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UBC Theses and Dissertations

A study of various computational methods for determining time optimal control of time delay system Morse, James Gregory


In this thesis some numerical techniques for obtaining the time optimal control of a class of time delay systems are studied and compared. The delays may be fixed or time varying. The delay systems considered, which need not be linear or time invariant, are those for which the time optimal control is bang-bang. The optimal control is found by carrying out a search in switching interval space. The method of Rosenbrock⁽²’³⁾ is used to find the switching intervals which maximize a performance index of the final states and terminal time. Kelly's⁽²¹⁾ method of gradients is shown to be applicable to systems with time varying time delays by using the costate equations of ref. [10]. The perturbations in the control are chosen in such a way that the descent in function space is changed to a steepest descent in switching interval space. In a third approach, a technique similar to that of Bryson and Denham⁽¹⁹⁾ is used to account for the terminal conditions directly. All the methods are illustrated by examples. The advantages of the direct search based on Rosenbrock's method are a) ease of programming and b) rapid convergence close to the optimum. However, initial convergence is slow when compared to that of either gradient method. Of the two gradient methods, that based on a penalty function approach was superior in ease of programming and convergence close to the optimum to that based on a descent to the final target set. Neither gradient scheme could match the rapid convergence of the Rosenbrock method close to the optimum

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