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A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos

Tom Lefebvre (UGent) , Frederik De Belie (UGent) and Guillaume Crevecoeur (UGent)
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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.
Keywords
Control and Systems Engineering, Software, Control and Optimization, Applied Mathematics, parametric dynamic model uncertainty, polynomial approximation theory, robust optimal control

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MLA
Lefebvre, Tom, et al. “A Framework for Robust Quadratic Optimal Control with Parametric Dynamic Model Uncertainty Using Polynomial Chaos.” OPTIMAL CONTROL APPLICATIONS & METHODS, 2020.
APA
Lefebvre, T., De Belie, F., & Crevecoeur, G. (2020). A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos. OPTIMAL CONTROL APPLICATIONS & METHODS.
Chicago author-date
Lefebvre, Tom, Frederik De Belie, and Guillaume Crevecoeur. 2020. “A Framework for Robust Quadratic Optimal Control with Parametric Dynamic Model Uncertainty Using Polynomial Chaos.” OPTIMAL CONTROL APPLICATIONS & METHODS.
Chicago author-date (all authors)
Lefebvre, Tom, Frederik De Belie, and Guillaume Crevecoeur. 2020. “A Framework for Robust Quadratic Optimal Control with Parametric Dynamic Model Uncertainty Using Polynomial Chaos.” OPTIMAL CONTROL APPLICATIONS & METHODS.
Vancouver
1.
Lefebvre T, De Belie F, Crevecoeur G. A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos. OPTIMAL CONTROL APPLICATIONS & METHODS. 2020;
IEEE
[1]
T. Lefebvre, F. De Belie, and G. Crevecoeur, “A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos,” OPTIMAL CONTROL APPLICATIONS & METHODS, 2020.
@article{8645329,
  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.},
  author       = {Lefebvre, Tom and De Belie, Frederik and Crevecoeur, Guillaume},
  issn         = {0143-2087},
  journal      = {OPTIMAL CONTROL APPLICATIONS & METHODS},
  keywords     = {Control and Systems Engineering,Software,Control and Optimization,Applied Mathematics,parametric dynamic model uncertainty,polynomial approximation theory,robust optimal control},
  language     = {eng},
  pages        = {16},
  title        = {A framework for robust quadratic optimal control with parametric dynamic model uncertainty using polynomial chaos},
  url          = {http://dx.doi.org/10.1002/oca.2575},
  year         = {2020},
}

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