Hybrid Dynamical Seeking Systems: Model-Free Feedback Decision-Making and Control (Eckman Award Lecture)

Abstract

The convergence of physical and digital systems in modern engineering applications has inevitably led to closed-loop systems that exhibit both continuous-time and discrete-time dynamics. These closed-loop architectures are modeled as hybrid dynamical systems, prevalent across various technological domains, including robotics, power grids, transportation networks, and manufacturing systems. Unlike traditional “smooth” ordinary differential equations or discrete-time recursions, solutions to hybrid dynamical systems are generally discontinuous, lack uniqueness, and have convergence and stability properties that are defined with respect to complex sets. Therefore, effectively designing and controlling such systems, especially under disturbances and uncertainty, is crucial for the development of autonomous and efficient data-driven engineering systems capable of achieving adaptive and self-optimizing behaviors. In this talk, I will delve into recent advancements in the analysis and design of feedback controllers that can achieve such properties in complex scenarios via the synergistic use of adaptive “seeking” dynamics, robust hybrid control, and decision-making algorithms. These controllers can be systematically designed and analyzed using modern tools from hybrid dynamical systems theory, which facilitate the incorporation of "exploration” and “exploitation" behaviors within complex closed-loop systems via multi-time scale tools and perturbation theory. The proposed methodology leads to a family of provably stable and robust algorithms suitable for solving model-free feedback stabilization and decision-making problems in single-agent and multi-agent systems for which smooth feedback solutions fall short.