Neural Network-Based Model Predictive Control with Input-to-State Stability

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.