Abstract: An approach of the generalized optimization for analog network design was elaborated by means of the optimum control theory formulation. This methodology generalizes the design process and generates a set of different design strategies that serves as a structural basis for the minimal-time design strategy construction. The main conception of this approach is the introduction of special control functions, which, on the one hand generalize the design process and, on the other hand, they give the possibility to control the design process to achieve the optimum of the design cost function for the minimal computer time. This possibility appears because of infinite number of different design strategies that exist within the bounds of the new theory. In this case a new quality appears due to the possibility of controlling the design process by redistributing computational expense between the circuit’s analysis and the procedure of parametric optimization. The problem of minimal-time network design strategy is formulated as a typical problem for some functional minimization of the control theory. The network optimization process in this case is defined as a controllable dynamic system.
An additional acceleration effect was discovered on the basis of new approach and it permits us the reducing of the computer design time additionally and serves as one of the fundamental notions for constructing the quasi-optimal-time design algorithm. This effect can be realized by means of changing of one design strategy to other with a special selection of the initial point of optimization process. Practical optimization of the different electronic networks shows that the potential computer time gain of the optimal strategy grows when the size and complexity of a network increase.
The conception of the Lyapunov function of the design process serves as one of the productive ideas to study the main properties of the time-optimal design algorithm. The Lyapunov function and its time derivative include the sufficient information to select more perspective design strategies from all of the different design strategies that exist in bounds of generalized optimization methodology. Analysis of behavior of the Lyapunov function during the optimization process shows a strong correlation between some characteristics of this function and a processor time. It means that the study of the Lyapunov function of design process helps us constructing the structure of the minimal-time network design algorithm.

Brief Biography of the Speaker:
Alexander Zemliak received the M.S. degree in electronic engineering from the Kiev Polytechnic Institute (KPI), Kiev, Ukraine, in 1972 and in mathematics from the Kiev University in 1975, and Ph.D. in electronic engineering from KPI in 1976. He is currently a Professor of Physics and Mathematics Department, Autonomous University of Puebla, and a Professor of the National Technical University of Ukraine "KPI" too. His research interests are in computer-aided RF and microwave circuit analysis, optimal design methodologies, computational electromagnetics, numerical techniques in the simulation, analysis and optimization of microwave devices. He has authored of two books, 6 chapters of books and over 250 papers in refereed journals and conference proceedings. From 1986 to 1994 he held some research grants from Ministry of Superior Education of Ukraine and industry. From 1998 to 2009 he held some grants from Mexican National Council of Science and Technology. He is a member of Ukrainian Scientific Society, National System of Investigators of Mexico, Senior Member of IEEE, member of IEICE, WSEAS and New York Academy of Sciences. He was a chairman of some international conferences in Mexico, member of technical program committee of some conferences around the world and invited lecturer of more than 10 international conferences. He obtained best paper award at National SOMI Conference, 1999 (Mexico), International conference IBERCHIP, 2002 (Mexico), International WSEAS Conference, 2009 (Turkey), International Conference IEEE EWDTS, 2009 (Russia). He is Editor-in-Chief of the WSEAS Transactions on Systems, Member of the Editorial Board of the WSEAS Transactions on Circuits and Systems, WSEAS Transactions on Electronics. He was a Reviewer of International Design Automation Conference-DAC, 2001–2003, USA; International Conference on Computing, Communication and Control Technologies-CCCT, 2004–2008, USA; World Multi-Conference on Systemics, Cybernetics and Informatics, 2003–2009, USA.