6b6bd0b3-28d2-47db-8d4b-a5857983982720210316035037200wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON COMPUTERS1109-275010.37394/23205http://wseas.org/wseas/cms.action?id=40262720202720201910.37394/23205.2020.19http://wseas.org/wseas/cms.action?id=23186Computer Time Minimizing for the Circuit OptimizationAlexanderZemliakDepartment of Physics and Mathematics, Autonomous University of Puebla, Puebla, MEXICO, also with Institute of Physics and Technology, National Technical University of Ukraine, UKRAINEThe solution of a problem of analogue circuit optimization is mathematically defined as a controllable dynamic system. In this context the minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known 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 behaviour of a Hamiltonian for various strategies of optimization. It is shown that in spite of the fact that the problem of optimization 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.410202041020207885https://www.wseas.org/multimedia/journals/computers/2020/a225105-058.pdf10.37394/23205.2020.19.11http://www.wseas.org/multimedia/journals/computers/2020/a225105-058.pdfJ.R. Bunch and D.J. Rose, (Eds.), Sparse Matrix Computations, Acad. Press, N.Y., 1976. O. Osterby and Z. Zlatev, Direct Methods for Sparse Matrices, Springer-Verlag, N.Y., 1983. N. Rabat, A.E. Ruehli, G.W. Mahoney and J.J. Coleman, A Survey of Macromodeling, Proc. of the IEEE Int. Symp. Circuits Systems, April, 1985, pp. 139-143. 10.1007/s00034-012-9469-zM. Tadeusiewicz, M. and A. Kuczynski, A very fast method for the DC analysis of diode-transistor circuits, Circuits Systems and Signal Processing, Vol. 32, No.3, 2013, pp. 433–451. 10.1109/proc.1981.12170R.K. Brayton, G.D. Hachtel and A.L. Sangiovanni-Vincentelli, A survey of optimization techniques for integrated-circuit design, Proceedings IEEE, Vol. 69, No. 10, 1981, pp. 1334–1362. A.E. Ruehli, (Ed.), Circuit analysis, simulation and design. part 2. Amsterdam: Elsevier Science Publishers, 1987. 10.1109/iccad.2003.159696G. Stehr, M. Pronath, F. Schenkel, H. Graeb and K. Antreich, Initial sizing of analog integrated circuits by centering within topology-given implicit specifications, Proceedings of the IEEE/ACM International Conference on CAD, 2003, pp. 241–246. 10.1109/43.905671M. Hershenson, S. Boyd and T. Lee, Optimal design of a CMOS op-amp via geometric programming. IEEE Transactions on CAD of Integrated Circuits and Systems, Vol. 20, No. 1, 2001, pp. 1–21. I.S. Kashirskiy and I.K. Trokhimenko, General optimization for electronic circuits, Tekhnika, Kiev, 1979. 10.1109/mwsym.1990.99588V. Rizzoli, A. Costanzo and C. Cecchetti, Numerical optimization of broadband nonlinear microwave circuits, IEEE MTT-S Int. Symp., Vol. 1, 1990, pp. 335-338. 10.1109/43.489099E.S. Ochotta, R.A.Rutenbar and L.R. Carley, Synthesis of High-Performance Analog Circuits in ASTRX/OBLX, IEEE Trans. on CAD, Vol.15, No. 3, 1996, pp. 273-294. A.M. Zemliak, Design of Analog Networks by Control Theory Methods, Part 1, Theory, Radioelectronics and Communications Systems, Vol. 47, No. 5, 2004, pp. 11-17. 10.3103/s0735272707110039A.M. Zemliak, Analysis of Dynamic Characteristics of Process of Designing Analogue Circuits, Radioelectronics and Communications Systems, Vol. 50, No. 11, 2007, pp. 603-608. A. Zemliak and T. Markina, Behaviour of Lyapunov ́s function for different strategies of circuit optimization, International Journal of Electronics, Vol. 102, N 4, 2015, pp. 619-634. 10.2307/2312867L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes, Interscience Publishers, Inc., N.Y., 1962. L.W. Neustadt, Synthesis of time-optimal co ntrol systems. J. Math. Analysis and Appl., Vol. 1, 1960, pp. 484–492. 10.1137/0304021J.B. Rosen, Iterative solution of nonlinear optimal control problems, J. SIAM, Control Series A, 1966, pp. 223–244. R.P. Fedorenko, Approximate Solution of Optimal Control Problems, Nauka, Moscow, 1978. 10.1137/130912219L. Bourdin and E. Trélat, Pontryagin maximum principle for finite dimensional nonlinear optimal control problems on time scales. SIAM J. Control Optim., Vol 51, No. 5, 2013, pp. 3781–3813.