  Adaptive dynamic programming is a collective term for a variety of approaches
to infinite-horizon optimal control. Common to all approaches is approximation
of the infinite-horizon cost function based on dynamic programming philosophy.
Typically, they also require knowledge of a dynamical model of the system. In
the current work, application of adaptive dynamic programming to a system whose
dynamical model is unknown to the controller is addressed. In order to realize
the control algorithm, a model of the system dynamics is estimated with a
Kalman filter. A stacked control scheme to boost the controller performance is
suggested. The functioning of the new approach was verified in simulation and
compared to the baseline represented by gradient descent on the running cost.
