You're invited to attend
Ethan N. Evans
(Advisor: Evangelos A. Theodorou)
“Spatio-Temporal Optimization for Control of Infinite Dimensional Systems in Robotics, Fluid Mechanics, and Quantum Mechanics”
Friday, July 23
The majority of systems in nature have a spatio-temporal dependence and can be described by Partial Differential Equations (PDEs). They are ubiquitous in science and engineering, and are of rising interest among the control, robotics, and machine learning communities. Related methods usually treat these infinite dimensional problems in finite dimensions with reduced order models. This leads to committing to specific approximation schemes and the subsequent control laws cannot generalize outside of the approximation schemes. Additionally, related work does not consider spatio-temporal descriptions of noise that realistically represent the stochastic nature of physical systems. This thesis develops a variety of approaches for control optimization and co-design optimization for PDE and stochastic PDE (SPDE) systems from a unified perspective that can be applied to macroscopic systems in robotics and fluid dynamics, as well as microscopic systems in quantum mechanics.
These approaches are each developed completely in the infinite dimensional Hilbert spaces where the systems are mathematically described, enabling the frameworks to be agnostic to the discretization scheme used to implement them. The first three developed approaches are applied in simulation to classical systems in fluid mechanics such as the Heat and Burgers equation. The fourth approach is developed for second-order SPDEs that arise in robotic systems, and are applied in simulation to systems in soft-robotics such as the Euler-Bernoulli equation and a biological model of a soft-robotic limb. Finally, several approaches are developed in the context of quantum feedback control of open quantum systems with non-demolition measurement, and one such approach is applied in simulation to perform explicit feedback control of the two qubit open quantum system.
- Prof. Evangelos A. Theodorou – School of Aerospace Engineering (advisor)
- Prof. Yongxin Chen – School of Aerospace Engineering
- Prof. Kyriakos Vamvoudakis – School of Aerospace Engineering
- Prof. Andrzej Swiech – School of Mathematics
- Prof. Mike DeWeese – UC Berkeley School of Physics
- Dr. Matthew Bays – Sr. Research Scientist at Naval Surface Warfare Center, Panama City Division