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Understanding and controlling complex systems

Periodic Reporting for period 1 - UCoCoS (Understanding and controlling complex systems)

Reporting period: 2016-04-01 to 2018-03-31

Europe faces major challenges in science, society and industry, induced by the complexity of our hyper-connected world. Examples are the climate change, infectious diseases, artificial interconnected systems whose dynamics are beyond our understanding such as the internet, the global banking system and the power grid. A demand of performance emerges at an unprecedented scale: collaborative sensors and robots so to ensure competitiveness of our European production industry, better management of our traffic flows, designing (de)synchronization mechanisms applicable in neuroscience, are examples illustrating the necessity to understand and control the dynamics of complex networks.

However, this requires a fundamentally new kind of complexity science. The traditional way of reducing a system to its components fails when the global dynamics are determined mainly by the interactions. Moreover, an interdisciplinary approach is necessary as revealing common principles is key in getting grip on the complexity.

The objectives of UCoCoS are to create a control-oriented framework for complex systems, and to define a common language, common methods, tools and software for the complexity scientist. Moreover, as the first training network on the theme, UCoCoS aims at i) creating a closely connected new generation of leading European scientists, capable of designing network structures and policies to affect the networks, and ii) initiating long-term partnerships and collaboration mechanisms leading to sustainable doctoral training.

The UCoCoS approach builds on recent developments in three domains (control, computer science, mechanical engineering) and stems from the identification of a unique combination of expertise within the consortium. Every ESR performs a cutting-edge project, strongly relying on the complementary expertise of the three academic beneficiaries and benefiting from training by non-academic partners from three different sectors.
In the first reporting period we strongly contributed to the three complementary research directions described below. Each one corresponds to a work package, centered around the PhD projects of two Early Stage Researchers (ESR). Each ESR is jointly supervised by advisors from two beneficiaries, in such a way that all three beneficiaries are strongly involved in each research direction. This explains why we do not follow the conventional listing of achievements per beneficiary.

Robustness of networks of interconnected systems and the analysis of emergent behavior
An established method to predict oscillatory solutions of nonlinear dynamical systems is the Harmonic Balance Method, which we have extended to networks of interconnected systems. The extensions consist of predicting oscillatory profiles, and of exploiting the network structure, which is important in terms of scalability with respect to size of the network. A second contributions concerns the development of observers, which serve to reconstruct the network state from measurements. We proposed a novel type of distributed observer that retrieves the state in a finite time, offering major advantages with respect to existing solutions in terms of convergence and robustness with respect to communication delays in the network, and we made a comparison between distributed and centralized observers.

Analysis of clustering in large networks
In order to analyze and control partially synchronous motion and clustering behavior in large network, the mathematical concept of partial synchronization manifold plays a crucial role. We developed novel algorithms for computing all partial synchronization manifold in a network, and for establishing corresponding dynamical decompositions, which are beneficial in the context of the stability assessment of clusters. Secondly we tackled the problem of state estimation for nonlinear systems with data-rate constraints. This resulted in novel observers which are data-efficient in the sense that lower or equivalent data-rates than other previously developed observers are obtained, whilst adding the robustness towards communication losses property. The rationale is that by getting a better understanding of the required data-rates, we will be able to exploit these data-rates in order to perform model reduction.

Control of complex system
The contributions are twofold. The first one stems from the fact that in large network it is often infeasible or costly to implement centralized controllers. Hence, we developed and validated novel methods for the design of decentralized or distributed controllers. The methods allow the design low-order controller, which are easy to implement, they take into account coupling delays which naturally arise in the context of networks, and under some conditions they allow to fully exploit a network structure, resulting in scalable algorithms. Second, complex networked systems involve data transmitted at sampling intervals that might be constant, varying or dependent on certain events. Additionally, the transmitted information is subjected to network effects such as data packet dropouts, asynchrony arising due to delays between sensors and actuators, etc. This necessitates the analysis of systems subject to aperiodic sampling and time varying delay. In the reporting period novel stability criteria were obtained.

In all three research directions the concepts of feedback, robustness and adaptation play a central role in the achieved developments, which stems from the distinctive control oriented view of UCoCoS.
With the original contributions described in the previous section and documented with scientific publications, we are gradually building a novel, control oriented framework for analyzing and controlling complex systems, which encompasses the spectrum from observation, analysis (analytical and numerical), prediction, to control.

To increase the potential impact of the scientific results a lot of attention has been paid to the development of computational tools and software (fourth work package). The methods designed for detecting partial synchronization manifolds and for synthesizing structured controllers have been implemented in a user-friendly publicly (among others, via the website http://ucocos-project.eu) software tool. As part of the dissemination strategy efforts are done to bridge research communities confronted with different aspects of complex systems (communities working on time-delay systems, networked control systems, physics and biology, nonlinear dynamics network science,…), by submission of contributions and participation to conferences in different domains.

The research within UCoCoS is at the foundations of complex systems’ science. However, the focus on common principles underlying the dynamics of complex systems, and on generic methods and tools serve the important strategic goal as training network, to provide dedicated training to a new generation of scientists, anticipating a strong need of complexity specialists.
UCoCoS flyer (back)
UCoCoS flyer (front)