Dynamics and optimal control of information transmission in complex systems

Temporal networks;Synchronization;Spreading dynamics;Consensus;Optimization;Parameter continuation

Li, Mingwu

关键词: Temporal networks;    Synchronization;    Spreading dynamics;    Consensus;    Optimization;    Parameter continuation;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/107907/LI-DISSERTATION-2020.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The objective of this dissertation is to develop computational tools for studying the way processes of information spreading in a complex system are related to the organization of interactions among the constituents of the system. We are interested in understanding how topology and sequencing of interactions affect information transmission on networks, and how these properties of the network may be optimally designed to achieve desired outcomes of information transmission.In Part I, spreading and consensus dynamics on time-varying networks are studied to explore how system parameters and network structures affect the process of information transmission. To understand how a given network feature affects the dynamics of processes occurring on the network, we compare measurements of such dynamics against the same measurements on a randomized reference model that lacks the feature in question. Structure-preserving randomization protocols are proposed and analyzed using spreading dynamics to reveal the potential bias of a commonly used reference model. Consensus dynamics on time-varying networks is systematically explored with the proposed randomization protocols. Simulation results highlight the sensitive dependence of the speed of consensus formation on the distribution of nodal lifetimes.In Part II, we develop tools for constrained design optimization that are motivated by i) the natural decomposition of some optimal control problems into weakly coupled sub-problems and ii) an initialization-free solution strategy based on principles of parameter continuation. The resultant computational platform, implemented in the COCO package, generalizes to arbitrary optimization problems with composite constraints. Using a predefined library of adjoints of common integro-differential boundary-value problem operators, this platform automates the construction of the necessary conditions for stationary points and extrema, also in the presence of inequality constraints. Examples from the theory of dynamical systems and optimal control show the application of an existing method of successive continuation to equality-constrained optimization problems, as well as an original generalization that also accommodates finite-dimensional inequality constraints.In Part III, we apply the platform developed in Part II to a class of optimal control problems for efficient information transmission on networks. We are particularly concerned with the optimal control of synchronization of phase oscillators on static networks and spreading dynamics on time-varying networks. Here, the control inputs are time-varying coupling strengths and transmission probabilities, respectively, that apply uniformly across all interactions. Motivated by the numerical results obtained using the computational platform, a unified analytical framework is shown to generically reduce these optimal control problems to a set of reference problems without differential constraints that may be solved analytically. The derivation shows that input homogeneity across the network results in universally constant optimal control inputs. Analysis of these predictions suggests that heterogeneity of both static and dynamic network structures can negatively affect the ability to achieve optimal information spreading.