Vietnam Journal of Mathematics

, Volume 47, Issue 4, pp 897–929 | Cite as

Exponentially Convergent Receding Horizon Strategy for Constrained Optimal Control

  • Wanting Xu
  • Mihai AnitescuEmail author
Original Article


Receding horizon control has been a widespread method in industrial control engineering as well as an extensively studied subject in control theory. In this work, we consider a lag L receding horizon strategy that applies the initial L optimal controls from each quadratic program to each receding horizon. We investigate a discrete-time and time-varying linear-quadratic optimal control problem that includes a nonzero reference trajectory and constraints on both state and control. We prove that, under boundedness and controllability conditions, the solution obtained by the receding horizon strategy converges to the solution of the full problem interval exponentially fast in the length of the receding horizon for some lag L. The exponential rate of convergence provides a systematic way of choosing the receding horizon length given a desired accuracy level. We illustrate our theoretical findings using a small, synthetic production cost model with real demand data.


Constrained optimal control Receding horizon control Sensitivity analysis 

Mathematics Subject Classification (2010)

49N10 49N35 49Q12 



We thank Prof. V. Zavala for pointing us to references about stability issues in rolling horizon control. We thank the anonymous referee of [30] who suggested that we look into RHC as well as the referee of this paper for important comments about our assumptions and scope relative to [11]. This material was based upon work supported by the U.S. Department of Energy, Office of Science, under Contract DE-AC02-06CH11347. M. A. acknowledges partial NSF funding through awards FP061151-01-PR and CNS-1545046.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ChicagoChicagoUSA
  2. 2.Mathematics and Computer Science DivisionArgonne National LaboratoryLemontUSA

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