Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Abstract

We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an algorithm and give performance guarantees for the resulting MPC closed loop system. Thereby, we significantly simplify the assumptions made in the literature so far by assuming strict dissipativity and the existence of a compatible terminal cost for one of the competing objective functions only. We give conditions which ensure asymptotic stability of the closed loop and, what is more, obtain performance estimates for all cost criteria. Numerical simulations on various instances illustrate our findings. The proposed algorithm requires the selection of an efficient solution in each iteration, thus we examine several selection rules and their impact on the results. and we also examine numerically how different selection rules impact the results

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

“…4), average constraints (Müller et al, 2014b,c;Rosenfelder et al, 2020), or by considering a multiobjective formulation (He et al, 2015), (Faulwasser et al, 2018, Sec. 9), (Soloperto et al, 2020;Eichfelder et al, 2022).…”

“…The introduction of economic MPC schemes in practice may be facilitated by formulations that also enable a user to flexibly set desired stability properties. Approaches to address this issue include Lyapunov constraints (Heidarinejad et al, 2012;Ellis et al, 2017), average constraints (Müller et al, 2014b,c), multi-objective formulations (Soloperto et al, 2020;Eichfelder et al, 2022), or using the external variable y e to flexibly change the cost online (cf. Köhler et al (2020c, Fig.…”