Stochastic Optimal Control using polynomial chaos variational integrators

Boutselis, George I.; Torre, Gerardo De La; Theodorou, Evangelos A.

doi:10.1109/acc.2016.7526707

Cited by 12 publications

(12 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, we seek to define a robust reformulation, K , of the deterministic objective, L . It will show rewarding to examine the direct application of the expected value operator,

E

, to L [ X , u ], as appears to be the main tendency in SOC …”

Section: Problem Settingmentioning

confidence: 99%

“…In the first term, we can recognize the deterministic kernel applied on the expected system behavior as in References . The second term penalizes the uncertainty on that response and is an inherent property of the problem statements as proposed in References .…”

Section: Problem Settingmentioning

confidence: 99%

“…the case where we propagate freely in the collocation space and project the result onto the coefficient space only when we need it. Although worth mentioning, given its frequent use, it was left out of scope onward.…”

Section: Deterministic Problem Reformulationmentioning

confidence: 99%

“…In more recent literature, several attempts were documented to accommodate general parametric model uncertainty into the SOC framework. Notable examples are given in References . These methods distinguish in two aspects from those mentioned above.…”

Section: Introductionmentioning

confidence: 99%

“…Usually, one applies a stochastic operator on the deterministic objective value. Tendencies are to substitute the random state for its expected value or to minimize the expected value of the random objective …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Lefebvre

Belie

Crevecoeur

2020

Optim Control Appl Methods

View full text Add to dashboard Cite

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. K E Y W O R D Sparametric dynamic model uncertainty, polynomial approximation theory, robust optimal control 1 Optim Control Appl Meth. 2020;41:833-848.wileyonlinelibrary.com/journal/oca

show abstract

“…Therefore, we seek to define a robust reformulation, K , of the deterministic objective, L . It will show rewarding to examine the direct application of the expected value operator,