Time-Certified Decision Making in Connected Autonomous Systems: Fixed-Time Equilibrium Seeking Control

Advances in connected transportation systems (CTS) will significantly reduce traffic accidents, CO2 emissions, and congestion, with impact estimated at $200B in the US alone. Humans cause a large share of challenges in CTS: they close loops, add uncertainty and dynamics, and preclude the use of model-based algorithms for control and optimization. Model-free controllers and algorithms with guarantees of stability, safety, and performance are critically needed in CTS and other industries. The main goal of this project is to advance the design and analysis of model-free optimization algorithms in settings where decision-making problems need to be solved, using real-time information, within a given time prescribed by the decision-making user. Such controllers have a tremendous potential to improve the performance of different applications in CTS but require advances beyond the traditional nonlinear control theory and its smooth feedback tools. The project incorporates collaborations with industry to inform the development of the algorithms with practical limitations imposed by computational processing, limited actuation and sensing, and intermittent communication networks, and cultivates a talent pipeline into important areas of national technology needs. The tools and algorithms developed will be integrated into graduate and undergraduate courses and disseminated through short courses and workshops offered at major conferences. The project will synthesize and analyze new classes of model-free fixed-time equilibrium-seeking controllers for decision-making tasks characterized by constrained variational inequalities. In contrast to traditional extremum seeking algorithms, which only achieve exponential convergence to the minimizer of the steady-state input-to-output map of a plant, the algorithms will achieve fixed-time and prescribed-time convergence via new feedback designs that combine super-linear feedback to accelerate convergence from a distance and sub-linear feedback to accelerate convergence near the extremum. The algorithms will be able to solve standard optimization problems, as well as multi-objective decision making problems with a well-defined Nash or Pareto set. The methodology will advance singular perturbation theory and averaging theory, so they are generalized from guaranteeing only asymptotic stability to guaranteeing fixed-time stability. The algorithms will be tested in different CTS applications, including traffic congestion control, model-free leader-follower tracking with time-varying personalized comfort-related payoff functions, and the coordination of connected mobile robotic networks. 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.