## Materials and Methods  
### Formulation of the Problem  
To develop an AIDS resource management algorithm, it is necessary to complete the following tasks: to develop a model of the dynamics (state) of the set of observed objects; set the observation model; and set the conditions of the optimization problem, i.e., determine the constraints and select the quality criterion. When solving this problem, it is necessary to synthesize an adequate dynamic model of the information process. The coordinates of the state vector can be various parameters of the controlled object, such as processor load, RAM usage, file system access, traffic intensity, energy consumption, etc. [25; 29]. It is obvious that these and many other parameters of controlled objects are random variables. The random nature of these values may be due to both internal factors related to the processes occurring inside the object of observation, and external. For example, the random response time to an echo request (RTT delay) may be related to both server load (internal factor) and connection speed and channel load throughout from the client to the server. Within the framework of the model, it is advisable to associate internal random factors with formative noise. External random influences affecting the result of measuring the parameters of the controlled object are taken into account in the observation model in the form of observation noise. It should be noted that within the framework of this ap-proach, the formative and noise observations should be Gaussian, which does not corre-spond to the real characteristics of information processes, therefore it is necessary to apply the Gaussian approximation method. This stage should be preceded by a full-scale ex-periment that allows you to identify the real statistical characteristics of the information random process and the observation process. After constructing state and observation models, the classical apparatus for managing observations can be used to solve the problem. The optimization problem is based on the terminal quality criterion and involves the implementation of an iterative procedure for synthesizing the observation plan [27; 28]. In the theory of control of observations, a differential equation of the following form is used as a dynamic model describing the state of a controlled object [27; 28]:  
\[{x_{i}}^{\prime}=S_{i}x_{i}+G_{i}q_{i},\;i=1,2,\ldots,\;x_{i}(t_{0i})=x_{i0}, \tag{1}\]  
\(x_{i}=x_{i}(t)\in R^{n_{i}}\)--the state vector of the \(i\)-th object; here and below entry \(\bullet^{\prime}\) means the operation of differentiation with respect to time \(t\), i.e., applied to (1)--\({x_{i}}^{\prime}=\frac{dx_{i}(t)}{dt}\); \(x_{i0}\)--Gaussian vector, for which \(M[x_{i0}]={x^{*}}_{i0}\), (\(M[\bullet]\) means the mathematical expectation operation), \(M[(x_{i0}-{x^{*}}_{i0})(x_{i0}-{x^{*}}_{i0})^{T}]=D_{i0}\) (operator \((\bullet)^{T}\) means transpose); \(t_{0i}\)--monitoring start time \(i\)-th object; \(G_{i}=G_{i}(t)\in R^{n_{i}\times n_{i}}\); \(q_{i}=q_{i}(t)\in R^{n_{i}}\)--white noise for which \(M[q_{i}(t)]=0\), \(M[q_{i}(t){q_{i}}^{T}(t-\mu)]=N_{iq}\delta(\mu)\), \(\delta(\mu)\)--delta function; \(N_{iq}\in R^{n_{i}\times n_{i}}\)--diagonal matrix. The observation model is described by the following relationship:  
\[u=\sum\limits_{i=1}^{I}\quad\gamma_{i}(C_{i}x_{i}+g_{i}),\;t\in[0,t_{f}], \tag{2}\]  
\(u=u(t)\in R^{2}\); \(\gamma_{i}=\gamma_{i}(t)\)--control function for \(i\)-th controlled object; \(C_{i}=C_{i}(t)\in R^{2\times n_{i}}\)--matrix that specifies the composition of controlled parameters \(i\)-th object; \(g_{i}=g_{i}(t)\in R^{2i}\)--is white Gaussian noise, \(M[g_{i}(t)]=0\), \(M[g_{i}(t)\delta_{i}(t-\mu)^{T}]=N_{ig}\delta(\mu)\); \(N_{ig}\in R^{2i\times x_{i}}\)--diagonal matrix; \(I\)--number of monitored objects in a time interval \([0,t_{f}]\). Control functions \(\gamma_{i}(t)\) and matrices \(C_{i}\) satisfy the following restrictions:  
\[