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Stabilizing GNEP-Based Model Predictive Control: Quasi-GNEPs and End Constraints

Submission Status:under review
  • We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP), in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the individual objectives of the players are interdependent and defined over a fixed time horizon. The feedback law is synthesized by moving-horizon model predictive control (MPC). We investigate the asymptotic stability of the resulting closed-loop dynamics. To this end, we introduce α-quasi GNEPs, a family of auxiliary problems based on a modification of the Nikaido–Isoda function, which approximate the original games. Basing the MPC scheme on these auxiliary problems, we derive conditions on the players’ objectives, which guarantee asymptotic stability of the closed-loop if stabilizing end constraints are enforced. This analysis is based on showing that the associated optimal-value function is a Lyapunov function. Additionally, we identify a suitable Lyapunov function for the MPC scheme based on the original GNEP, whose solution fulfills the stabilizing end constraints. The theoretical results are complemented by numerical experiments.

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Author:Falk M. Hante, Martin Schmidt, Antonia Topalovic
Document Type:Preprint
Language:English
Date of Publication (online):2024/06/13
Release Date:2024/06/13
Tag:Closed-loop stability; Generalized Nash equilibrium problems; Model predictive control; Non-cooperative distributed control
Page Number:26
Institutes:Humboldt-Universität zu Berlin
Universität Trier
Subprojects:A03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International