Multiobjective Model Predictive Control for Stabilizing Cost Criteria

Titelangaben

Grüne, Lars ; Stieler, Marleen:
Multiobjective Model Predictive Control for Stabilizing Cost Criteria.
In: Discrete and Continuous Dynamical Systems. Series B. Bd. 24 (2019) Heft 8 . - S. 3905-3928.
ISSN 1531-3492
DOI: https://doi.org/10.3934/dcdsb.2018336

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Abstract

In this paper we demonstrate how multiobjective optimal control problems can be solved by means of model predictive control. For our analysis we restrict ourselves to finite-dimensional control systems in discrete time. We show that convergence of the MPC closed-loop trajectory as well as upper bounds on the closed-loop performance for all objectives can be established if the ‘right’ Pareto-optimal control sequence is chosen in the iterations. It turns out that approximating the whole Pareto front is not necessary for that choice. Moreover, we provide statements on the relation of the MPC performance to the values of Pareto-optimal solutions on the infinite horizon, i.e. we investigate on the inifinite-horizon optimality of our MPC controller.