## 1 Introduction
Thus, the use of the Kalman filter in intrusion detection systems is relevant and promising, since this approach corresponds well to the logic of the problem being solved. The Kalman filtering algorithm shows good results in the presence of a large amount of a priori data about the filtered process. Based on these data, the so-called \"reference trajectory\" is constructed, which is already used in the a posteriori block. This is consistent with the principles of intrusion detection systems based on statistics, for which a model of \"normal\" behavior is built based on statistical observations, which is later used to identify abnormal behavior. However, it is much easier to identify anomalies after filtering the information process, since this eliminates the influence of random factors. A significant reserve for improving the quality indicators of filtering the dynamic trajectory of controlled objects is the optimization of the control of observation processes. At present, there is a well-developed mathematical apparatus for the optimal control of observations, which is used in practice in navigation systems, radar, and information-measuring systems [26; 27; 28]. However, at present, there are many technical problems for which this mathematical apparatus could also be successfully used, for example, in communication network monitoring systems, intrusion detection systems, etc. Therefore, within the framework of this article, we will consider the features of applying the classical theory of observation management in AIDS. There are currently two main directions in the theory of observation management [28]. The first of them is related to the use of static and regression models of the processes being evaluated. The second direction is related to the optimization of observation management in dynamic systems. Dynamic optimization problems of measuring processes are interpreted as problems of controlling the accuracy of Kalman filtration. This interpretation is the most general, since it includes simpler cases corresponding to the theory of planning regression experiments. The noted generality lies in the possibility of including in the dynamic model of the experiment such factors as: the stochastic nature of the information process, the correlation of observation errors, restrictions on the intensity of measurements, as well as a number of other factors, which are either impossible or difficult to account for within the regression model. The more general nature of the planning tasks determines the complexity of their solution in the initial statements. This is explained by the complexity of the model of the observed process described in the case of continuous time by a system of stochastic differential equations. There are several approaches to solving such problems. The first of them treats the initial optimization problem as a problem of controlling directly the accuracy of the Kalman filter. The accuracy characteristics of the Kalman filter are determined by the a posteriori covariance matrix of estimation errors and described by a nonlinear matrix differential equation (the Riccati equation). This equation defines a \"fictitious\" dynamic system for which various optimization problems can be formulated [28]. The terminal-type quality criteria are used here. This approach is based on the application of the Pontryagin maximum principle, which provides, according to [28], necessary and sufficient optimality conditions. However, the application of this approach to the synthesis of optimal laws for controlling observations encounters a number of difficulties. This is due to the fact that in order to determine the optimal control functions, it is necessary to solve a matrix nonlinear two-point boundary value problem [28]. Due to the nonlinearity of the Riccati equation, as well as the large dimension of the covariance matrix of estimation errors, the solution of this problem is problematic and requires the use of rather complex numerical methods that do not always have a sufficient degree of convergence.