Designing neural network control policies under parametric uncertainty: A Koopman operator approach

Solving the optimisation problem associated with nonlinear model predictive control (MPC) on-line when considering uncertainty is often infeasible due to the large computational times. One approach is to avoid the online optimisation by using an imitation learning approach where a neural network or other approximator is trained on offline solutions of the MPC problem. This can be computationally costly as the potential system behaviour must be fully represented in the data, which requires many MPC solutions. In this work we propose a new method to train a neural feedback controller in closed loop for problems with uncertainty in parameters and/or the initial conditions. Our method does not require solving MPC problems off-line to generate training data, instead we optimise the neural network directly on the MPC objective in a single shooting approach, with expectations evaluated in their Koopman expectation form using a quadrature algorithm. The proposed method is demonstrated on three problems. The optimised controllers for these problems show good performance, and have an average evaluation time of less than 4 /xs.