  Control of a dynamical system without the knowledge of dynamics is an
important and challenging task. Modern machine learning approaches, such as
deep neural networks (DNNs), allow for the estimation of a dynamics model from
control inputs and corresponding state observation outputs. Such data-driven
models are often utilized for the derivation of model-based controllers.
However, in general, there are no guarantees that a model represented by DNNs
will be controllable according to the formal control-theoretical meaning of
controllability, which is crucial for the design of effective controllers. This
often precludes the use of DNN-estimated models in applications, where formal
controllability guarantees are required. In this proof-of-the-concept work, we
propose a control-theoretical method that explicitly enhances models estimated
from data with controllability. That is achieved by augmenting the model
estimation objective with a controllability constraint, which penalizes models
with a low degree of controllability. As a result, the models estimated with
the proposed controllability constraint allow for the derivation of more
efficient controllers, they are interpretable by the control-theoretical
quantities and have a lower long-term prediction error. The proposed method
provides new insights on the connection between the DNN-based estimation of
unknown dynamics and the control-theoretical guarantees of the solution
properties. We demonstrate the superiority of the proposed method in two
standard classical control systems with state observation given by low
resolution high-dimensional images.
