Title:
Optimization-based methods for deterministic and stochastic control: Algorithmic development, analysis and applications on mechanical systems & fields
Optimization-based methods for deterministic and stochastic control: Algorithmic development, analysis and applications on mechanical systems & fields
Author(s)
Boutselis, Georgios
Advisor(s)
Theodorou, Evangelos A.
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Abstract
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 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 highlighted by substantial numerical results on simulated test cases.
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Date Issued
2019-12-17
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Text
Resource Subtype
Dissertation