Optimization of dynamic systems with rigorous path constraint satisfaction

Rigorous satisfaction of path constraints in dynamic optimization is important since they often reflect the safety and quality limits of a process. A difficulty that arises is that they have to be fulfilled during the whole time horizon. Most existing methods discretize these infinite constraints and cannot guarantee the satisfaction at all times. Fu et al. (2015) proposed an algorithm that finitely returns an approximate KKT-optimal point that satisfies the path constraints rigorously. Only a finite number of interior-point constraints is needed due to an adaptive restriction of the right-hand side of the path constraints. However, this algorithm may require many iterations, as only one interior-point constraint is added per iteration. In this work, it is shown that adding more constraints at each iteration leads to improvements both in CPU time and number of iterations. One considered method is the inclusion of all local violation maxima time points. Another idea is to detect the segments, where the constraints are violated and include the middle and end-points of these segments. The algorithm is extended to treat differential-algebraic equation systems of index 1. The Williams-Otto semi-batch reactor is used as a numerical case study to demonstrate the effectiveness of the faster population methods.