Optimization of some Non-linear Control Systems by means of Bellmans' Equation and Dimensional Analysis†
- 1 April 1966
- journal article
- research article
- Published by Taylor & Francis in International Journal of Control
- Vol. 3 (4) , 359-394
- https://doi.org/10.1080/00207176608921390
Abstract
For some simple control sytems, controllers are found which minimize integral-square-error- and similar performance criteria, subject to a constraint on control signal magnitude. The method used is that of setting up and solving Bellman's partial differential equation of continuous dynamic programming. Dimensional methods are used in the solution of Bellman's equation. The techniques are close to those of Wonham (1963), which are discussed and clarified. It is shown incidentally that the conventional pi theorem of dimensional theory is invalid when certain variables can change sign. A modified pi theorem, applicable to variables which can change sign, is proved.Keywords
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