Learning-based controllers, and especially learning-based model predictive controllers, have been used for a number of different applications with great success. In spite of good performance, a lot of these cases lack stability guarantees. In this paper we consider a scenario where the dynamics of a nonlinear system are unknown, but where input and output data are available. A prediction model is learned from data using a neural network, which in turn is used in a nonlinear model predictive control scheme. The closed-loop system is shown to be input-to-state stable with respect to the prediction error of the learned model. The approach is tested and verified in simulations, by employing the controller to a benchmark system, namely a continuous stirred tank reactor plant. Simulations show that the proposed controller successfully drives the system from random initial conditions, to a reference equilibrium point, even in the presence of noise. The results also verify the theoretical stability result.

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Low complexity of a system model is essential for its use in real-time applications. However, sparse identification methods commonly have stringent requirements that exclude them from being applied in an industrial setting. In this article, we introduce a flexible method for the sparse identification of dynamical systems described by ordinary differential equations. Our method relieves many of the requirements imposed by other methods that relate to the structure of the model and the dataset, such as fixed sampling rates, full state measurements, and linearity of the model. The Levenberg-Marquardt algorithm is used to solve the identification problem. We show that the Levenberg-Marquardt algorithm can be written in a form that enables parallel computing, which greatly diminishes the time required to solve the identification problem. An efficient backward elimination strategy is presented to construct a lean system model.