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Suboptimal Explicit RHC via Approximate Multiparametric Quadratic Programming


A. Bemporad, C. Filippi

vol. AUT02-07

Algorithms for solving multiparametric quadratic programming (mp-QP) were recently proposed in [1,2] for computing explicit Receding Horizon Control (RHC) laws for linear systems subject to linear constraints on input and state variables. The reason for this interest is that the solution to mp-QP is a piecewise affine function of the state vector and thus it is easily implementable on-line. The main drawback of solving mp-QP exactly is that whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. In this paper we address the problem of finding approximate solutions to mp-QP, where the degree of approximation is arbitrary and allows to trade off between optimality and a smaller number of cells in the piecewise affine solution. We provide analytic formulas for bounding the errors on the optimal value and the optimizer, and for guaranteeing that the resulting suboptimal RHC law provides closed-loop stability and constraint fulfillment.

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% Autogenerated BibTeX entry
@TechReport { BemFil:2002:IFA_92,
    author={A. Bemporad and C. Filippi},
    title={{Suboptimal Explicit RHC via Approximate Multiparametric
	  Quadratic Programming}},
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