We strongly contributed to three complementary research directions, each one corresponding to a work package, centered around the PhD projects of two ESRs. The research results and publications that were algorithmic in nature, were accompanied by software tools, integrated in the UCoCoS software package (main deliverable of WP4), available at the GitHub repository.
WP1. Robustness and emergent behavior
As a first research direction we focused on analyzing pattern formation in coupled nonlinear systems. We extended the Multivariable Harmonic Balance towards the approximation and prediction of oscillatory profiles and patterns in networks with possibly delay in the coupling, thereby paying attention to scalability with the network size. The method can be used as a building block for numerical continuation and bifurcation analysis, which are main tools for the analysis of nonlinear dynamical systems and widely used in physics, biology and engineering.
A second contribution concerns the development of observers, which serve to reconstruct the network state from sensor measurements. Centralized concepts, where all sensor data are collected and processed at one place, prove themselves infeasible for complex systems, due to the scale and heterogeneity of the system or communication constraints. We developed and analyzed a novel class of distributed observers that retrieve the state of the network in a finite time, offering major advantages over existing solutions, in terms of convergence and robustness with respect to communication delays in the information exchange over the network.
WP2. Network reduction and clustering
Due to a weakening of the coupling strength or larger time-delays, networks of coupled systems may exhibit a form of incomplete synchronization, where some but not all systems behave synchronously, which we refer to as partial or cluster synchronization. We developed analysis methods and computational tools for cluster synchronization, and we introduced the important notion of practical partial synchronization. We also made the leap from analysis to synthesis, by designing distributed controllers that achieve synchronized period motion in a leader-free scenario.
In the context of reduced modeling, we analyzed data-rate problems for dynamical systems, which find many real-world applications such as systems connected through wireless technologies or micro-electromechanical systems. We designed observers for a communication network with losses and data-rate constraints, and derived expressions for the minimum data-rate of the channels. The observer was then adapted to a network consensus problem. We also used an event-triggered communication strategy to significantly reduce the average communication rate, and tested the developed communication protocols through experiments on mobile robots.
WP3. Control of complex systems
We studied the optimization of the network topology by designing constrained controllers (i.e. controllers with limited access to the system information), and we addressed the optimization of measurement and action communication links. The first main contribution consisted of a unifying methodology for the design of robust constrained controllers for delay systems, grounded in eigenvalue optimization. We focused on decentralized and overlapping controllers, and applied the novel methodology to the adaptive cruise control problem, in collaboration with partner TNO.
As a second main contribution we proposed numerical methods for the optimization of communication sequences (in terms of communication frequency and tolerable latencies), while ensuring a fast and/or robust control. By providing numerical tools that aid in deciding the trade-off between the bounds on communication bandwidth and time-varying feedback latencies, we could decide on the feasibility of control policies.
Exploitation and dissemination
In our publication strategy we paid a lot of attention to diversification in terms of journals and conferences, aiming at reaching different research communities confronted with complex systems.
Next to the dedicated UCoCoS workshops, the results were advertised with contributions at many international conferences, including two special UCoCoS sessions. An important added value for the training of the ESRs were the 5th IFAC Conference on Analysis and Control of Chaotic Systems, and the 38th Benelux Meeting on Systems and Control, co-organized by the principal investigators of UCoCoS.
Other means of dissemination are the project website, a flyer, the UCoCoS LinkedIn page, and a video describing the experiments with mobile robots performed in the framework of WP2-3. In order to reach the general public and to promote STEM programs, we advertised UCoCoS at open door days of our institutes, to high-school students participating in the “science week” at KU Leuven, and we created a dedicated section on the UCoCoS website.
