# 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
### System Behavior and Activity  
According to the definition (1), the current state of the system \(\mathbb{S}\) is described by the set of values \(x_{i}\in X_{i}\) that characterize it in the problem being solved:  
\[x=(x_{1},x_{2},\ldots,x_{n}),\quad x_{i}\in X_{i},\quad i=1,2,\ldots,n. \tag{8}\]  
at the same time,  
\[x\in X,\,\,X\subseteq X_{1}\times X_{2}\times\ldots\times X_{n}.\]Which values \(x_{i}\) will belong to the set (8) depends on the nature of the system in consideration and the task for which the system is intended. For the case of continuous time \(t\in T=[t_{0},t_{f}]\) and a finite dimensional vector of state \(x\in X\subseteq\mathcal{R}^{n}\) the set of states at all moments can be described as follows:  
\[x(t)=(x_{1}(t),x_{2}(t),\ldots,x_{n}(t))=[x_{1}(t)x_{2}(t)\ldots x_{n}(t)]^{T}. \tag{9}\]  
For the case of discrete time \(t\in\{t_{i}\},\ i=1,\ldots,N\) instead of continuous trajectories (9) in the state space, we should consider their discretized versions of the following form:  
\[x(t_{i})=\{(x_{1}(t_{i}),x_{2}(t_{i}),\ldots,x_{n}(t_{i}))\},\quad i=0,1, \ldots,N. \tag{10}\]  
For (10), the _behavior_ of the system \(\mathbb{S}\) will be the sequence of its states \(x(t_{i})\in X\), which are tied to the corresponding time moments \(t_{i}\in T\); i.e.,  
\[\{\langle x(t_{i}),t_{i}\rangle\},\quad t_{i}\in[t_{0},t_{f}]\subseteq T, \quad i=0,1,\ldots,N. \tag{11}\]  
Let us also introduce the concept of _activity_ of the system \(\mathbb{S}\), which is a sequence of actions taken by this system. Each of the actions is based on information about the current situation, i.e., about situational awareness, and about the current goals of the system \(\mathbb{S}\) operation. The implemented action leads to some results. Symbolically, each step of the process called activity can be represented as follows:  
\[\langle\text{situation, goal}\rangle\Rightarrow\text{action}\Rightarrow\text{ result} \tag{12}\]  
The concept of a situation is naturally divided into two components. The first of them will be called the internal situation and denoted as \(\Lambda_{int}(\mathcal{R}^{W},t)\). Its components characterize the current state of the system \(\mathbb{S}\), while the components of the external situation \(\Lambda_{ext}(\mathcal{R}^{W},t)\) are related to the fragment of objective reality \(\mathcal{R}^{W}\), from which the system \(\mathbb{S}\) in question is excluded:  
\[\lambda(t)=\langle\lambda_{ext}(t),\lambda_{int}(t)\rangle;\quad\lambda(t)\in \Lambda,\ \lambda_{ext}(t)\in\Lambda_{ext},\ \lambda_{int}(t)\in\Lambda_{int};\quad\Lambda=\Lambda_{int}\cup\Lambda_{ext}. \tag{13}\]  
\(\lambda(t)\), \(\lambda_{ext}(t)\), and \(\lambda_{int}(t)\) are the components of the total \(\Lambda\), external \(\Lambda_{ext}\), and internal \(\Lambda_{int}\) situation, respectively. Using (13), the relationship (12) can be rewritten as  
\[\{\langle\lambda(t_{i}),\gamma(t_{i})\rangle\}\xrightarrow{\Phi^{S}}\lambda (t_{i+1}),\quad i=0,1,2,\ldots,N, \tag{14}\]  
or in a different way,  
\[\lambda(t_{i+1})=\Phi^{S}(\langle\lambda(t_{i}),\gamma(t_{i})\rangle,\quad i =0,1,2,\ldots,N.\]  
\(\lambda(t_{i})\in\Lambda\) is the current situation, \(\gamma(t_{i})\in\Gamma\) is the current target, and \(\Phi^{S}\) is the law of system evolution \(\mathbb{S}\). As it is easy to see, the \"result\" in (12), attached to time marks, is nothing but the behavior of the system; that is, the behavior of the system \(\mathbb{S}\) is the consequence of its activity. For the subject of this article, it would be more accurate to say \"controlling the activity and behavior of the system \(\mathbb{S}\).\" Still, we use the shorter version \"behavior control\" everywhere. Such usage is justified by the fact that we are interested not so much in the activity of the system \(\mathbb{S}\) as in the result to which this activity causes, i.e., the behavior of the system \(\mathbb{S}\). As noted above, along with the concept of situation, the idea of situational awareness plays an important role.