A multipoint shooting feasible-SQP method for optimal control of state-constrained parabolic DAE systems

Optimal control problem for parabolic differential-algebraic equations (PDAE) systems with spatially sensitive state-constraints and technological constraints is considered. Multipoint shooting approach is proposed to attack such problems. It is well suited to deal with unstable and ill-conditioned PDAE systems. This approach consists in the partitioning of the time-space domain into shorter layers, which allows us to fully parallelize the computations and to employ the reliable PDAE solvers. A new modified method of this kind is developed. It converts the multipoint shooting problem having mixed equality and inequality constraints into the purely inequality constrained problem. The results of the consecutive layer shots are exploited to determine a feasible shooting solution of the converted problem. The knowledge of such a solution is crucial for the use of highly efficient feasible-SQP methods avoiding the incompatibility of the constraints of the QP subproblems (versus the infeasible path SQP methods). The applications of the method proposed to the optimization of some heat transfer processes as well as chemical production processes performed in tubular reactors are discussed.