Alexander Zemliak



Application of Maximum Principle for Time Minimization of Circuit Design Process

pdf PDF



The possibility of applying the maximum principle of Pontryagin to the problem of optimisation of electronic circuits is analysed. 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 maximum 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 to some orders of magnitude.



Circuit optimisation, controllable dynamic system, optimisation strategies, maximum principle of Pontryagin



[1] O. Osterby and Z. Zlatev, Direct Methods for Sparse Matrices, New York, NY: Springer- Verlag, 1983.

[2] N. Rabat, A.E. Ruehli, G.W. Mahoney, and J.J. Coleman, A survey of macromodelling, Proc. of IEEE Int. Symp. CAS, 1985, pp. 139–143.

[3] M. Tadeusiewicz, 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.

[4] R.K. Brayton, G.D. Hachtel, and A.L. Sangiovanni-Vincentelli, A survey of optimization techniques for integrated-circuit design, Proc IEEE, Vol. 69, No. 10, 1981, pp. 1334-1362.

[5] G. Stehr, M. Pronath, F. Schenkel, H. Graeb, and K. Antreich, Initial sizing of analog integrated circuits by centering within topology-given implicit specifications, Proc. IEEE/ACM Int. Conf. CAD, 2003, pp. 241–246.

[6] M. Hershenson, S. Boyd, and T. Lee, Optimal design of a CMOS op-amp via geometric programming, IEEE Trans.CAD of Integr. Circ. Sys., Vol. 20, No. 1, 2001, pp. 1–21. [7] I.S. Kashirskiy, and Y.K. Trokhimenko, General optimization of electronic circuits, Kiev: Tekhnika, 1979.

[8] V. Rizzoli, A. Costanzo, and C. Cecchetti, Numerical optimization of broadband nonlinear microwave circuits, Proc. IEEE MTT-S Int. Symp., Vol. 1, 1990, pp. 335–338.

[9] E.S. Ochotta, R.A. Rutenbar, and L.R. Carley, Synthesis of high-performance analog circuits in ASTRX/OBLX, IEEE Trans. CAD Integr. Circ. Sys., Vol. 15, 1996, pp. 273–294.

[10] A. Zemliak, Analog System Design Problem Formulation by Optimum Control Theory, IEICE Trans. Fundam., Vol. E84-A, 2001, pp. 2029-2041.

[11] A.M. Zemliak, Comparative Analysis of the Lyapunov Function for Different Strategies of Analogue Circuits Design, Radioelectron. and Communic. Sys., Vol. 51, No. 5, 2008, pp. 233- 238.

[12] A.M. Zemliak, Analysis of Dynamic Characteristics of a Minimal-Time Circuit Optimization Process, Int. J. of Mathematic Models and Methods in Applied Sciences, Vol. 1, No. 1, 2007, pp. 1-10.

[13] L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko, The Mathematical Theory of Optimal Processes, New York: Interscience Publishers, Inc., 1962.

[14] L.W. Neustadt, Synthesis of time-optimal control systems, J. Math. Analysis Applications, Vol. 1, No. 2, 1960, pp. 484-492. [15] J.B. Rosen, Iterative Solution of Nonlinear Optimal Control Problems, J. SIAM, Control Series A, 1966, pp. 223-244.

[16] L. 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.

[17] A. Zemliak, Maximum principle for problem of circuit optimization, Electronics Letters, Vol. 52, No. 9, 2016, pp. 695-697.

[18] A.M. Zemliak, Acceleration Effect of System Design Process, IEICE Trans. Fundam., Vol. E85-A, No. 7, 2002, pp. 1751-1759.

Cite this paper

Alexander Zemliak. (2017) Application of Maximum Principle for Time Minimization of Circuit Design Process. International Journal of Circuits and Electronics, 2, 57-63


Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0