Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control

Abstract

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 twosided 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.

Sequential Hierarchical Least-Squares Programming for Prioritized Non-Linear Optimal Control

“…Here the subproblems exhibit a banded structure which, when properly exploited, only leads to a linear instead of cubic increase of the computational complexity with the length of the control horizon (Wang and Boyd 2010). A block-wise Quasi-Newton method for banded Jacobian updates in non-linear optimal control has been proposed for example in (Hespanhol and Quirynen 2021). Sparsity preserving nullspace bases for nullspace method based solvers have been proposed in numerous work (Topcu 1979;Yang et al 2019;.…”