Generation of discrete first‐ and second‐order sensitivities for single shooting

In this work, an approach to the forward generation of discrete first‐ and second‐order sensitivities is proposed. For this purpose, an algorithm has been developed, which can basically be applied to general implicit differential‐algebraic equation (DAE) systems. Moreover, the approach has been tailored to both the generation of directional derivatives and sensitivities with respect to discontinuous control trajectories. The implementation of the method is discussed here for the orthogonal collocation method based on Legendre–Gauss–Radau points and considering the linear implicit DAE type, which arises in problems related to chemical engineering. Lastly, the approach has been applied to three case studies of different complexities. The corresponding performance for the generation of Jacobian and Hessian information is discussed in detail. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3110–3122, 2012