Approximate Dynamic Programming for Generation of Robustly Stable Feedback Controllers

Jakob Björnberg and Moritz Diehl ()
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Jakob Björnberg: University of Cambridge, Center of Mathematical Sciences
Moritz Diehl: Optimization in Engineering Center (OPTEC), Electrical Engineering Department (ESAT)

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2008, pp 69-85 from Springer

Abstract: 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.

Keywords: Dynamic Programming; Model Predictive Control; Approximate Dynamic Program; Nonlinear Model Predictive Control; Model Predictive Control Controller (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-79409-7_6

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DOI: 10.1007/978-3-540-79409-7_6

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