# Protocol for Energy-Efficiency in Networked Control Systems Based on WSN
## 6 Example of Application of the Energy-Efficiency Protocol
### Results
#### 6.3.4. Energy Saving Protocol: Application Guidelines and the Comparison of the Three Approaches
This value of \(L\) can be chosen based on the results of energy consumption obtained for \(A1\), since the network starts its operation in a certain configuration with a finite and fixed value of \(L\) common to all nodes, such that it does not violate the norm degradation criterion imposed by the designer, and also allows an acceptable \(\mathcal{H}_{\infty}\) performance. Similarly to \(A2\), knowing that each node assumes _a priori_ the value \(L=L_{max}\) and then converges to \(L=L_{min}\) (except the nodes connected to the sensors or actuators, red circles in Figure 4, that remain fixed in \(L_{max}\)), it is sufficient to compute all the different combinations of network settings (Table 7), and the corresponding transitionprobability matrices, stabilizing controllers, \(\mathcal{H}_{\infty}\) closed-loop norm (Figure 8a), norm degradation \(\mathrm{Y}_{H}\), and network global energy consumption (Figure 8c). Aiming to compare both performance and energy consumption of all three approaches and their advantages with respect to the classical approach (that assumes the unrealistic hypothesis of a full-reliable network), the \(\mathcal{H}_{\infty}\) closed-loop norm and the value of \(E_{GE}\) obtained with each one of the methods are presented in Figure 9. Observe in Figure 9a that, as expected, the \(\mathcal{H}_{\infty}\) norm associated with the classical approach is the optimal one and, therefore, an lower bound for the second approach (\(A_{2}\) with \(L\in\{\infty,5\}\)), since the starting setting of the network imposes \(L=\infty\) for all nodes. Also note that, the \(\mathcal{H}_{\infty}\) performance obtained for the first method (\(A1\)) with \(L=8\) is a lower bound for the third approach (\(A_{3}\) with \(L\in\{8,5\}\)), since, in this case, all the network nodes are set in \(L=8\) in the starting setting. Furthermore, the \(\mathcal{H}_{\infty}\) results for \(A1\) with \(L=5\) are always superior than those obtained with any other method, because, even for \(A_{2}\) with \(L\in\{\infty,5\}\) and \(A_{3}\) with \(L\in\{8,5\}\), the nodes connected to sensors and actuators are assumed operating with unlimited energy (\(L=\infty\) for \(A2\) and \(L=8\) for \(A3\)). The same explanation can be used to justify why the \(\mathcal{H}_{\infty}\) closed-loop norm provided by \(A2\) is always better than the values provided by \(A3\) even if all the intermediate nodes converge to \(L=5\). On the other hand, it is noteworthy to mention that the features that can classify a given method as unfavorable in terms of \(\mathcal{H}_{\infty}\) performance are the same that allow greater energy savings (see Figure 9b). Note, for instance, that \(A3\) tends to save less energy than \(A1\) with \(L=5\) (because the network nodes operate, for a certain time-window, in a more reliable working mode: \(L=8\)) but it consumes less energy than \(A2\) (because no network node operates in full-reliable working mode when using \(A3\)). To evaluate how much better is \(A3\) with \(L\in\{8,5\}\) than \(A2\) with \(L\in\{\infty,5\}\) or \(A1\) with \(L=5\), the trade-off index (\(\Theta\)) is presented in Figure 10 for each distinct network setting indexed by \(I_{L_{\infty}}\). First, note that by employing \(A1\) with \(L=5\), the trade-off is negative (see Figure 7). By employing \(A2\), there are only two network settings that present a positive trade-off, since, in a large time-window, several nodes are maintained in full-reliable working mode. On the other hand, when using \(A3\), there are six network settings that present a positive trade-off and even when negative, the trade-off associated to \(A3\) is better than the other methods. In short, note that the third approach always produces better results in terms of energy savings than the second method, which starts from the setting similar to the classical control case.