CAREER: Nonsmooth Control Systems for Societal Networks with Data-Assisted Feedback Loops: Theory and Algorithms

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The overarching goal of this CAREER proposal is to formally advance the analysis and synthesis of hybrid and non-smooth data-assisted controllers, which are algorithms that: (a) incorporate data-driven mechanisms in the closed-loop system for the purpose of real-time estimation, learning, and adaptation; and (b) are characterized by hybrid and non-smooth dynamical systems able to meet stringent robustness, stability and transient demands that are mathematically unachievable using smooth control techniques. The research is motivated by technological advances that have made devices for actuation, sensing, computation, and communication increasingly portable, inexpensive, and prevalent in networked engineering systems, including robotic networks, the power grid, and connected transportation systems. In these applications, the increasing complexity of the underlying (hybrid) dynamical systems and their corresponding decision-making problems have exposed the fundamental limitations of traditional smooth feedback control and optimization methods. The research plan will seek to overcome these limitations by developing a new paradigm of data-assisted network control based on hybrid control theory for multi-agent systems deployed over cyber-physical infrastructure. The project incorporates a strong educational and outreach plan that will involve active recruitment and mentorship of students from diverse backgrounds via summer enrichment camps, as well as after-school programs for middle and high-school students. The outreach plan also includes the development of a regional workshop in the broad areas of control and autonomous systems, as well as active collaborations with industry and national laboratories to inform and guide the research. The research project will leverage recent mathematical tools developed in hybrid control theory, further integrated and developed in three cohesive research thrusts: 1) The development of robust data-assisted switched and non-smooth controllers able to overcome obstructions to smooth stabilization, tracking, and optimization by switching between multiple feedback-based algorithms that use concurrently real-time and recorded data generated by the system under control; 2) The robust coordination of multi-agent data-assisted controllers to synergistically exploit their individual capabilities to obtain a desired network-wide performance, while preserving suitable scalability properties with respect to the size of the network and their data requirements; 3) The analysis and synthesis of strategic data-assisted controllers for multi-agent systems where certain individual agents systematically and dynamically manipulate their data for the purpose of deception without inducing unstable behaviors in the closed-loop system. The theoretical principles uncovered in the project, as well as the proposed algorithms, will be tested and validated in realistic numerical and experimental engineering systems.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.