An Optimization Problem in Circuits

Author

Desoer, Charles A.

Volume

Issue

fYear

1965

fDate

3/1/1965 12:00:00 AM

Firstpage

Lastpage

Abstract

Let $\\eta$ be a linear, time-invariant, lumped two-port driven at its port 1 by a voltage source e. and loaded at its port 2 by a variable capacitor $C$ . The values of C are restricted by $C_{m}\\leq \\leq C_{m}$ , where $C_{M}$ and $C_{m}$ , are given positive constants. Given this inequality constraint on $C$ , any initial state of $\\eta$ , a time interval $[0, T]$ , and a performance criterion $\\phi$ it is shown that the law of variation of C as a function of time which maximizes the value taken by $\\phi$ at the state at time $T$ is bang-bang, i.e., $C(\\cdot)$ is piecewise constant and takes only the values $C_{m}$ and $C_{M}$ . A subsidiary result as well as some interpretations are also given.

Keywords

Capacitance; Capacitors; Circuits; Constraint optimization; Laplace equations; Nonlinear equations; Vectors; Voltage control;

fLanguage

English

Journal_Title

Circuit Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9324

Type

jour

DOI

10.1109/TCT.1965.1082368

Filename

1082368

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1159758