), [PERSON] _et al._ provide a survey on reliability protocol schemes based on retransmission and redundancy. For overcoming data loss, the use of data retransmission techniques and data redundancy is proposed, so that the destination can rebuild lost data from extra transmitted information. In [PERSON] _et al._ (2018), [PERSON] _et al._ propose two algorithms that adjust the node transmission power considering the distance to its two-hop neighbors and to the base station. In [PERSON] _et al._ (2018), [PERSON] _et al._ propose an adaptive power control routing protocol for underwater sensor networks. That protocol runs in two phases: first, the base station arranges the network so that nodes are clustered according to their distance to the base station, and second, nodes in a cluster must determine which one has the higher energy to become the cluster gateway to the base station. In [PERSON] _et al._ (2018), [PERSON] _et al._ survey different routing protocols for underwater acoustic sensor networks, focusing on their energy consumption. Summarizing, routing protocols based on node location could reduce energy consumption, compared to those that do not locate neighbors, but increase node memory footprint and processor overhead. Conversely, location-free routing protocols provide worse network latency and increase overall network energy consumption, because of the cooperation among nodes to get network routes to the destination, but are gentle with node computational resources. In [PERSON] _et al._ (2018), [PERSON] _et al._ discuss how to improve network resilience by modifying the network topology and/or the routing protocol. In [PERSON] _et al._ (2018), [PERSON] _et al._ show how radio diversity improves network reliability though there is a slight increase in the energy consumption. Nodes' radio transceivers use dual widely-spaced radio frequencies through spatially-separated antennas. That approach only requires new hardware for the node (new radio transceivers and antennas) and does not imply any overload on the node processor or memory, as software or protocols already deployed are not changed. Nevertheless, there is an energy overload of 33%. In a previous work [PERSON] _et al._ (2018), we propose a self-adaptive strategy, based on fuzzy control, which adapts each node transmission power to achieve an optimal number of neighbors (an optimal node degree). This optimal number of neighbors guarantees the node a high likelihood to reach any other node in the WSAN and only depends on the parameters of the specific WSAN: the deployment area and the number of nodes per m\({}^{2}\). The node transmission power is dynamically adapted, and thus, the energy consumption is optimized. Such a self-adaptive strategy was carried out as described in another previous work [PERSON] _et al._ (2018), where the proposed fuzzy control system running in each node in a WSAN includes two feedback control loops as depicted in Figure 1. A primary feedback control manages the node transmission power considering both its real and targeted number of neighbors, as mentioned in the previous paragraph.