  This paper develops a data-based approach to the closed-loop output feedback
control of nonlinear dynamical systems with a partial nonlinear observation
model. We propose an information state based approach to rigorously transform
the partially observed problem into a fully observed problem where the
information state consists of the past several observations and control inputs.
We further show the equivalence of the transformed and the initial partially
observed optimal control problems and provide the conditions to solve for the
deterministic optimal solution. We develop a data based generalization of the
iterative Linear Quadratic Regulator (iLQR) to partially observed systems using
a local linear time varying model of the information state dynamics
approximated by an Autoregressive moving average (ARMA) model, that is
generated using only the input-output data. This open-loop trajectory
optimization solution is then used to design a local feedback control law, and
the composite law then provides an optimum solution to the partially observed
feedback design problem. The efficacy of the developed method is shown by
controlling complex high dimensional nonlinear dynamical systems in the
presence of model and sensing uncertainty.
