Learning an approximate model predictive controller with guarantees

Abstract

In this thesis, a supervised learning framework to approximate a model predictive controller (MPC) with guarantees on stability and constraint satisfaction is proposed. The approximate controller has a reduced computational complexity in comparison to standard MPC which makes it possible to implement the resulting controller for systems with a high sampling rate on a cheap hardware. The framework can be used for a wide class of nonlinear systems. In order to obtain closed-loop guarantees for the approximate MPC, a robust MPC (RMPC) with robustness to bounded input disturbances is used which guarantees stability and constraint satisfaction if the input is approximated with a bound on the approximation error. The RMPC can be sampled offline and hence, any standard supervised learning technique can be used to approximate the MPC from samples. Neural networks (NN) are discussed in this thesis as one suitable approximation method. To guarantee a bound on the approximation error, statistical learning bounds are used. A method based on Hoeffding’s Inequality is proposed to validate that the approximate MPC satisfies these bounds with high confidence. This validation method is suited for any approximation method. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the approximated MPC. Within this thesis, an algorithm to obtain automatically an approximate controller is proposed. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem for which we learn a neural network controller that guarantees stability and constraint satisfaction. The combination of robust control and statistical validation can also be used for other learning based control methods to obtain guarantees on stability and constraint satisfaction.