A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos. (30th January 2020)

• Record Type: Journal Article
• Authors: Lefebvre, Tom; De Belie, Frederik; Crevecoeur, Guillaume
• Is Part Of: Optimal control applications and methods. Volume 41:Number 3(2020)
• Page Start: 833
• Page End: 848
• Publication Date: 2020-01-30
• Subjects: parametric dynamic model uncertainty -- polynomial approximation theory -- robust optimal control; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2575
• Languages: English
• ISSNs: 0143-2087

Abstract

Abstract: We propose a framework tailored to robust optimal control (OC) problems subject to parametric model uncertainty of system dynamics. First, we identify a generic class of robust objective kernels that are based on the class of deterministic quadratic objectives. It is demonstrated how such kernels can be expressed as a function of the stochastic moments of the state and how the objective terms relate to the robustness and performance of the optimal solution. Second, we engage the generalized polynomial chaos (gPC) framework to propagate uncertainty along the state trajectory. Integrating both frameworks makes way to reformulate the problem as a deterministic OC problem in function of the gPC expansion coefficients that can be solved using existing methods. We apply the framework to solve the problem of robust optimal startup behavior of a nonlinear mechanical drivetrain that is subject to a bifurcation in its dynamics.