Parametric Optimal Design Of Uncertain Dynamical Systems

• Main Author: Hays, Joseph T.
• Other Authors: Mechanical Engineering
• Format: Others
• Published: Virginia Tech 2014
• Subjects: 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)
• Online Access: http://hdl.handle.net/10919/28850; http://scholar.lib.vt.edu/theses/available/etd-09012011-162500/

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. === Ph. D.