Approximate robust dynamic programming and robustly stable MPC

  • Authors:

  • Jakob BjöRnberg;Moritz Diehl

  • Affiliations:

  • Centre for Mathematical Sciences, Wilberforce Road, CB3 0WB Cambridge, UK;IWR, University of Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2006

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Abstract

We present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The approximation method uses polyhedral representations of the cost-to-go function and feasible set, and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming [Bemporad, A., Borrelli, F., & Morari, M. (2003). Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9), 1600-1606; Diehl, M., & Bjornberg, J. (2004). Robust dynamic programming for min-max model predictive control of constrained uncertain systems. IEEE Transactions on Automatic Control, 49(12), 2253-2257]. We show how to apply the method to robust MPC, and give conditions that guarantee closed-loop stability. We finish by applying the method to a state constrained tutorial example, a parking car with uncertain mass.