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The time-optimal design of linear dynamic systems

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2 Author(s)
Horne, G. ; Nova Scotia Technical College, Halifax, Nova Scotia ; Bernholtz, B.

The following general time-optimal design problem is studied: determine a real constant square matrix,A, subject to specified constraints, to minimize the transit time between specified endpoints while satisfying the vector differential equationdot{x}(t) = Ax(t). Two specific kinds of constraints onAare considered: 1) where the individual elements ofAare free but the matrix as a whole must satisfyQ(A) leq hat{Q}whereQ(A)is a specified homogeneous function of the elements ofAandhat{Q}is a given upper bound and 2) where the elements ofAare individually bounded. Theoretical results show that both problems can be solved by first solving a related minimum cost fixed time problem. The latter problem is solved iteratively by using the generalized Newton-Raphson method for two point boundary value problems to provide a set of linear equations at each iteration. The cost functionQis then minimized subject to these equations using appropriate optimization techniques.

Published in:

Automatic Control, IEEE Transactions on  (Volume:19 ,  Issue: 3 )

Date of Publication:

Jun 1974

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