# The Double Description Method for the Approximation of Explicit MPC Control Laws

Author(s):C.N. Jones, M. Morari |
Conference/Journal:Conference on Decision and Control (CDC), Cancun, Mexico |

Abstract:A standard model predictive controller (MPC) can be written as a parametric optimization problem whose solution is a piecewise affine (PWA) map from the measured state to the optimal control input. The primary limitation of this optimal ‘explicit solution’ is that the complexity can grow quickly with problem size, and so in this paper we seek to compute approximate explicit control laws that can tradeoff complexity for approximation error. This computation is accomplished in a two-phase process: First, inner and outer polyhedral approximations of the the convex cost function of the parametric problem are computed with an algorithm based on an extension to the classic double-description method; a convex hull approach. The proposed method has two main advantages from a control point of view: it is an incremental approach, meaning that an approximation of any specified complexity can be produced and it operates on implicitly-defined convex sets, meaning that the optimal solution of the parametric problem is not required. In the second phase of the algorithm, a feasible approximate control law is computed that has the cost function derived in the first phase. For this purpose, a new interpolation method is introduced based on recent work on barycentric interpolation. The resulting control law is continuous, although non-linear and defined over a non-simplical polytopic partition of the state space. The non-simplical nature of the partition generates significantly simpler approximate control laws than current competing methods, as demonstrated on computational examples. | Year:2008 |

Type of Publication:(01)Article | |

Supervisor:M. Morari | |

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% Autogenerated BibTeX entry @InProceedings { JonMor:2008:IFA_3103, author={C.N. Jones and M. Morari}, title={{The Double Description Method for the Approximation of Explicit MPC Control Laws}}, booktitle={Conference on Decision and Control (CDC)}, pages={}, year={2008}, address={Cancun, Mexico}, month=dec, url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=3103} } | |

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