On the Implementation of a Preconditioned Riccati Recursion based Primal-Dual Interior-Point Algorithm for Input Constrained Optimal Control Problems*

Morten Ryberg Wahlgreen, John Bagterp Jørgensen*

*Corresponding author for this work

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Abstract

We present a preconditioned interior-point algorithm tailored for input constrained quadratic programmings (QPs) arising in optimal control problems (OCPs). The implicit approach to OCPs results in large sparse QPs, which we utilized by a tailored Riccati recursion algorithm. The Riccati recursion algorithm requires the solution of a set of small dense linear sub-systems of equations. The proposed preconditioner is an easily invertible diagonal matrix, which we apply in every linear sub-system of equations. We solve a target tracking OCP for a linearized modified quadruple tank system in Matlab. The computational results indicate that ill-conditioning in the sub-systems are reduced and that the additional CPU time for preconditioning is negligible. Additionally, the paper presents a detailed description of the proposed algorithm and serves as an implementation guide for the algorithm.

Original languageEnglish
Book seriesIFAC-PapersOnLine
Volume55
Issue number7
Pages (from-to)346-351
ISSN2405-8963
DOIs
Publication statusPublished - 2022
Event13th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems - Busan, Korea, Republic of
Duration: 14 Jun 202217 Jun 2022

Conference

Conference13th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems
Country/TerritoryKorea, Republic of
CityBusan
Period14/06/202217/06/2022

Keywords

  • Interior-point method
  • Optimal Control Problem
  • Preconditioning
  • Quadratic programming
  • Riccati recursion

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