Algorithm for Calculating Noise Immunity of Cognitive Dynamic Systems in the State Space

Abstract

The research method consists in applying the state space method, widely used in the study of automatic dynamical systems, to describe the behavior of cognitive systems. It is assumed, that at the input of the cognitive system, there is a signal and interference described by Poisson point processes, modeling the amount of information, the amount of emotional stress, etc., corresponding to each event. The cognitive properties of the system in the paper are taken into account by two circumstances. Firstly, events localized in time are characterized in the paper not only by the Poisson distribution of the times of their occurrence, but also by some random variables that characterize the importance (significance) events for the system. A typical example is the attribution of a certain amount of information to each event, if an information processing system is modeled. Another example is the emotional reaction of a person to the appearance of stress, described in a classic work on psychology. In this case, the point is the event that causes stress, and the effects of stress on the system are modeled by the relative magnitude of stress in accordance with the Holmes and Rahe scale. Secondly, the cognitive system processes, assimilates, adapts to the impact that each event has on it with its inherent speed. In this paper, this phenomenon is modeled as the passage of a point process through a dynamic system described by differential equations. Such processes are called filtered point processes. Examples of impacts are given and, for simplicity, an assumption is made about the magnitude of the impact as the amount of information received by the system when an event occurs. Thus, the model of a cognitive system is a dynamic system described by a differential equation in the state space, at the input of which messages with a certain information load appear at random discrete moments of time.As for any technical system, the cognitive system faces the task of evaluating the quality of its work. In this regard, the paper substantiates the use of a convenient quality index from an engineering point of view and an appropriate criterion in the form of a signal – interference ratio. The new results are differential equations in the state space for the mathematical expectations of the signal and interference, as well as an algorithm for calculating the noise immunity of the cognitive system. As an example, a graph of the noise immunity of a particular cognitive system is calculated and presented, confirming an intuitive idea of its behavior.In conclusion, it is noted that the main result of the paper is an algorithm for calculating the noise immunity of cognitive systems using differential equations that allow calculating the behavior of non-stationary cognitive systems under any point impacts described by a non-stationary function of the intensities of the appearance of points. The equations of behavior of the mathematical expectation of the processed information are reduced to a canonical form, which allows them to be applied to a variety of practical tasks, for example, to the description of hierarchical cognitive structures when the output of one level is the input of another.