Type of Document	Dissertation
Author	Hays, Joseph T
Author's Email Address	joehays@vt.edu
URN	etd-09012011-162500
Title	Parametric Optimal Design Of Uncertain Dynamical Systems
Degree	PhD
Department	Mechanical Engineering
Advisory Committee	Advisor Name Title Hong, Dennis W. Committee Co-Chair Sandu, Adrian Committee Co-Chair Sandu, Corina Committee Co-Chair Ross, Shane D. Committee Member Southward, Steve C. Committee Member
Keywords	Ordinary Differential Equations (ODEs) Trajectory Planning Motion Planning Generalized Polynomial Chaos (gPC) Uncertainty Quantification Multi-Objective Optimization (MOO) Nonlinear Programming (NLP) Dynamic Optimization Optimal Control Robust Design Optimization (RDO) Collocation Uncertainty Apportionment Tolerance Allocation Multibody Dynamics Differential Algebraic Equations (DAEs)
Date of Defense	2011-08-25
Availability	unrestricted
Abstract This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost.
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