Collaborative Research: Closed-loop Optimization and Control of Physical Networks Subject to Dynamic Costs, Constraints, and Disturbances

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This project will advance a fundamentally new control framework, utilizing streams of heterogeneous data to optimize the behavior of complex and dynamic networked systems with pervasive sensing and computing capabilities, operating in uncertain and changing environments. Existing workhorse control and optimization methodologies assume a large separation of time scales, sufficient to justify complete decoupling of the optimization and control tasks. However, this assumption is increasingly invalid for modern critical infrastructure and social platforms. This project represents a new approach for optimal and reliable decision-making on time scales comparable to the dynamics of the underlying physical and logistic systems, by using new mathematical principles of analysis and synthesis to control the collective behavior of agents and the underlying physical dynamics. The key concept is to continuously drive the dynamical system towards solution trajectories of optimization problems that have costs, constraints, and inputs which change over time. In the context of future transportation networks, the approach is well-aligned with the objective of moving people and cargo efficiently and sustainably, and with the integration of connected and autonomous vehicles. Similar application opportunities occur in areas such as energy, robotics, and autonomous systems, with the common feature of interconnected cooperative and non-cooperative agents interacting via multiple heterogeneous physical and virtual networks. The project will also impact undergraduate and graduate engineering students, and K-12 students through a comprehensive outreach and educational plan that includes STEM camps, engaging activities to promote the recruitment of female students and students from under-served communities and minority schools into the STEM pipeline, and curriculum enhancement initiatives.Traditional decision-making architectures in networked systems and critical infrastructures are grounded on explicit spatio-temporal boundaries between model-based network-level optimization (producing setpoints in a feed-forward fashion) and local closed-loop control (regulating the dynamical system to the setpoints while rejecting disturbances). The modus operandi of these traditional architectures has worked well in settings where the underlying dynamics of the physical systems are slower than the solution time required by network-level optimization tasks, network models and data structures are available, and problem inputs can be pervasively collected in a timely and reliable manner. Such assumptions, however, are becoming increasingly inadequate in dynamic settings where batch approaches fail to solve the underlying optimization problems on a time scale that matches the dynamics of the networked physical systems, physical models (embedded into the optimization task) are difficult to estimate accurately, and (unknown) disturbances evolve rapidly and unpredictably. This project will generate new mathematical principles for the synthesis and analysis of online data-based algorithms that drive the collective behavior of agents and physical dynamics to desired operational points. In particular, the desired equilibrium points coincide with solution trajectories of time-varying optimization problems formalizing performance metrics and operational constraints associated with the dynamical system. The interconnected-system framework under study compresses the time scales between control and optimization tasks to continuously drive the dynamic behavior of physical systems to network-optimal and stable points. The research seeks to expand the class of problems to which this project vision can be applied, develop predictive controllers with information streams, and synthesize novel distributed algorithmic solutions for interconnected systems. The technical approach focuses on networked transportation systems as the arena to materialize the theoretical and algorithmic advances and provide innovative control and optimization strategies. Beyond transportation, benefits are expected to propagate in the broader optimization and control communities, with applications in multiple domains including control of epidemics, robotic networks, social networks, and energy infrastructures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.