TR2018-119

Quasi-Newton Jacobian and Hessian Updates for Pseudospectral based NMPC


    •  Quirynen, R., Hespanhol, P., "Quasi-Newton Jacobian and Hessian Updates for Pseudospectral based NMPC", IFAC Conference on Nonlinear Model Predictive Control (NMPC), DOI: 10.1016/​j.ifacol.2018.10.169, August 2018, vol. 51, pp. 22-27.
      BibTeX TR2018-119 PDF
      • @inproceedings{Quirynen2018aug,
      • author = {Quirynen, Rien and Hespanhol, Pedro},
      • title = {Quasi-Newton Jacobian and Hessian Updates for Pseudospectral based NMPC},
      • booktitle = {IFAC Conference on Nonlinear Model Predictive Control (NMPC)},
      • year = 2018,
      • volume = 51,
      • number = 20,
      • pages = {22--27},
      • month = aug,
      • publisher = {Elsevier},
      • doi = {10.1016/j.ifacol.2018.10.169},
      • url = {https://www.merl.com/publications/TR2018-119}
      • }
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  • Research Areas:

    Control, Dynamical Systems, Optimization

Abstract:

Pseudospectral and collocation methods form a popular direct approach to solving continuous-time optimal control problems. Lifted Newton-type algorithms have been proposed as a computationally efficient way to implement online pseudospectral methods for nonlinear model predictive control (NMPC). The present paper extends this work based on a rank-one Jacobian update formula for the nonlinear system dynamics. In addition, we describe an algorithm implementation where this rank-one Jacobian update can be used directly to compute a low-rank update to the condensed Hessian, resulting in an overall quadratic computational complexity for each iteration. A preliminary C code implementation is shown to allow considerable numerical speedups for the optimal control case study of the nonlinear chain of masses.

 

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