### Abstract

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 language | English |
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Title of host publication | Proceedings of European Control Conference (ECC) 2014 |

Publisher | IEEE |

Publication date | 2014 |

Pages | 115-120 |

DOIs | |

Publication status | Published - 2014 |

Event | 13th European Control Conference (ECC) 2014 - Strasbourg Convention and Exhibition Center, Strasbourg, France Duration: 24 Jun 2014 → 27 Jun 2014 Conference number: 13 http://www.ecc14.eu/ |

### Conference

Conference | 13th European Control Conference (ECC) 2014 |
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Number | 13 |

Location | Strasbourg Convention and Exhibition Center |

Country | France |

City | Strasbourg |

Period | 24/06/2014 → 27/06/2014 |

Internet address |

### Keywords

- 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

## Cite this

Sokoler, L. E., Frison, G., Andersen, M. S., & Jørgensen, J. B. (2014). Input-constrained model predictive control via the alternating direction method of multipliers. In

*Proceedings of European Control Conference (ECC) 2014*(pp. 115-120). IEEE. https://doi.org/10.1109/ECC.2014.6862441