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Approximate Dynamic Programming for Generation of Robustly Stable Feedback Controllers

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Jakob Björnberg

    (University of Cambridge, Center of Mathematical Sciences)

  • Moritz Diehl

    (Optimization in Engineering Center (OPTEC), Electrical Engineering Department (ESAT))

Abstract

In this paper, we present a technique for approximate robust dynamic programming that allows to generate feedback controllers with guaranteed stability, even for worst case disturbances. Our approach is closely related to robust variants of the Model Predictive Control (MPC), and 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 dynamic programming for robust MPC [1, 8]. In this paper, we derive novel conditions for guaranteeing closed loop stability that are based on the concept of a “uroborus”. We finish by applying the method to a state constrained tutorial example, a parking car with uncertain mass.

Suggested Citation

  • Jakob Björnberg & Moritz Diehl, 2008. "Approximate Dynamic Programming for Generation of Robustly Stable Feedback Controllers," Springer Books, in: Hans Georg Bock & Ekaterina Kostina & Hoang Xuan Phu & Rolf Rannacher (ed.), Modeling, Simulation and Optimization of Complex Processes, pages 69-85, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-79409-7_6
    DOI: 10.1007/978-3-540-79409-7_6
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