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.

中文翻译：

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基于多项式混沌的带参数动态模型不确定性的鲁棒二次最优控制框架

我们提出了一种针对鲁棒最优控制（OC）问题而量身定制的框架，该问题受系统动力学的参数模型不确定性的影响。首先，我们确定一类基于确定性二次目标的健壮目标内核。证明了如何将这些核表示为状态的随机矩的函数，以及客观术语如何与最优解的鲁棒性和性能相关。其次，我们采用广义多项式混沌（gPC）框架来沿状态轨迹传播不确定性。将这两个框架整合在一起，可以将问题重新确定为确定性OC问题，具体取决于可以使用现有方法解决的gPC膨胀系数的函数。