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Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming

Author

Listed:
  • A. Bemporad

    (Università di Siena)

  • C. Filippi

    (Università di Padova)

Abstract

Algorithms for solving multiparametric quadratic programming (MPQP) were recently proposed in Refs. 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 MPQP is a piecewise affine function of the state vector and thus it is easily implementable online. The main drawback of solving MPQP 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 MPQP, where the degree of approximation is arbitrary and allows to tradeoff 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.

Suggested Citation

  • A. Bemporad & C. Filippi, 2003. "Suboptimal Explicit Receding Horizon Control via Approximate Multiparametric Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 9-38, April.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:1:d:10.1023_a:1023696221899
    DOI: 10.1023/A:1023696221899
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    Cited by:

    1. C. Filippi, 2004. "An Algorithm for Approximate Multiparametric Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 73-95, January.
    2. Simon Clinet & Jean-Franc{c}ois Perreton & Serge Reydellet, 2021. "Optimal trading: a model predictive control approach," Papers 2110.11008, arXiv.org, revised Nov 2021.

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