Hybrid And Networked Dynamical sYstems – HANDY

Networked dynamical systems are ubiquitous in current and emerging technologies. From energy grids, fleets of connected autonomous vehicles to online social networks, the same scenario arises in each case: dynamical units interact locally to achieve a global behavior. When considering a networked system as a whole, very often continuous-time dynamics are affected by instantaneous changes, called jumps, leading to so-called hybrid dynamical systems. The jumps may originate from (i) the intrinsic dynamics of the nodes, like in multimedia delivery with fixed rate encoding, (ii) intrinsic limitations of the control actions, possibly constrained to a finite set of possible selections, like in power converters within energy grids, (iii) the creation/loss of links or the addition/removal of nodes like in renewable energy systems and social networks. Hybrid phenomena thus play an essential role in these control applications, and call upon the development of novel adapted tools for stability and performance analysis and control design. In this context, the aim of HANDY project is to provide methodological control-oriented tools for realistic networked models, which account for hybrid phenomena. The project brings together researchers from four units (LAAS in Toulouse, CRAN in Nancy, GIPSA in Grenoble and LSS in Gif-sur-Yvette), with expertise in various domains of automatic control, ranging from geometric control and optimization, switched systems, hybrid dynamics, nonlinear control, and multi-agent systems.

HANDY is a fundamental research project organized in three main technical work-packages. In the first work-package, the necessary theory to suitably represent and analyze interconnections of hybrid dynamical systems will be developed. To this end, input-output properties of stand-alone hybrid systems will be investigated, as building blocks for their interconnections. Then, these interconnections will be addressed: when suitable properties are ensured for each subsystem, the stability of the overall system must follow under appropriate conditions on the interconnection pattern. The second work-package concentrates on multi-agent architectures and the interplay between the interconnection graph and the local node dynamics. Several fundamental questions regarding multi-agent systems subject to hybrid phenomena will be investigated, such as varying number of nodes, or more generally time-varying graph topologies. The second work-package will also address peculiar aspects related to multi-layered structures in large-scale networks emerging from several sources and generating multiple time scales and emergent collective dynamics. Both work-packages will draw inspiration and undergo verification of the relevance of the developed tools against test studies arising in micro-grids, coordinated motion control, multimedia recovery and opinion dynamics: these applications are the object of the third work-package.