By

Georgios Boutselis

(Advisor: Prof. Evangelos Theodorou)

4:00 PM, Monday 09 Dec 2019

Knight Building, Conference room 317

OPTIMIZATION-BASED METHODS FOR DETERMINISTIC AND STOCHASTIC CONTROL:

ALGORITHMIC DEVELOPMENT, ANALYSIS AND

APPLICATIONS ON MECHANICAL SYSTEMS & FIELDS

Summary:

Developing efficient control 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. Of equal importance are

state and control constraints, which must be effectively handled for safety critical systems.

To proceed, the majority of works in controls and reinforcement learning literature

deals with systems lying in finite-dimensional 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.

This work attempts to address the challenges mentioned above. We will develop numerical

optimal control methods that explicitly incorporate modeling uncertainty, as well as deterministic and probabilistic constraints, into prediction and decision making. Our iterative

schemes provide scalability by relying on dynamic programming principles and 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 will be highlighted by substantial numerical results on simulated test cases.

Committee Members:

Prof. Evangelos Theodorou (Advisor, AE)

Prof. Melvin Leok (Department of Mathematics, University of California, San Diego)

Prof. Yongxin Chen (AE)

Prof. Andrzej Swiech (MATH)

Prof. Efstathios Bakolas (AE, The University of Texas at Austin)