Adaptive Control of Impulse Processes in Complex Systems Cognitive Maps with Multirate Coordinates Sampling

Abstract

Cognitive map (CM) is a popular method of complex systems description. The system of first-order difference equations in variables increment, based on weighting coefficients of CM, is used to describe impulse process of the system. If different vertices coordinates of CM are measured with different frequencies multirate sampling impulse process model should be developed. The current paper proposes such a model and adds external control vectors with multirate sampling to allow to affect impulse process dynamics. To stabilize this multirate system’s coordinates at predefined levels two optimality criteria are proposed and correspondent control laws are derived. Controls are also multirate, i.e. frequently measured coordinates are affected by controls frequently and infrequent coordinates are affected with longer sampling period. For the case when weighting coefficients of CM are unknown or varying special algorithm of their estimation is developed. The results are verified by simulation performed for CM of a bank.