Home         Authors   Papers   Year of conference   Themes   Organizations        To MES conference

Application of the maximum principle of Pontryagin for a problem of circuit optimization
Authors
	Zemliak A.M.
Date of publication
	2016
Abstract
	The possibility of application of the maximum principle for creation of the optimal control vector and the optimal trajectory for circuit optimization process is investigated. The example of optimization of simple nonlinear circuit for which the analytical solution of the problem was obtained is analyzed. The solution of a problem of circuit optimization for minimum CPU time is obtained on basis of the maximum principle of Pontryagin. The analysis of the process of optimization for a similar example which is carried out earlier has shown that in case of negative initial values of some variables the emergence of special effect of acceleration of the optimization process, which reduces the CPU time for circuit optimization by several orders of magnitude, is possible. The question, whether it is possible to obtain similar result on the basis of application of the maximum principle of Pontryagin remained open during a long time. The affirmative answer would allow to underpin a mathematical basis under earlier obtained results, and also to open new prospects. In the paper it is shown that the effect of acceleration of optimization process that was studied earlier coincides with the solution obtained on the basis of the maximum principle. This fact is theoretical justification of effect of acceleration. On the other hand the maximum principle can be a basis for development of optimization algorithm for electronic circuits with the minimum expenses of CPU time. The analysis of the optimization process of the analyzed circuit has shown that application of the maximum principle a really allows to find the optimum structure of the control function u(t), by means of iterative procedure. Criterion of the end of procedure is invariable value of a Hamiltonian. At the same time considerable reduction of CPU time in comparison with traditional approach is observed. The obtained results allow to claim that search of optimal strategy of circuit design can be run on the basis of the maximum principle of Pontryagin. This principle is mathematical justification of the theory of optimum design developed earlier. At the same time the maximum principle can be the practical tool at creation of optimum algorithm of circuit design.
Keywords
	design of analog circuits, optimal strategy, theory of control, maximum principle of Pontryagin, acceleration effect of the optimization process.
Library reference
	Zemliak A.M. Application of the maximum principle of Pontryagin for a problem of circuit optimization // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 1. P. 94-100.
URL of paper
	http://www.mes-conference.ru/data/year2016/pdf/D035.pdf