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Stability Analysis of Unconstrained Receding Horizon Control Schemes
(2011)

Karl Worthmann
 In this thesis we are concerned with receding horizon control (RHC), also known as model predictive control. In particular, schemes which neither incorporate terminal constraints nor costs are considered. Our goal is to ensure a relaxed Lyapunov inequality which allows to conclude asymptotic stability of the RHC closed loop and, in addition, to quantify the loss of performance in comparison to infinite horizon optimal control. To this end, a (stability) condition is derived based on a controllability assumption. Then, a sensitivity analysis is carried out with respect to the most important parameters in our RHC strategy: the prediction and the control horizon. Here, the proposed stability condition is exploited in order to deduce guidelines to suitably design receding horizon stage costs. Furthermore, symmetry and monotonicity properties are rigorously shown which pave the way in order to develop algorithms such that the prediction horizon and, thus, the computational costs can be reduced while maintaining a desired performance guarantee.
Since many practically relevant discrete time systems are induced by sampled differential equations, effects linked to employing faster sampling and, thus, more accurate discretizations are analyzed. In this context a growth condition which may, e.g., reflect continuity properties, is introduced and the proposed methodology is generalized to this setting  a decisive step towards so called accumulated bounds which further improve our stability estimates and, thus, allow to derive tighter performance bounds. Moreover, the applicability and effectiveness of the presented results are demonstrated by several examples including a class of reaction diffusion equations.