Sequential l1 quadratic programming for nonlinear model predictive control

Dimitri Boiroux, John Bagterp Jørgensen

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In this paper, we present and describe a computationally efficient sequential l1 quadratic programming (Sl1QP) algorithm for Nonlinear Model Predictive Control (NMPC). We use a tailored trust region sequential quadratic programming for the solution of the optimal control problem (OCP) involved in the NMPC algorithm. We use a multiple shooting approach for numerical integration and sensitivity computation. A second order correction ensures a faster convergence of the SQP algorithm. We exploit the structure of the OCP by using an efficient primal-dual interior point algorithm based on Riccati factorizations and a block diagonal BFGS update of the Hessian matrix. The complexity scales linearly with the prediction horizon length. We numerically evaluate and compare the performance of our algorithm on a numerical example.

Original languageEnglish
Book seriesIFAC-PapersOnLine
Issue number1
Pages (from-to)474-479
Publication statusPublished - 1 Jan 2019
Event12th IFAC Symposium on Dynamics and Control of Process Systems - Jurerê Beach Village Hotel, Florianópolis , Brazil
Duration: 23 Apr 201926 Apr 2019
Conference number: 12


Conference12th IFAC Symposium on Dynamics and Control of Process Systems
LocationJurerê Beach Village Hotel
Internet address


  • Nonlinear model predictive control
  • Sequential quadratic programming
  • Trust region algorithm


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