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Control of a dynamical system without the knowledge of dynamics is animportant and challenging task. Modern machine learning approaches, such asdeep neural networks (DNNs), allow for the estimation of a dynamics model fromcontrol inputs and corresponding state observation outputs. Such data-drivenmodels are often utilized for the derivation of model-based controllers.However, in general, there are no guarantees that a model represented by DNNswill be controllable according to the formal control-theoretical meaning ofcontrollability, which is crucial for the design of effective controllers. Thisoften precludes the use of DNN-estimated models in applications, where formalcontrollability guarantees are required. In this proof-of-the-concept work, wepropose a control-theoretical method that explicitly enhances models estimatedfrom data with controllability. That is achieved by augmenting the modelestimation objective with a controllability constraint, which penalizes modelswith a low degree of controllability. As a result, the models estimated withthe proposed controllability constraint allow for the derivation of moreefficient controllers, they are interpretable by the control-theoreticalquantities and have a lower long-term prediction error. The proposed methodprovides new insights on the connection between the DNN-based estimation ofunknown dynamics and the control-theoretical guarantees of the solutionproperties. We demonstrate the superiority of the proposed method in twostandard classical control systems with state observation given by lowresolution high-dimensional images.

Controllability-Constrained Deep Network Models for Enhanced Control of Dynamical Systems