##
**Offline model predictive control based on weighted projection over polytopes.**
*(English)*
Zbl 1342.93057

Summary: This work presents a novel offline model predictive control technique for tracking of constrained systems. The quadratic programming problem, commonly found in constrained control methods, is replaced by sequential offline set projections based on priority given to the decision variables. If a preference is established in terms of which decision variables are more desirable, the optimization problem can be solved by sequentially choosing the most important variables and performing a membership test with the projection of the constraint closed set over the related dimensions. Thus, real-time optimization is replaced by offline projection operations and online one-dimensional membership tests. This concept of decision variable prioritization is then applied to a form of model predictive control: feasible target tracking. Three quadratic programming problems are replaced by the proposed method. In the first problem, attainable steady-state demands are computed based on the performance of the plant.
The reachable target command is then filtered in terms of dynamic admissibility, creating feasible inputs to the plant. Finally, the control is computed considering the current state and disturbance vectors along with the feasible and attainable command. Simulations of the method executing a path-following task are presented, demonstrating its benefits with negligible online computational burden.

### MSC:

93B40 | Computational methods in systems theory (MSC2010) |

90C20 | Quadratic programming |

### Keywords:

model predictive control; weighted projection over polytopes; quadratic programming; decision variable prioritization
PDF
BibTeX
XML
Cite

\textit{F. A. de Almeida}, J. Appl. Math. 2015, Article ID 741348, 14 p. (2015; Zbl 1342.93057)

Full Text:
DOI

### References:

[1] | Rawlings, J. B.; Mayne, D. Q., Model Predictive Control: Theory and Design (2009), Madison, Wis, USA: Nob Hill Publishing, Madison, Wis, USA |

[2] | Hartley, E. N.; Trodden, P. A.; Richards, A. G.; Maciejowski, J. M., Model predictive control system design and implementation for spacecraft rendezvous, Control Engineering Practice, 20, 7, 695-713 (2012) |

[3] | Richards, A.; How, J. P., Aircraft trajectory planning with collision avoidance using mixed integer linear programming, Proceedings of the American Control Conference |

[4] | Keviczky, T.; Balas, G. J., Software-enabled receding horizon control for autonomous unmanned aerial vehicle guidance, Journal of Guidance, Control, and Dynamics, 29, 3, 680-694 (2006) |

[5] | de Almeida, F. A.; Leissling, D., Fault-tolerant model predictive control with flight-test results, Journal of Guidance, Control, and Dynamics, 33, 2, 363-375 (2010) |

[6] | Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N., The explicit linear quadratic regulator for constrained systems, Automatica, 38, 1, 3-20 (2002) · Zbl 0999.93018 |

[7] | Richter, S.; Jones, C. N.; Morari, M., Computational complexity certification for real-time MPC with input constraints based on the fast gradient method, IEEE Transactions on Automatic Control, 57, 6, 1391-1403 (2012) · Zbl 1369.93348 |

[8] | Jerez, J. L.; Constantinides, G. A.; Kerrigan, E. C., Towards a fixed point QP solver for predictive control, Proceedings of the 51st IEEE Conference on Decision and Control |

[9] | Jacklin, S. A., Closing the certification gaps in adaptive flight control software, Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit |

[10] | Monnigmann, M.; Jost, M., Vertex based calculation of explicit MPC laws, Proceedings of the American Control Conference (ACC ’12) |

[11] | de Almeida, F. A., Reference management for fault-tolerant model predictive control, Journal of Guidance, Control, and Dynamics, 34, 1, 44-56 (2011) |

[12] | Maeder, U.; Borrelli, F.; Morari, M., Linear offset-free model predictive control, Automatica, 45, 10, 2214-2222 (2009) · Zbl 1179.93078 |

[13] | Pannocchia, G.; Kerrigan, E. C., Offset-free receding horizon control of constrained linear systems, AIChE Journal, 51, 12, 3134-3146 (2005) |

[14] | Boyd, S.; Vandenberghe, L., Convex Optimization (2009), Cambridge, UK: Cambridge University Press, Cambridge, UK |

[15] | Rossiter, J. A.; Kouvaritakis, B.; Rice, M. J., A numerically robust state-space approach to stable-predictive control strategies, Automatica, 34, 1, 65-73 (1998) · Zbl 0913.93022 |

[16] | Chisci, L.; Zappa, G., Dual mode predictive tracking of piecewise constant references for constrained linear systems, International Journal of Control, 76, 1, 61-72 (2003) · Zbl 1078.93028 |

[17] | Rawlings, J. B.; Angeli, D.; Bates, C. N., Fundamentals of economic model predictive control, Proceedings of the 51st IEEE Conference on Decision and Control (CDC ’12) |

[18] | Shead, L. R.; Rossiter, J. A., Feasibility for non-square linear MPC, Proceedings of the American Control Conference (ACC ’07), IEEE |

[19] | de Almeida, F. A.; Guerra, E. B.; D’Oliveira, F. A.; Mello, A. W., Constrained linear quadratic tracker for optimal flight performance, Journal of Guidance, Control, and Dynamics, 35, 6, 1911-1918 (2012) |

[20] | Dubins, L. E., On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents, The American Journal of Mathematics, 79, 3, 497-516 (1957) · Zbl 0098.35401 |

[21] | Tsourdos, A.; White, B.; Shanmugavel, M., Cooperative Path Planning of Unmanned Aerial Vehicles (2010), Chichester, UK: John Wiley & Sons, Chichester, UK |

[22] | Galisteu, D. G.; de Almeida, F. A., Three-dimensional guidance filter for autonomous collision avoidance, Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit |

[23] | Bryson, A. E., Control of Spacecraft and Aircraft (1994), Princeton, NJ, USA: Princeton University Press, Princeton, NJ, USA |

[24] | Kvasnica, M., Real-Time Model Predictive Control via Multi-Parametric Programming: Theory and Tools (2009), Saarbrucken, Germany: VDM, Saarbrucken, Germany |

[25] | Fletcher, R., Practical Methods of Optimization. Practical Methods of Optimization, A Wiley-Interscience Publication (1987), West Sussex, UK: John Wiley & Sons, West Sussex, UK · Zbl 0905.65002 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.