Analysis of Some Special Functions for a Problem of Optimization of Analog Circuits

Further development of a generalized methodology for optimizing analog circuits is proposed. This methodology is based on the theory of optimal control. We have transformed the problem of minimizing the CPU time needed to optimize the circuit into the classical problem of minimizing the function in optimal control theory. In this case, we represent the process of optimizing the analog circuit as a controlled dynamic system. To analyze the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. The new special functions allow us to predict the CPU time for circuit optimization by analyzing the characteristics of the initial part of the process. It has been established that for any optimization strategy, there is a correlation between the behavior of these functions and the CPU time corresponding to these strategies.