ACSE Research Seminar in Sheffield
Today I am giving a research seminar in Sheffield, at the Department of Automatic Control & Systems Engineering of the University of Sheffield.
A structural approach to dynamical networks
Dynamical networks are systems whose behaviour results from the interaction of several dynamic subsystems. Interactions occur according to a given topology, which can be visually represented as a graph. Structural investigation aims at assessing general properties based on the system structure (essential, qualitative information about the system), without any quantitative knowledge of the system parameters (or even of numerical bounds).
The main purpose is to establish how local interactions can affect the global behaviour of the dynamical network. In particular, systems whose structure is defined by the associated graph, or hyper-graph, will be considered. This class of systems includes both natural systems, for instance biochemical systems, food webs and social networks, and artificial systems, such as production and distribution systems, telecommunication systems, computer networks and vehicle platoons.
The so-called “BDC-decomposition” will be presented as a local and global tool for the structural analysis of dynamical networks, with a special focus on biochemical systems. Based on this decomposition, criteria can be obtained to structurally assess the stability of the system and the sign of steady-state input-output influences. Also, a structural classification of the transitions to instability (either oscillatory or multistationary) that can occur in systems having a sign-definite Jacobian, or consisting of the sign-definite interaction of stable monotone subsystems, will be illustrated.
In a dynamical network, local interactions can also be designed to obtain the desired global behaviour. Network-decentralised control strategies will be considered, in which several control agents act locally and make their decisions based on local information only. Precisely, each control agent is associated with an arc and has knowledge exclusively about variables related to the nodes that it directly affects. Some theoretical results on network-decentralised stabilisability for linear systems and for nonlinear compartmental systems will be presented, showing that network-decentralised stabilisability is equivalent to stabilisability under suitable conditions. Finally, the asymptotic optimality properties of network-decentralised controllers will be presented.