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Computations and time‐optimal controls
Author(s) -
Kaya C. Yalçin,
Noakes J. Lyle
Publication year - 1996
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199607/09)17:3<171::aid-oca571>3.0.co;2-9
Subject(s) - computation , concatenation (mathematics) , arc (geometry) , constant (computer programming) , point (geometry) , computer science , algorithm , optimal control , control (management) , mathematics , control theory (sociology) , mathematical optimization , arithmetic , artificial intelligence , geometry , programming language
Abstract A new control method, the switching time computation (STC) method (Kaya, C. Y. and J. L. Noakes, Proc. 33rd IEEE Conf. on Decision and Control , Orlando, FL, 1994, pp. 3823–3824), is described in detail for single‐input non‐linear systems, and the mathematical reasoning behind it is explained. A concatenation of constant‐input arcs is used to get from an initial point to the target, and an optimization procedure is employed to find the necessary time lengths of the arcs. General difficulties of the STC method in finding the necessary arc time lengths are emphasized and exemplified. The STC method is incorporated in a time‐optimal bang‐bang control (TOBC) algorithm. The results of the application of the TOBC algorithm to the van der Pol equation, a third‐order non‐linear system and a non‐linear dynamical model of the F‐8 aircraft are presented. The STC method is shown to be fast by making comparisons with a general optimal control software package.