Eduardo Schultz, a PhD student at RWTH/Aachen under the supervision of Pr Alexander Mitsos, is visiting the LAGEP this month, and will give a seminar on Friday 27 October 14h, room Jacques Bordet.

**Title**: Dynamic optimization with inequality path constraints

Dynamic optimization with inequality path constraints is present in several engineering problems, where the models are usually described by a system of ODEs, DAEs or PDEs. These problems are infinite problems with infinite degrees of freedom and infinite constraints, since the optimization is performed over the independent variables domain. Most of the methods available in the literature to solve dynamic optimization problems do not guarantee the satisfaction of constraints over the entire domain. Two algorithms are presented in order to solve dynamic optimization problems which guarantee satisfaction of path constraints. The first algorithm is applied to systems described by PDEs, based on an adaptavie restriction and relaxation of the path constraint, extending the algorithm developed by Fu et al., 20151. The second one is a new algorithm based on Taylor approximation of the path constraint, that can be applied to ODEs and DAEs. Both algorithms are ilustrated by a case study composed by a PFR reactor where the objective is to maximize the concentration of product leaving the reactor, controlling the temperature in the jacket and without violating the maximum temperature inside the reactor.

1Fu J et al., 2015, Local optimization of dynamic programs with guaranteed satisfaction of path constraints, AUTOMATICA, Vol: 62, Pages: 184-192.