On Minimal Time of Process of Circuit Optimisation 
 


Authors 
 Zemliak A.M. 
Date of publication 
 2018 
DOI 
 10.31114/2078770720181110117 

Abstract 
 The process of analogue circuit optimisation is mathematically defined as a controllable dynamic system. In this context the minimisation of the processor time of designing can be formulated as a problem of time minimisation for transitional process of dynamic system. A special control vector that changes the internal structure of the main equations of optimisation procedure serves as a principal tool for searching the best strategies of the optimisation process. The creation of the best strategy of the optimisation having the minimum processor time leads to search of the structure of control vector providing the minimum of a special functional that can be defined as CPU time. In this case a wellknown maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimisation. The possibility of applying the maximum principle to the problem of optimisation of electronic circuits is analyzed in detail. It is shown that in spite of the fact that the problem of optimisation is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude. 
Keywords 
 circuit optimisation, controllable dynamic system, optimisation strategies, maximum principle of Pontryagin. 
Library reference 
 Zemliak A.M. On Minimal Time of Process of Circuit Optimisation // Problems of Perspective Micro and Nanoelectronic Systems Development  2018. Issue 1. P. 110117. 
URL of paper 
 http://www.mesconference.ru/data/year2018/pdf/D044.pdf 