Abstract: Complex and chaotic non-equilibrium dynamic behavior occurs in diverse applications. Some common examples are: instabilities in aerospace applications, air-flow dynamics in buildings, non-stationary behavior in networks such as traffic networks or communication networks, dynamic biological phenomena such as replication and folding of DNA. While the field of Dynamical Systems has seen important advances in classification and analysis of such behavior, its impact on applications - particularly in nonlinear control theory - remains an open and exciting area of investigation. In this talk, I will highlight the striking interplay between Dynamics and Control. I will do so with the aid of Lyapunov functions, which are widely used for nonlinear control. I will introduce these functions, review their construction, and highlight some of their inadequacies. By combining ideas from the field of stochastic dynamics with control, I will then propose a generalization for overcoming some of these inadequacies. I will show its applicability to both stability analysis and control of non-equilibrium behavior. Results on computations and future directions for applications will also be provided.