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

This paper deals with optimal trajectory generation of linear dynamic systems commanded between two fixed states in a prescribed final time. From the literature, it is well known that the optimal solution of this problem satisfies first-order linear differential equations in the state and costate variables. 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 both direct and indirect methods. The computational trade-offs of these methods are discussed.