Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control
For practitioners of nonlinear model predictive control requiring real-time solutions, this work provides a more efficient algorithm with theoretical convergence guarantees.
The paper presents a local convergence analysis for an adjoint-based SQP algorithm with block-wise quasi-Newton Jacobian updates for nonlinear optimal control, demonstrating computational efficiency by avoiding matrix factorizations and matrix-matrix operations in implicit integration schemes, validated on two NMPC case studies.
Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This paper provides a local convergence analysis for the recently proposed adjoint-based sequential quadratic programming~(SQP) algorithm that is based on a block-structured variant of the two-sided rank-one~(TR1) quasi-Newton update formula to efficiently compute Jacobian matrix approximations in a sparsity preserving fashion. A particularly efficient algorithm implementation is proposed in case an implicit integration scheme is used for discretization of the optimal control problem, in which matrix factorization and matrix-matrix operations can be avoided entirely. The convergence analysis results as well as the computational performance of the proposed optimization algorithm are illustrated for two simulation case studies of nonlinear MPC.