Title page for ETD etd-04092010-000752

Type of Document Dissertation
Author Blanchard, Emmanuel Dominique
URN etd-04092010-000752
Title Polynomial Chaos Approaches to Parameter Estimation and Control Design for Mechanical Systems with Uncertain Parameters
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Sandu, Adrian Committee Chair
Sandu, Corina Committee Co-Chair
Ahmadian, Mehdi Committee Member
Borggaard, Jeffrey T. Committee Member
Leo, Donald J. Committee Member
  • Collocation
  • Polynomial Chaos
  • Parametric Uncertainty
  • Parameter Estimation
  • Extended Kalman Filter (EKF)
  • Bayesian Estimation
  • Vehicle Dynamics
  • Control Design
  • Robust Control
  • LQR
Date of Defense 2010-03-26
Availability unrestricted
Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical systems with uncertainty.

This study has led to new computational approaches for parameter estimation in nonlinear mechanical systems. The first approach is a polynomial-chaos based Bayesian approach in which maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. The second approach is based on the Extended Kalman Filter (EKF). The error covariances needed for the EKF approach are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The advantages and drawbacks of each method have been investigated.

This study has demonstrated the effectiveness of the polynomial chaos approach for control systems analysis. For control system design the study has focused on the LQR problem when dealing with parametric uncertainties. The LQR problem was written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework. The solution to the H∞ problem as well as the H2 problem can be seen as extensions of the LQR problem. This method might therefore have the potential of being a first step towards the development of computationally efficient numerical methods for H∞ design with parametric uncertainties.

I would like to gratefully acknowledge the support provided for this work under NASA Grant NNL05AA18A.

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