Direct and indirect optimization of linear time-invariant dynamic systems using transformations

This paper deals with optimal trajectory generation of linear dynamic syste ms commanded between two fixed states in a prescribed final time. From the literature, it is well known that the optimal solution of this problem sati sfies first-order linear differential equations in the state and costate va riables. In this paper, a new procedure is presented for optimization where transformations are used to embed the state equations explicitly into the cost functional. The resulting transformed functional is then solved by bot h direct and indirect methods. The computational trade-offs of these method s are discussed. Copyright (C) 1998 John Wiley & Sons, Ltd.