Fast Recursive SQP MethodsforLarge - Scale Optimal Control Problems

Direct boundary value problem methods in combination with SQP iteration have proved to be very successful in solving nonlinear optimal control problems. Such methods use parameterized control functions, discretize the state di erential equations by, e.g., multiple shooting or collocation, and treat the discretized boundary value problem as an equality constraint in a large, nonlinear, constrained optimization problem. In real-life applications several thousand variables may appear in the NLP. Solution by standard techniques is therefore impractical. This dissertation develops a general concept for a class of structured direct SQP methods based on a decoupling strategy. A careful choice of the discretization reveals an inherent multistage block structure of the QP subproblems. We present a recursive solution algorithm for the associated KKT systems which makes full use of this sparse structure, and propose a structure-preserving primal-dual interior point method for treating the generally large number of path inequality constraints. Extensive numerical tests including a comparison with other sparse solvers document the high e ciency of the recursive algorithm.