Premium
On some optimal control problems for electrical circuits
Author(s) -
Altmann Kristof,
Stingelin Simon,
Tröltzsch Fredi
Publication year - 2014
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.1889
Subject(s) - optimal control , maximum principle , control theory (sociology) , nonlinear system , principal (computer security) , electronic circuit , pontryagin's minimum principle , electrical network , mathematics , multigrid method , terminal (telecommunication) , computer science , mathematical optimization , differential equation , control (management) , engineering , electrical engineering , mathematical analysis , telecommunications , physics , quantum mechanics , artificial intelligence , operating system
Some optimal control problems for linear and nonlinear ordinary differential equations related to the optimal switching between different magnetic fields are considered. The main aim is to move an electrical initial current by a controllable voltage in shortest time to a desired terminal current and to hold it afterwards. Necessary optimality conditions are derived by Pontryagin's principle and a formal Lagrange technique. In the case of a linear system, the principal structure of time‐optimal controls is discussed. The associated optimality systems are solved by a one‐shot strategy using a multigrid software package. Various numerical examples are discussed. Copyright © 2013 John Wiley & Sons, Ltd.