Linearizing nonlinear dynamics using deep learning

The majority of systems of practical interest are characterized by nonlinear dynamics. This renders the control and optimization of such systems a complex task owing to their nonlinear behaviour. Standard methods of dealing with nonlinear systems such as linearizing around a fixed point may not be an effective strategy for many systems, thus requiring an alternative approach. For this reason, we propose a novel deep learning framework to discover a transformation of a nonlinear dynamical system to an equivalent higher dimensional linear system using data generated from identification experiments. We demonstrate that the resulting learned linear representation accurately captures the dynamics of the original system for a wide range of conditions defined by the training dataset used. As a result of this, we show that the learned linear model can subsequently be used for the successful control of the original system. We demonstrate this by applying the proposed framework to three examples; a benchmark example from the literature, and two practical, complex nonlinear dynamical systems from the chemical engineering domain: the Continuous Stirred Tank Reactor (CSTR) system and finally the four-tank system.