  Iterative linear quadratic regulator (iLQR) has gained wide popularity in
addressing trajectory optimization problems with nonlinear system models.
However, as a model-based shooting method, it relies heavily on an accurate
system model to update the optimal control actions and the trajectory
determined with forward integration, thus becoming vulnerable to inevitable
model inaccuracies. Recently, substantial research efforts in learning-based
methods for optimal control problems have been progressing significantly in
addressing unknown system models, particularly when the system has complex
interactions with the environment. Yet a deep neural network is normally
required to fit substantial scale of sampling data. In this work, we present
Neural-iLQR, a learning-aided shooting method over the unconstrained control
space, in which a neural network with a simple structure is used to represent
the local system model. In this framework, the trajectory optimization task is
achieved with simultaneous refinement of the optimal policy and the neural
network iteratively, without relying on the prior knowledge of the system
model. Through comprehensive evaluations on two illustrative control tasks, the
proposed method is shown to outperform the conventional iLQR significantly in
the presence of inaccuracies in system models.
