TR2020-086

Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control


    •  Quirynen, R., Hespanhol, P., "Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control", Journal of Optimization Methods and Software, DOI: 10.1080/​10556788.2019.1653869, June 2020.
      BibTeX TR2020-086 PDF
      • @article{Quirynen2020jun,
      • author = {Quirynen, Rien and Hespanhol, Pedro},
      • title = {Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control},
      • journal = {Journal of Optimization Methods and Software},
      • year = 2020,
      • month = jun,
      • doi = {10.1080/10556788.2019.1653869},
      • url = {https://www.merl.com/publications/TR2020-086}
      • }
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  • Research Areas:

    Control, Optimization

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.

 

  • Related Publication

  •  Hespanhol, P., Quirynen, R., "Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control", arXiv, March 2019.
    BibTeX arXiv
    • @article{Hespanhol2019mar2,
    • author = {Hespanhol, Pedro and Quirynen, Rien},
    • title = {Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control},
    • journal = {arXiv},
    • year = 2019,
    • month = mar,
    • url = {https://arxiv.org/abs/1903.08720}
    • }