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A multiresolution approximation method for fast explicit model predictive control


S. Summers, C.N. Jones, J. Lygeros, M. Morari

IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2530 - 2541

A model predictive control law is given by the solution to a parametric optimization problem that can be pre-computed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolets. The resulting interpolation is shown to be everywhere feasible and continuous. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a grid hierarchy, convergence to a stabilizing control law is guaranteed and the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. Two examples are provided; A two-dimensional example with an evaluation speed of $31$ ns and a four-dimensional example with an evaluation speed of $119$ ns.


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% Autogenerated BibTeX entry
@Article { SumEtal:2011:IFA_3723,
    author={S. Summers and C.N. Jones and J. Lygeros and M. Morari},
    title={{A multiresolution approximation method for fast explicit
	  model predictive control}},
    journal={IEEE Transactions on Automatic Control},
    pages={2530 -- 2541},
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