Suboptimality estimates for NMPC schemes

Lars Grüne, Universität Bayreuth

Presentation Grüne

Abstract. We present estimates for the performance of optimization based NMPCschemes without stabilizing terminal constraints. Using relaxed dynamicprogramming estimates we show how a priori information about controllabilityproperties of the system as well as online information obtained numerically fromthe closed loop trajectory can be used in order to derive bounds on the infinitehorizon performance of the NMPC closed loop. The bounds obtained this way areexpressed in terms of the optimal infinite horizon cost and thus give anestimate for the degree of suboptimality of the NMPC controller. Furthermore, weshow how these estimates can be used for the analysis of networked NMPC schemes.As an outlook, we sketch some ideas on how these techniques may be generalizedto decentralized NMPC controllers.