# American Institute of Mathematical Sciences

May  2002, 2(2): 295-307. doi: 10.3934/dcdsb.2002.2.295

## Asymptotic tracking in DC-to-DC nonlinear power converters

 1 Institut de'Organizació i Control de Sistemes Industrials, Universitat Politècnicade Catalunya, Avda. Diagonal 647, Pl. 11, 08028 Barcelona, Spain, Spain

Received  April 2001 Revised  January 2002 Published  February 2002

The aim of this paper is to solve a tracking problem in a particular second order control system that requires indirect control. A complete knowledge of the plant parameters is assumed. The calculation of the indirect tracking depends on the solution of an inverse problem given by an ordinary differential equation. In spite of the instability of the generic solution of the differential equation, the existence of a bounded, periodic solution for the tracking of a periodic signal is proved. Finally, the periodic solution is approximated by the harmonic balance method, and the original tracking problem is solved.
Citation: E. Fossas-Colet, J.M. Olm-Miras. Asymptotic tracking in DC-to-DC nonlinear power converters. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 295-307. doi: 10.3934/dcdsb.2002.2.295
 [1] Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39 [2] Tayel Dabbous. Identification for systems governed by nonlinear interval differential equations. Journal of Industrial & Management Optimization, 2012, 8 (3) : 765-780. doi: 10.3934/jimo.2012.8.765 [3] Yuriy Golovaty, Anna Marciniak-Czochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations. Communications on Pure & Applied Analysis, 2012, 11 (1) : 229-241. doi: 10.3934/cpaa.2012.11.229 [4] Serge Nicaise. Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021057 [5] Yuxiang Zhang, Shiwang Ma. Some existence results on periodic and subharmonic solutions of ordinary $P$-Laplacian systems. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 251-260. doi: 10.3934/dcdsb.2009.12.251 [6] Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of first-order ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 281-298. doi: 10.3934/dcdsb.2014.19.281 [7] Alessandro Fonda, Fabio Zanolin. Bounded solutions of nonlinear second order ordinary differential equations. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 91-98. doi: 10.3934/dcds.1998.4.91 [8] Fabrício Cristófani, Ademir Pastor. Nonlinear stability of periodic-wave solutions for systems of dispersive equations. Communications on Pure & Applied Analysis, 2020, 19 (10) : 5015-5032. doi: 10.3934/cpaa.2020225 [9] Anatoli F. Ivanov, Sergei Trofimchuk. Periodic solutions and their stability of a differential-difference equation. Conference Publications, 2009, 2009 (Special) : 385-393. doi: 10.3934/proc.2009.2009.385 [10] Qi Yao, Linshan Wang, Yangfan Wang. Existence-uniqueness and stability of the mild periodic solutions to a class of delayed stochastic partial differential equations and its applications. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4727-4743. doi: 10.3934/dcdsb.2020310 [11] Zhengxin Zhou. On the Poincaré mapping and periodic solutions of nonautonomous differential systems. Communications on Pure & Applied Analysis, 2007, 6 (2) : 541-547. doi: 10.3934/cpaa.2007.6.541 [12] Bernard Dacorogna, Alessandro Ferriero. Regularity and selecting principles for implicit ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 87-101. doi: 10.3934/dcdsb.2009.11.87 [13] Zvi Artstein. Averaging of ordinary differential equations with slowly varying averages. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 353-365. doi: 10.3934/dcdsb.2010.14.353 [14] Urszula Ledzewicz, Stanislaw Walczak. Optimal control of systems governed by some elliptic equations. Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 279-290. doi: 10.3934/dcds.1999.5.279 [15] Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 [16] Yingjie Bi, Siyu Liu, Yong Li. Periodic solutions of differential-algebraic equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1383-1395. doi: 10.3934/dcdsb.2019232 [17] Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167 [18] Adriana Buică, Jean–Pierre Françoise, Jaume Llibre. Periodic solutions of nonlinear periodic differential systems with a small parameter. Communications on Pure & Applied Analysis, 2007, 6 (1) : 103-111. doi: 10.3934/cpaa.2007.6.103 [19] Armengol Gasull, Héctor Giacomini, Maite Grau. On the stability of periodic orbits for differential systems in $\mathbb{R}^n$. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 495-509. doi: 10.3934/dcdsb.2008.10.495 [20] Jifeng Chu, Zaitao Liang, Fangfang Liao, Shiping Lu. Existence and stability of periodic solutions for relativistic singular equations. Communications on Pure & Applied Analysis, 2017, 16 (2) : 591-609. doi: 10.3934/cpaa.2017029

2020 Impact Factor: 1.327