A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems

Abstract

Direct boundary value problem methods in connection with SQP iteration have proven very successful in solving nonlinear optimal control problems. Such methods use parameterized control functions, discretize the state differential equations by, e.g., multiple shooting or collocation, and treat the discretized BVP as an equality-constraint in a large nonlinear constrained optimization problem. In realistic applications several thousands of variables can appear in the NLP. Solution by standard techniques is therefore impractical. A careful choice of the discretization leads to QP subproblems possessing a very special m-stage block-sparse structure, where m is the grid size. The paper presents a recursive solution algorithm that fully exploits this QP sparseness to generate a factorization of the inverse of the KKT matrix in O(m) operations. A structure-preserving primal-dual barrier method is proposed for treating the generally large number of state and control inequality constraints.