Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

The authors would like to acknowledge financial support from the project Estancias de movilidad en el extranjero "Jose Castillejo" para jóvenes doctores (JC2011-0054) of the Spanish “Ministerio de Educación”, and from the Spanish “Ministerio de Ciencia e Innovacion” (CTQ2012-37039-C02-02). The authors also acknowledge financial support from the Center of Process Decision-making at Carnegie Mellon University.