Adaptive Parameter Identification for a Class of Neural Mass Models with Application to Ergatic Systems

Abstract

This paper considers one of the problems that arise in the developing of the ergatic brain-computer interfaces. This technology allows a person to control various mechatronic systems through the "power of thought", i.e. based on the registration of electrical activity of the brain. The problem is the complexity and poor knowledge of the brain. To describe the electrical activity of the brain, various models of neural ensembles are used, one of which is the neural mass model proposed by Jansen and Rit in 1995. To tune the parameters of this model according to real data, it is proposed to use an adaptive parameter identifier. An important condition for the synthesis of an adaptive identifier is that only the system output, which is the potential difference between two points of the head, can be measured. At the beginning, it is assumed that the entire state vector of the neural mass model is available for measurement. An identifier is synthesized to tune the parameters of such a system and its convergence is proved using the Lyapunov function method. Further, the obtained identifier is refined in such a way that it uses only the output of the system. To do this, using the finite difference method, the output derivative of the neural mass model is approximately calculated, which is used to make several replacements of the unknown components of the state vector. It is very difficult to analytically prove the convergence of the obtained adaptive parameter identifier, therefore, the possibility of using it to estimate the parameters of a neural mass model is checked using simulation. The synthesized identifier uses only the system output to tune the parameters, which in the future will allow us to consider real data instead of the system output. Thus, this identifier can be used to tune the parameters of the neural mass model based on real data.