Constrained Neural Networks for Approximate Nonlinear Model Predictive Control

Solving Non-Linear Model Predictive Control (NMPC) online is often challenging due to the computational complexities involved. This issue can be avoided by approximating the optimization problem using supervised learning methods which comes with a trade-off on the optimality and/or constraint satisfaction. In this paper, a novel supervised learning framework for approximating NMPC is proposed, where we explicitly impart constraint knowledge within the neural networks. This knowledge is inherited by augmenting the loss function of the neural networks during the training phase with insights from KKT conditions. Logarithmic barrier functions are utilized to augment the loss function including conditions of primal and dual feasibility. The proposed framework can be applied to other machine learning based parametric approximators. This approach is easy to implement and its efficacy is demonstrated on a benchmark NMPC problem for continuous stirred tank reactor (CSTR).