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Analysis of optimization process of analog circuits on the basis of Lyapunov function
Authors
	Zemliak A.M.
	Markina T.M.
Date of publication
	2016
Abstract
	The process of optimization of an electronic circuit is defined on the basis of the generalized theory as the dynamic operated system which is defined by the differential or difference equations for the state variables and system of restrictions which is the mathematical model of the electronic circuit. Basic element of this theory is the control vector. Each new value of this vector defines new strategy of designing and new trajectory in space of parameters. The number of possible strategies of optimization of a circuit determined by the time-dependent control vector is infinitely, however a set of the strategies defining structural basis of designing with the invariable control vector is finite and equal to 2M. Earlier defined concept of function of Lyapunov of process of optimization is used. The process of optimization of analog circuits is analyzed on the basis of derivatives of this function. The integrated function of a relative derivative of time of the Lyapunov function was used as the criterion allowing to compare various strategies. The behavior of this function is closely connected with processor time of procedure of optimization. A good separation of the curves corresponding to various strategies is observed. The hypothesis of strong correlation between behavior of function of Lyapunov of any strategy of optimization and the CPU time is confirmed. Function graphs that correspond to the smaller processor time, lie above others. Thus, analyzing and comparing the behavior of function of Lyapunov for various strategies of optimization, it is possible to draw conclusions about the perspective strategies, from the point of view of speed. The behavior of the derivative of the Lyapunov function of optimization process computed as a logarithm from Lyapunov function is unambiguously connected with the total CPU time necessary for circuit optimization. It allows to compare various strategies of optimization at the initial stage of the process and to choose the best strategy possessing the minimum processor time without the necessity for carrying out full procedure of optimization for each strategy. Numerical results of optimization of various analog circuits confirm a possibility of the choice of the best, in sense of speed, strategy of the optimization allowing solving a problem of design in several orders of magnitude faster than traditional approach.
Keywords
	optimum design of circuits, set of strategies of optimization, theory of control, Lyapunov function.
Library reference
	Zemliak A.M., Markina T.M. Analysis of optimization process of analog circuits on the basis of Lyapunov function // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 1. P. 86-93.
URL of paper
	http://www.mes-conference.ru/data/year2016/pdf/D034.pdf