For uncertain network controlled dynamical systems operating away from equilibrium, the proposed research will discover analytical methods and computational tools for the a) prediction of instabilities in network systems with multiple sources of uncertainties; b) identification of feedback mechanisms and critical parameters responsible for the emergence of nonequilibrium dynamics in networks; c) design of controller for a class of network control dynamical systems. The theoretical discovery of this proposal is motivated with regard to its application to the electric power grid, for the computation of stability margin and for online transient stability analysis in power systems.
Intellectual Merit: The proposed research is in the unification and development of methods and tools from the ergodic theory of dynamical systems and control approaches for the purpose of its application to network controlled dynamical systems with uncertainty. The distinctive feature of our proposed approach is that it treats several aspects of uncertainty amplification specific to networked systems in a unified way. Namely, it allows us to handle the uncertainty of the communication links, the uncertainty in the system interactions, and the uncertainty in the networked system evolution. This unified framework has allowed the PI to make two fundamental contributions for the analysis and control of uncertain nonlinear systems over networks. The first contribution is in the use of ergodic theory-based framework to provide linear programming-based analytical and computational solution for stability verification and control design of complex nonequilibrium dynamics in nonlinear system. The second contribution arises in the derivation of fundamental limitation results for the stabilization and observation of nonlinear systems with uncertainty at the input and output channels. The PI propose to further extend these methods to discover analytical methods and computational tools for the analysis and control of network controlled dynamical systems with particular focus on addressing two main challenges, namely uncertainty and self-emergent nonequilibrium dynamics in the network systems.
Broader Impact: The theoretical and computational tools developed in the proposal have applications in the emerging areas of network systems, including biological and social networks. Our results on identification of feedback mechanisms for the emergence of complex nonequilibrium dynamics in network systems can be applied to biological networks to help understand the consequence of genetic modification, and for guiding experiments design for modifying such behavior. For social networks such as disease spread, the proposed uncertainty-based modeling framework and theoretical research can be used to provide conditions for the prevention or spread of an epidemic. The interdisciplinary nature of this project will provide ample opportunities to train graduate students in leading-edge research that cuts across multiple disciplines. These interdisciplinary components will be integrated into a larger educational effort to offer engineering students a solid foundation and training in complex systems, as well as in control and dynamics.
