Collaborative Research: A Distributed Approximate Dynamic Programming Approach for Robust Adaptive Control of Multiscale Dynamical Systems

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This project will develop a new type of general multiagent system for management and control of complex systems, in which the agents work together in a fully cooperative way to maximize global performance over time, in the face of nonlinearity and complexity. As a testbed to prove the value of the new approach, they will simulate the challenges of: (1) earthquake response, representing a class of disasters with very rapid occurrence, short lead times and restricted geographic extent; and (2) drought-induced famine relief, representing the class of disasters with longer forecast and lead times, and larger geographic extent. The results will be widely disseminated and will feed into programs for education and outreach, including a Research Experience for Undergraduates (REU) site at Duke and the NSF-funded IGERT on Wireless Intelligent Sensor Networks, feeding into summer schools and international partnerships.The key challenge here is to develop a new version of adaptive, approximate dynamic programming (ADP) which is fully distributed,to address the case of multiscale dynamical systems. The work builds on recent work of the lead PI on Distributed Optimal Control (DOC),and includes development of optimal restriction operators for dimensionality reduction in parts of the system, and exploitation of methods from the field of partial differential equations (PDE) and stochastic differential equations (SDE).