# Situational Awareness and Problems of Its Formation in the Tasks of UAV Behavior Control
## 2 UAV as a Controllable Dynamic System Operating under Uncertainty Conditions
### Kinds of Controllable Dynamic Systems  
The state of a dynamic system \(\mathbb{S}\) changes over time under the influence of some external and/or internal factors [73; 74; 75]. The set of external factors characterizes the impact on the system \(\mathbb{S}\) of the environment \(\mathcal{E}\) in which the system operates. Internal factors characterize the system \(\mathbb{S}\) in terms of its structure, characteristics, and behavioral features. Internal factors include, in particular, events affecting the properties of the \(\mathbb{S}\) system, such as failures of its equipment, structural damage, and impacts on controls that affect the behavior of the system. Obviously, in terms of their potential capabilities, different variants of dynamic systems will differ significantly from each other. In [72; 76], a hierarchy of types of such systems has been introduced. Its detailed description can be found in these books. This section will briefly discuss the essence of this hierarchy and show the place of UAVs in this hierarchy. As shown in [72; 76], the system \(\mathbb{S}\) in its general form can be defined as follows:  
\[ \begin{split}\mathbb{S}=\langle X^{S},\Phi^{S},W^{S}\rangle,\\ X^{S}=\{X_{i}^{S}\},\,i=& 1,\ldots,N_{S};\,\,\,\,\Phi^{S}=\{ \Phi_{j}^{S}\},\,j=1,\ldots,N_{R};\\ W^{S}=\langle T^{S},\,E^{S}\rangle,\,\,T^{S}\subseteq T.\end{split}  \tag{1}\]  
In this definition, \(X^{S}=\{X_{i}^{S}\}\), \(i=1,\ldots,N_{S}\) represents the set of _structures_ of the system \(\mathbb{S}\). The structures \(X_{i}^{S}\) that are part of this set specify the values \(x_{i}\) describing the state of the system \(\mathbb{S}\), the regions of definition of these values \(X_{i}\), and the relations between them. Here \(X^{S}\subseteq X\) is the area of the acceptable values of the system states (1), \(x_{1}\in X_{1},\ldots,x_{n}\in X_{n},\,\,\,\,X=X_{1}\times\ldots\times X_{n}\). The element \(\Phi^{S}=\{\Phi_{j}^{S}\}\), \(j=1,\ldots,N_{R}\) of the definition (1), is the set of rules (transformations, algorithms, procedures) that specify the evolution of the system state \(\mathbb{S}\). In addition, the definition (1) includes such an element as \(W^{S}=\langle T^{S},E^{S}\rangle\). It can be interpreted as the clock of the \(\mathbb{S}\) system. In the definition of \(W^{S}\) there are two sets of moments of time, namely, system time \(T^{S}\) (the set of moments of time of system operation) and world time \(T\) as the set of all possible moments of time. In this definition there is also an element \(E^{S}\) representing the mechanism of system activity \(\mathbb{S}\), i.e., a kind of clock generator. The system \(\mathbb{S}\) does not exist in isolation, but in interaction with the environment \(\mathcal{E}\)--i.e., \(\mathbb{S}\leftrightarrows\mathcal{E}\). This situation means that the environment \(\mathcal{E}\) influences the system \(\mathbb{S}\), which response to these influences and, in turn, also influences the environment. Depending on the properties of the system \(\mathbb{S}\), and the nature of its interactions with the environment \(\mathcal{E}\), the following hierarchy of types of dynamic systems, ordered by increasing their capabilities and, accordingly, complexity, can be constructed:  
\[\mathbb{S}=\mathbb{D}\mathbb{S}\subset\mathbb{V}\mathbb{S}\subset\mathbb{C} \mathbb{S}\subset\mathbb{A}\mathbb{S}\subset\mathbb{I}\mathbb{S}. \tag{2}\]  
The interaction of \(\mathbb{S}\) with the environment \(\mathcal{E}\) can be either passive or active. Examples of passive interaction \(\mathbb{S}\leftrightarrows\mathcal{E}\) give the motion of an artillery shell or an unguided missile under the influence of gravity and aerodynamic forces. Systems of this kind are unguided. In the hierarchy (2), they include systems of the \(\mathbb{D}\mathbb{S}\) and \(\mathbb{V}\mathbb{S}\) classes. Systems of \(\mathbb{D}\mathbb{S}\) class (deterministic system) react to the same influences in the same way; i.e., there is no influence of random factors on their behavior.