Optimization-based methods for deterministic and stochastic control: Algorithmic development, analysis and applications on mechanical systems & fields

Numerical optimal control;Geometric control;Discrete mechanics;Uncertainty quantification;Stochastic partial differential equations;Dynamic programming;Sampling control

Boutselis, Georgios ; Theodorou, Evangelos Aerospace Engineering Leok, Melvin Swiech, Andrzej Bakolas, Efstathios Chen, Yongxin ; Theodorou, Evangelos

University:Georgia Institute of Technology

Department:Aerospace Engineering

关键词: Numerical optimal control;    Geometric control;    Discrete mechanics;    Uncertainty quantification;    Stochastic partial differential equations;    Dynamic programming;    Sampling control;   

Others  :  https://smartech.gatech.edu/bitstream/1853/62726/1/BOUTSELIS-DISSERTATION-2020.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Developing efficient control algorithms for practical scenarios remains a key challenge for the scientific community. Towards this goal, optimal control theory has been widely employedover the past decades, with applications both in simulated and real environments. Unfortunately, standard model-based approaches become highly ineffective when modelingaccuracy degrades. This may stem from erroneous estimates of physical parameters (e.g., friction coefficients, moments of inertia), or dynamics components which are inherentlyhard 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.