J. Hahn, “Distributed Model Predictive Control with Uncertain Communication In: Kassel University Press, ISBN: 978-3-7376-1241-8,” 2025.
Abstract
This thesis deals with model predictive control for distributed systems that aim at solving a common task cooperatively. Specifically, two schemes are presented in which the controllers of all subsystems simultaneously compute a prediction for the local behavior of their own subsystem, and in which these predictions are communicated to the local controllers of neighboring subsystems. The local controllers can then plan their own behavior based on the received information. However, due to imperfect communication, the regular reception of new information cannot be guaranteed, i.e. outdated information must be used in case information is lost through communication. Since subsystems may not adhere exactly to their previously predicted and communicated behavior, other subsystems have to compensate for previously unknown uncertainties and disturbances, and the predicted future behavior is thus uncertain. Similarly, the current behavior of another subsystem is uncertain if information about it is lost during transmission. Therefore, this thesis focuses on incorporating network-induced uncertainties into predictive control strategies, and it presents strategies that account for the fact that a prediction of a neighboring subsystem may be uncertain in order to safely maintain constraints that may be partly imposed by such a subsystem. In addition, the control strategies are designed to use predictions provided by the network controller that contain information about the communication network itself to improve the performance of the distributed system. Since the planning about the future behavior strongly depends on the considered type of uncertainty, two different control strategies are presented and analyzed. In the first one, disturbances and uncertainties are assumed to be bounded, such that robust control is used to robustly satisfy local and coupled constraints. In contrast, the second strategy deals with the stochastic modeling of disturbances, resulting in a fully stochastic system model. Here, stochastic optimization is used to plan the future behavior to ensure that the constraints are satisfied with a predefined probability. Both control strategies rely mainly on the optimization-based computation of the future behavior, such that the stability of the control concepts is proved by using terminal sets and terminal constraints. In the case of robust control, the computation of the terminal set is based on rather complex and time-consuming set computations, whereas in the stochastic setup it is only necessary to solve a Lyapunov-equation to obtain ellipsoidal terminal sets. While this requires less offline computations, the optimization problem, which must be solved repeatedly online, involves conic rather than linear constraints as in the robust setup and thus requires more computation during operation. For both the stochastic and the robust distributed control schemes, the proof of concept and the proof of performance improvement are presented by using numerical simulations.
BibTex
@book{doi:10.17170/kobra-2025080411346,
author = {Hahn, Jannik},
title = {Distributed Model Predictive Control with Uncertain Communication},
keywords = {620 and Modellprädiktive Regelung and Optimierung },
copyright = {http://creativecommons.org/licenses/by-sa/4.0/},
language = {en},
year = {2025}
}
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