Parallel Simultaneous Approach for optimal control of DAE systems

In the paper two approaches of parallelization for solving optimal control problems of ODE and index-1 DAE systems were presented and discussed. DAE Optimization Problem can be treated by Direct Nonlinear Programming Approach in two manners, known as Sequential Approach and Simultaneous Approach. Simultaneous Approach seems to be more reliable, because provides initial states in periods and discretized control variables. Therefore there is a possibility of efficient use of Optimization with multiple shooting, which was developed to handle unstable DAE systems. In the article some parallelization methods of the Sequential Quadratic Programming were discussed and compared both in the Jacobian calculation and the numerical integration of DAE models. Augmented objective function, based on Mathematical Programming with Complementarity Constraints, was proposed. The illustrative simulations of Catalyst Mixing Problem were performed in MATLAB, which is a commonly known programming environment.