Posted January 17, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Tobias Breiten, Technical University of Berlin
On the Approximability of Koopman-Based Operator Lyapunov Equations
Computing the Lyapunov function of a system plays a crucial role in optimal feedback control, for example when the policy iteration is used. This talk will focus on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay, which justifies finite rank approximations with numerical methods. The usefulness for numerical computations will also be demonstrated with two short examples. This is joint work with Bernhard Höveler (TU Berlin).
Posted January 16, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Jorge Poveda, University of California, San Diego
Donald P. Eckman, NSF CAREER, and AFOSR Young Investigator Program Awardee
Multi-Time Scale Hybrid Dynamical Systems for Model-Free Control and Optimization
Hybrid dynamical systems, which combine continuous-time and discrete-time dynamics, are prevalent in various engineering applications such as robotics, manufacturing systems, power grids, and transportation networks. Effectively analyzing and controlling these systems is crucial for developing autonomous and efficient engineering systems capable of real-time adaptation and self-optimization. This talk will delve into recent advancements in controlling and optimizing hybrid dynamical systems using multi-time scale techniques. These methods facilitate the systematic incorporation and analysis of both "exploration and exploitation" behaviors within complex control systems through singular perturbation and averaging theory, resulting in a range of provably stable and robust algorithms suitable for model-free control and optimization. Practical engineering system examples will be used to illustrate these theoretical tools.