Hays, Joseph T.2014-03-142014-03-142011-08-25etd-09012011-162500http://hdl.handle.net/10919/28850This 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.In CopyrightOrdinary Differential Equations (ODEs)Trajectory PlanningMotion PlanningGeneralized Polynomial Chaos (gPC)Uncertainty QuantificationMulti-Objective Optimization (MOO)Nonlinear Programming (NLP)Dynamic OptimizationOptimal ControlRobust Design Optimization (RDO)CollocationUncertainty ApportionmentTolerance AllocationMultibody DynamicsDifferential Algebraic Equations (DAEs)Dissertationhttp://scholar.lib.vt.edu/theses/available/etd-09012011-162500/