Input-constrained model predictive control via the alternating direction method of multipliers

Leo Emil Sokoler, Gianluca Frison, Martin S. Andersen, John Bagterp Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


This paper presents an algorithm, based on the alternating direction method of multipliers, for the convex optimal control problem arising in input-constrained model predictive control. We develop an efficient implementation of the algorithm for the extended linear quadratic control problem (LQCP) with input and input-rate limits. The algorithm alternates between solving an extended LQCP and a highly structured quadratic program. These quadratic programs are solved using a Riccati iteration procedure, and a structure-exploiting interior-point method, respectively. The computational cost per iteration is quadratic in the dimensions of the controlled system, and linear in the length of the prediction horizon. Simulations show that the approach proposed in this paper is more than an order of magnitude faster than several state-of-the-art quadratic programming algorithms, and that the difference in computation time grows with the problem size. We improve the method further using a warm-start procedure.
Original languageEnglish
Title of host publicationProceedings of European Control Conference (ECC) 2014
Publication date2014
Publication statusPublished - 2014
Event13th European Control Conference (ECC) 2014 - Strasbourg Convention and Exhibition Center, Strasbourg, France
Duration: 24 Jun 201427 Jun 2014
Conference number: 13


Conference13th European Control Conference (ECC) 2014
LocationStrasbourg Convention and Exhibition Center
Internet address


  • convex programming
  • optimal control
  • predictive control
  • quadratic programming
  • Riccati equations
  • Power, Energy and Industry Applications
  • Robotics and Control Systems
  • Signal Processing and Analysis
  • Transportation
  • Benchmark testing
  • Control systems
  • convex optimal control problem
  • direction method
  • extended linear quadratic control problem
  • Heuristic algorithms
  • highly structured quadratic program
  • input-constrained model predictive control
  • LQCP
  • multipliers
  • Optimization
  • Prediction algorithms
  • prediction horizon
  • Predictive control
  • quadratic programming algorithms
  • quadratic programs
  • Riccati iteration procedure
  • structure-exploiting interior-point method
  • Vectors
  • warm-start procedure


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