Batch distillation of binary mixtures: preliminary analysis of optimal control

This paper develops a theory of singular arc, and the correspond- ing second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation

Due to the presence of tabulated data in the physical model, the exact expression of the singular control cannot be obtained from the time derivatives of the switching function..

Abstract— We present a theory of singular arc, and the corresponding second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation

For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition

By a qualitative analysis of these optimal control problems we are able to detect an asymptotic behaviour of the shape of the corre- sponding optimal trajectories, in case the

Index Terms— optimal control, singular control, second or- der optimality condition, weak optimality, shooting algorithm, Gauss-Newton

The proof of our main result, Theorem 1, concerning the bang-bang property for time optimal controls governed by semilinear heat equation with local control is given in section

Furthermore, since the anesthesia model presents multiple time scale dynamics that can be split in two groups : fast and slow and since the BIS is a direct function of the fast ones,