Calculus of Variations, Functional Analysis, Vector Ring and Optimum Control†
- 1 September 1964
- journal article
- control section
- Published by Taylor & Francis in Journal of Electronics and Control
- Vol. 17 (3) , 345-360
- https://doi.org/10.1080/00207216408937710
Abstract
In this paper it has boon shown that a certain class of regulator problems which has been recently solved by functional analysis techniques can also be solved with the help of the calculus of variations provided generalized functions are also admitted to competition. The equivalence of the two techniques has been exhibited. The algebra of vector rings has been developed in the sequel which makes it easier to treat the nth-order systems as a straightforward generalization of the first-order system. Finally the expression for the optimum control function for a more general norm has boon deduced with the help of calculus of variations. Also the bang-bang principle of Bellman et al. follows as a consequence of the theory.Keywords
This publication has 1 reference indexed in Scilit:
- On the “bang-bang” control problemQuarterly of Applied Mathematics, 1956