The transition from large centralized complex control systems to distributed configurations that rely on a network of a very large number of interconnected simpler subsystems is ongoing and inevitable in many applications. It is attributed to the quest for resilience, flexibility, and scalability in a multitude of engineering fields with far-reaching societal impact. Although many design methods for distributed and decentralized control systems are available, most of them rely on a centralized design procedure requiring some form of global information of the whole system. Clearly, beyond a certain scale of the network, these centralized design procedures for distributed controllers are no longer feasible and we refer to the corresponding systems as ultra large-scale systems (ULSS). For these ULSS, design algorithms are needed that are distributed themselves among the subsystems and are subject to stringent requirements regarding communication, computation, and memory usage of each subsystem. In this paper, a set of requirements is provided that assures a feasible real-time implementation of all phases of a control solution on an ultra large scale. State-of-the-art approaches are reviewed in the light of these requirements and the challenges hampering the development of befitting control algorithms are pinpointed. Comparing the challenges with the current progress leads to the identification and motivation of promising research directions.

@article{PedrosoBatistaEtAl2025ULSS,
author = {Leonardo Pedroso and Pedro Batista and W. P. M. H. Heemels},
title = {Distributed Design of Ultra Large-Scale Control Systems: Progress, Challenges, and Prospects},
journal = {Annual Reviews in Control},
year = {2025},
volume = {59C},
pages = {100987},
note = {in press}
}

When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism design manage to steer the aggregate users choices to the desired optimum by using monetary tolls, such approaches bear the inherent drawback of discriminating against users with a lower income. More recently, incentive schemes based on artificial currencies have been studied with the goal of achieving a system-optimal resource allocation that is also fair. In this resource-sharing context, this paper focuses on repeated weighted congestion game with two resources, where users contribute to the congestion to different extents that are captured by individual weights. First, we address the broad concept of fairness by providing a rigorous mathematical characterization of the distinct societal metrics of equity and equality, i.e., the concepts of providing equal outcomes and equal opportunities, respectively. Second, we devise weight-dependent and time-invariant optimal pricing policies to maximize equity and equality, and prove convergence of the aggregate user choices to the system-optimum. In our framework it is always possible to achieve system-optimal allocations with perfect equity, while the maximum equality that can be reached may not be perfect, which is also shown via numerical simulations.

@inproceedings{PedrosoAgazziEtAl2024EqtEql,
author = {Leonardo Pedroso and Andrea Agazzi and W. P. M. H. Heemels and Mauro Salazar},
title = {Fair Artificial Currency Incentives in Repeated Weighted Congestion Games: Equity vs. Equality},
booktitle = {63rd IEEE Conference on Decision and Control},
year = {2024},
pages = {954-959},
doi = {10.1109/CDC56724.2024.10886786}
}

The design of a decentralized and distributed filtering solution for large-scale networks of interconnected systems is addressed considering (i) generic nonlinear dynamics and (ii) generic coupled nonlinear outputs in a generic, possibly time-varying, topology. The local filters, which follow the structure of the extended Kalman filter, are implemented in each system, which estimates its own state exclusively. To be suitable for the heavily restricted implementation to very large-scale systems, a novel algorithm is proposed, which: (i) does not rely on instantaneous data transmission; (ii) allows local communication exclusively; and (iii) requires computational, memory, and data transmission resources for each system that do not scale with the dimension of the network. The scalability of the proposed algorithm allows for its application to the cooperative localization problem of very large-scale systems. In particular, it is applied herein to the on-board position estimation problem of LEO mega-constellations using GNSS featuring numerical simulations for the Starlink constellation.

@article{PedrosoBatista2023DistributedEKF,
author = {Leonardo Pedroso and Pedro Batista},
title = {Distributed decentralized {EKF} for very large-scale networks with application to satellite mega-constellations navigation},
journal = {Control Engineering Practice},
year = {2023},
volume = {135},
pages = {105509},
doi = {10.1016/j.conengprac.2023.105509}
}