Synthesis of adaptive mathematical models of onboard electronic systems of the spacecraft through the application of mathematical homologous structures

The article discusses the issues of the synthesis of adaptive mathematical models applied to the problems of technical diagnostics of on-board electronic systems of the spacecraft. The authors formulated the problem of the synthesis of adaptive models of on-board radio-electronic systems of spacecraft in a general form using the transformation of the source mathematical structure into the homologous structure with smaller dimension. An approach to the synthesis of adaptive models on the basis of using mathematical apparatus of finite state machines is presented. The novelty of the approach lies in the fact that a homologous structure with smaller dimension is synthesized by transformation of the relations between the elements of a set of controlled parameters (output variables of FSM model). An example of the synthesis of the mathematical model of the on-board telemetry system’s central unit, adaptive to the control process of technical condition, is given. Efficiency of the synthesized adaptive model of on-board radio-electronic systems was evaluated by solving the Chinese postman problem.