Learning-based Approximate Model Predictive Control with Guarantees: Joining Neural Networks with Recent Robust MPC

In this work, we present a model predictive control (MPC) method for applications in complex constrained physical systems. We base our work on a novel robust model predictive control (RMPC) scheme guaranteeing constraint satisfaction and recursive feasibility under disturbances. The used scheme keeps the computational complexity comparable to the nominal case. We adopt this approach and extend it by practical useful additions, such as robust dynamic set point tracking and the handling of nonlinear constraints in the output function. We are able to demonstrate this method’s practical significance by controlling a complex robotic system (MPI Apollo robot). Furthermore we tackle the inherent computational complexity of the optimization problem by approximating the RMPC controller with neural network (NN) regression. By only using the NN, we are able to control the robot in a much more dynamic way due to a computational speed-up of several magnitudes. Finally, we also analyze the quality of the approximation by providing closed loop statistical guarantees for the NN controller, also taking into account additional experimentally validated non-idealities of our model. Most of the code, including the TensorFlow NN inference, is fully written in C++ and available on the Max Planck Autonomous Motion Department Gitlab server.