# A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer
## 6 Conclusions  
The paper presented a design procedure for a two-channel synergetic state observer for a system of secured information transmission with a chaotic carrier. A system based on a synergetic state observer has the following advantages: (i) it allows estimation of up to two signals simultaneously; (ii) it does not require chaotic synchronization of the receiver and transmitter; (iii) it does not require determining the Lyapunov function; (iv) the observer structure is not rigid, the structure is not postulated in advance, but is determined during the design procedure based on the model of a chaotic generator; and (v) it provides direct application to systems with nonlinear dynamics without linearization of generator's nonlinear model.  
The simulation results confirmed the viability of the proposed procedure and the capability of organizing a system of chaotic information transmission. A qualitative assessment of the image transmission results according to Figure 13 confirms the possibility of secure image transmission with sufficient reliability because the quantitative value of the error plays a secondary role in such tasks. During the test transmission of rectangular pulses (the simulation results in Figure 13a,b a significant signal recovery error is observed; the recovery error can reach 25% of the amplitude of the useful signal. However, the error is pulsed, so its presence does not interfere with the conclusion about the original waveform. Moreover, such an error can be eliminated by additional signal processing using digital filtering and smoothing algorithms.  
It seems that additional research on the accuracy of the useful signal recovery is needed. According to Figures 13 and 22, the receiver quality may be acceptable for the transmission of some images, but in the case of numerical message transmission, a procedure of error detection and a recovery process is necessary. One potential solution is to make the frequency of the useful signal significantly lower than the fundamental frequency of oscillations of the chaotic system. In addition, future research should make an extra study to explore the impact of the observer's tune parameter \(\alpha\) not only for speed of estimation but for receiver quality. It is reasonable to explore application of some smoothing and filtration algorithms in order to decrease or eliminate a useful signal reconstruction error at the receiver side on the output of the synergetic observer. Meanwhile, the receiver error may be also related to the MATLAB system solver. It thus may be necessary to repeat the simulation in LabView or in a future hardware-implemented system. In addition, errors can occur due to external influences on the communication channel. Thus, one way to increase the accuracy is by including digital filtration algorithms into the system schematic.  
In further studies, it will be useful to numerically compare the resulting synergetic observer with other methods of signal recovery. In addition, as we introduce the useful signal as a function directly into the structure of the generator of chaotic oscillations multiplicatively, another topic for further research may be a deep estimation of actual steganography of the transmitted signal on the output of the chaotic generator.  
Conceptualization, A.M.; methodology, A.M.; software, J.D.; validation, A.M., J.D., A.N., and C.F.; formal analysis, A.M.; investigation, A.M., J.D., A.N., and C.F.; resources, A.M.; data curation, J.D.; writing--original draft preparation, A.M. and J.D.; writing--review and editing, A.M., A.N. and C.F.; visualization, J.D.; supervision, A.N. and C.F.; project administration, A.M.; funding acquisition, A.M. All authors have read and agreed to the published version of the manuscript. This work was funded by the Southern Federal University.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.