Ph.D. Thesis Proposal – Georgios Boutselis (Advisor: Prof. Evangelos Theodorou)

Title: “Optimization-based stochastic control methods: Algorithmic Development, Analysis and Applications on Mechanical Systems & Fields”

Date: Monday, April 22, 2019

Time: 1:00 PM - 3:00 PM

Location: G021 Classroom, Molecular Science & Engineering Building (MSE)

Committee:   

• Professor Evangelos A. Theodorou, Committee Chair, School of Aerospace Engineering, Georgia Institute of Technology
• Professor Patricio Antonio Vela, School of Electrical and Computer Engineering, Georgia Institute of Technology
• Professor Melvin Leok, Department of Mathematics, University of California, San Diego
• Professor Andrzej Swiech, School of Mathematics, Georgia Institute of Technology
• Professor Yongxin Chen, School of Aerospace Engineering, Georgia Institute of Technology

Abstract:

Developing efficient control and decision-making algorithms for practical scenarios remains a key challenge for the scientific community. Towards this goal, optimal control theory has been widely employed over the past decades, with applications both in simulated and real environments. Unfortunately, standard model-based approaches become highly ineffective when modeling accuracy degrades. This may stem from erroneous estimates of physical parameters (e.g., friction coefficients, moments of inertia), or dynamics components which are inherently hard to model. System uncertainty should therefore be properly handled within control methodologies for both theoretical and practical purposes.

To proceed, the majority of works in controls and reinforcement learning literature deals with systems lying in Euclidean spaces. For many interesting applications in aerospace engineering, robotics and physics, however, we must often consider dynamics with more “challenging” configuration spaces. These include systems evolving on differentiable manifolds, as well as systems described by stochastic partial differential equations. Some problem examples of the former case are spacecraft attitude control, modeling of elastic beams and control of quantum spin systems. Regarding the latter, we have control of thermal/fluid flows, chemical reactors and advanced batteries to name a few.

This proposal attempts to address the challenges mentioned above. We will develop numerical optimal control methods that explicitly incorporate modeling uncertainty into prediction and decision making. Our iterative schemes provide scalability by relying on dynamic programming principles as well as sampling-based techniques. Depending upon different problem setups, we will handle uncertainty by employing suitable concepts from machine learning and uncertainty quantification theory. Moreover, we will show that well-known numerical control methods can be extended for mechanical systems evolving on manifolds, and dynamics described by stochastic partial differential equations. Our algorithmic derivations utilize key concepts from optimal control and optimization theory, and in some cases, theoretical results will be provided on the convergence properties of the proposed methods. The effectiveness and applicability of our approach are also highlighted by substantial numerical results on simulated test cases. The proposal concludes by discussing current limitations, as well as our future research agenda on theoretical extensions, computational schemes and applications on real autonomous systems.