Stability and performance analysis of NMPC : Detectable stage costs and general terminal costs

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Köhler, Johannes ; Zeilinger, Melanie ; Grüne, Lars:
Stability and performance analysis of NMPC : Detectable stage costs and general terminal costs.
Bayreuth ; Zürich , 2021 . - 16 S.

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Abstract

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated in a numerical example.