An Optimization Problem in Circuits
- 1 March 1965
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 12 (1) , 28-31
- https://doi.org/10.1109/tct.1965.1082368
Abstract
Let\etabe 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 capacitorC. The values of C are restricted byC_{m}\leq \leq C_{m}, whereC_{M}andC_{m}, are given positive constants. Given this inequality constraint onC, any initial state of\eta, a time interval[0, T], and a performance criterion\phiit is shown that the law of variation of C as a function of time which maximizes the value taken by\phiat the state at timeTis bang-bang, i.e.,C(\cdot)is piecewise constant and takes only the valuesC_{m}andC_{M}. A subsidiary result as well as some interpretations are also given.Keywords
This publication has 4 references indexed in Scilit:
- On the necessary condition for optimal control of nonlinear systemsJournal d'Analyse Mathématique, 1964
- CANONICAL STRUCTURE OF LINEAR DYNAMICAL SYSTEMSProceedings of the National Academy of Sciences, 1962
- The existence of optimal controls.The Michigan Mathematical Journal, 1962
- The bang bang servo problem treated by variational techniquesInformation and Control, 1959