A modified multipoint shooting feasible-SQP method for optimal control of DAE systems

Optimal control problem for state-constrained differential-algebraic (DAE) systems is considered. Such problems can be attacked by the multiple shooting approach well suited to unstable and ill-conditioned dynamic systems. According to this approach the control interval is partitioned into shorter intervals allowing the parallelization of computations with the reliable using of DAE solvers. A new modified method of this kind is proposed, which converts the partitioned problem with mixed equality and inequality constraints into the purely inequality constrained problem. An algorithm for obtaining a feasible initial solution of the converted problem is described. A feasible-SQP algorithm based on an active set strategy is applied to the converted problem. It avoids the inconsistency of the constraints of the QP subproblems (versus the infeasible path SQP methods) and delivers a locally optimal solution of the basic problem preserving all its constraints (including the equality ones), which is of a high practical meaning. Some further developments concerning the regularization of suboptimal solutions for large-scale DAE optimal control problems and multilevel versions of the method proposed are also discussed. The theoretical considerations are illustrated by a numerical example of optimization of a complex DAE chemical engineering system.