# 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  
Before comparing the performance and energy consumption provided by the three proposed methods, a summarized sequence of operations that must be performed to apply the proposed energy saving protocol is described, step-by-step, in what follows. 1. The output-feedback controller is designed considering the classical control theory (full-reliable network, \(L=\infty\), \(P_{S}=1\)) and the optimal value for the \(\mathcal{H}_{\infty}\) norm of the closed-loop system is calculated;
2. The designer chooses a maximum value for the \(\mathcal{H}_{\infty}\) norm degradation (when compared with the optimum \(\mathcal{H}_{\infty}\) norm computed in step 1: Y\({}_{H}\)), which may be considered acceptable within the project specifications;
3. Consider the implementation of the first and most simple heuristic procedure of energy saving protocol: Trade-off approach (\(L\) fixed and unique), named \(A1\) in this section. Choose a maximum number of allowed transmissions (\(L\)) and determine the associated transition probability matrix to finally compute the controllers and the \(\mathcal{H}_{\infty}\) closed-loop norm (using Lemmas 2 and 3) and the network global energy consumption (\(E_{GE}\) from Equation (23));
4. If the \(\mathcal{H}_{\infty}\) norm degradation (rate between the norm obtained with packet loss and the one using the classical approach, without loss, Y\({}_{H}\)) satisfies the performance required by the designer, it is possible to reduce the value of \(L\), implying a more accentuated reduction in the energy consumption. Otherwise, a value of \(L\) greater than the previous one must be chosen (increasing the network reliability and consequently the probability of successful transmissions) to satisfy the maximum norm degradation determined by the designer in step 2;
5. Assuming the new value of \(L\) set in step 4, the third and fourth steps are repeated such that the maximum number of allowed transmissions converge to a minimum value (\(L_{min}\)) that simultaneously respects the norm degradation criterion and maximizes the energy savings (best trade-off \(\Theta\) achieved). Considering the implementation of the second heuristic method of energy saving protocol (\(L\) variable from \(\infty\) to a fixed and finite value), named \(A2\) in this section, it is known, from the results obtained for \(A1\) (steps 1 to 5), the minimum value of \(L\) common to all network nodes which does not violate the criterion of norm degradation imposed by the designer. Also knowing that in the second heuristic (\(A2\)), each network node assumes _a priori_ the value \(L=\infty\) and then the maximum number of allowed transmissions converges to \(L=L_{min}\) (except the nodes connected to the sensors or actuators, red circles in Figure 4), it is enough to compute all the different combinations of network settings (Table 6), and the corresponding transition probability matrices, stabilizing controllers, \(\mathcal{H}_{\infty}\) closed-loop norm (Figure 6a), norm degradation Y\({}_{H}\), and network global energy consumption (Figure 6c). Observe that \(A2\) can be less efficient in terms of energy consumption than \(A1\) because the network nodes operate, during a certain time-window, in full-reliable working mode. However, it is more efficient in terms of \(\mathcal{H}_{\infty}\) performance because the network nodes operate, during a certain time-window, close to the optimal solution. Finally, for the implementation of the third heuristic method of energy saving protocol (\(L\) variable inside a set of values fixed and finite), named \(A3\) in this section, besides determining a maximum value for the \(\mathcal{H}_{\infty}\) norm degradation (as done for \(A1\) and \(A2\)), the designer must also set the maximum global energy consumption by choosing an upper bound for the maximum number of allowed transmissions for each node (\(L_{max}\)).