Adjoint-based SQP method with block-wise quasi-Newton Jacobian updates for nonlinear optimal control. (3rd September 2021)

• Record Type: Journal Article
• Authors: Hespanhol, Pedro; Quirynen, Rien
• Is Part Of: Optimization methods and software. Volume 36:Number 5(2021)
• Page Start: 1030
• Page End: 1058
• Publication Date: 2021-09-03
• Subjects: Nonlinear model predictive control -- sequential quadratic programming -- quasi-Newton updates -- convergence analysis -- direct collocation -- multiple shooting; 49K15 -- 49M37 -- 90C53 -- 65K05; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1653869
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : Nonlinear model predictive control (NMPC) generally requires the solution of a non-convex dynamic 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 NMPC.