Learning an Approximate Model Predictive Controller with Guarantees
This work addresses the computational burden of MPC for nonlinear systems, offering a practical solution with verifiable safety guarantees, though it is incremental as it builds on existing MPC and learning techniques.
The paper tackles the problem of reducing computational complexity in model predictive control (MPC) by proposing a supervised learning framework to approximate MPC with guarantees on stability and constraint satisfaction, using a robust MPC design combined with statistical learning bounds to achieve closed-loop statistical guarantees.
A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.