# Protocol for Energy-Efficiency in Networked Control Systems Based on WSN
## 7 Conclusions  
This paper handled the problem of energy efficiency in NCS scenario. To perform the design of a stabilizing dynamic output-feedback controller connected through a semi-reliable communication network to the plant, a discrete-time representation based on MJLS is proposed. The synthesis of the controller is made in two steps: (i) the design of a state-observer and (ii) the design of a state-feedback controller. Although both steps provide optimal solutions individually, the joint procedure provides a sub-optimal solution. The first contribution of the paper is the modeling of the Makov chain in terms of the packets that group the information about the control or measurement output signals, such that the packet loss or the successful transmission of those packets affect the accessibility of the chain modes and the computation of the global transition probability matrix of the MJLS. The second contribution is to evaluate the behavior of the network global energy consumption levels associated to three distinct energy saving protocols, which are defined in terms of the maximum number of transmissions allowed by the nodes (\(L\)). The first method uses a single, fixed and finite value of \(L\), implying a closed-loop system with degraded performance but energy consumption levels lower than the classical case. The second approach employs a finite set of values of \(L\), starting from the case without packet loss (\(L=\infty\)), such that the initial \(\mathcal{H}_{\infty}\) performance is similar to the one obtained by the classical control case, and then it switches to a set of finite values of \(L\), generating a group of energy saving working modes. The third technique join the advantages of the two previous approaches: as the first method, it always operates in a energy saving working mode (when compared with the classical control case), however, as done in the second approach, it generates a set of distinct working modes where the resource saving can compensate the performance degradation. Summarizing, as shown in the simulation results obtained for the control of a linearized model of a coupled multi-level tank through a semi-reliable communication network with a particular topology, all three approaches are suitable solutions to achieve some energy efficiency in the NCS problem. Each one of them may be more suitable than the others depending on the controlled system, on the network topology or the designer priorities.  
[PERSON], C.D.[PERSON], [PERSON], and [PERSON] designed the proposed protocol and mathematical models. [PERSON] was the general supervisor of the work, contributing with ideas, detailed revisions, and results validation. [PERSON] and [PERSON] contributed with the numerical examples and validation.  
Figure 10: Trade-off (\(\Theta\)) of the system evaluated in terms of the distinct network settings \(\xi\) according with \(I_{Lm}\) for: (**a**) the second approach (\(A2\) with \(L\in\{\infty,5\}\)) and (**b**) the third approach (\(A3\) with \(L\in\{8,5\}\)).  
**Funding:** This research was funded by University of the Bio-Bio, Chile grant number DIUBB GI 160210/EF, and Brazilian agencies CNPq grant number 408782/2017-0, CAPES and FAPESP grant numbers 2014/22881-1 and 2017/18785-5.  
**Acknowledgments:** [PERSON] acknowledges School of Electrical Engineering of University of the Bio-Bio for providing the technical support for the development of the paper during his visit between October 2017 and January 2018.  
**Conflicts of Interest:** The authors declare no conflict of interest.