# A Data Secured Communication System Design Procedure with a Chaotic Carrier and Synergetic Observer
## 2 Related Works and Methods Overview  
The overall issues and approaches of chaotic communications when using chaotic modulation schemes were briefly described by [PERSON] and [PERSON] [21]. According to their study [21], the most common modulation schemes are: chaos shift keying (CSK); differential chaos shift keying (DCSK); additive chaos modulation (ACM); and multiplicative chaos modulation (MCM). CSK and DCSK provide secure communication by shifting between two identical or different chaotic generators. ACM and MCM provide mixing of the useful signal directly into the mathematical model of a chaotic generator in a linear (additive) or nonlinear (multiplicative) manner. In all of these schemes, one of the data secure factors is a chaotic carrier signal frequency ten times greater than the useful signal frequency or more. ACM with a combination of MCM was explored by [PERSON] in the 1990s [22] in several papers, where he proves that this kind of combined modulation does not provide security for a 3 rd order system. In addition, we note that using only MCM is a more secure approach due to nonlinear mixing of the useful signal and MCM as a secure scheme is thus widely used in much research as indicated below. Different approaches and applications of chaotic data communication systems design have been illustrated in several recent papers [23; 24; 25; 26]. Examples of CSK and DCSK were presented by [PERSON] et al. [23] and [PERSON] et al. [24]. Chaotic generator parameter modulation was used by [PERSON] [25] as well as an adaptive synchronization approach based on Lyapunov stability theory for the receiver design procedure. The problem of such approaches is how to select the Lyapunov function in the general case of chaotic communication system design. An example of chaotic phase modulation of couple modified Rossler oscillators for transmission of analog information was presented by [PERSON] et al. [26]. Thus MCM could be the most simple and secure configuration of the transmitter block of a chaotic communication system but it requires a powerful procedure to reconstruct a useful signal at the receiver side. The use of a state observer for reconstructing a useful signal in information transmission systems has been shown previously by [PERSON] and [PERSON] [27; 28], [PERSON] [29], and [PERSON] et al. [30]. Moreover, the observer-based approach is widely used in recent works of various authors in chaos communication system design and other applications. For example, [PERSON] and [PERSON] [31] demonstrate a method of estimating the unmeasured state variable to derive a plant dynamics full-order model, but only for a linear system. [PERSON] and [PERSON] [32] built a disturbance observer to eliminate noise in an industrial system. A geometric approach to transform the original strongly detectability system into a strongly observable and detectable subsystem was used by [PERSON] and [PERSON] [33]. The problem of observer-based synchronization was explored by [PERSON] and [PERSON] [34]. Another most promising approach of secure data transmission systems control and synchronization is observer design for sliding mode control (SMC) as explored by [PERSON] et al. [35]. Finally, [PERSON] et al. [36] explored the problem of line equilibrium chaotic system synchronization based on state observer design for a rectangular system. However, the state observers used in earlier research [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37] reduce to the synergetic state observers [38; 39; 40] used in our work. Table 1 summarizes distinctive features of some of the explored reconstruction techniques to provide a more visible comparison between different works and approaches in the field and highlight the merit of a synergetic state observer.