Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification
This work addresses the challenge of ensuring stability and performance guarantees in neural network-based imitation controllers for control systems, representing an incremental advancement in error analysis and dataset optimization.
The paper tackles the problem of bounding approximation error in imitation learning for model predictive control (MPC) using neural networks, by deriving a Lipschitz-based error bound that guides dataset design and introducing a training adjustment to reduce dataset density, resulting in improved predictive capabilities and a closer match to the original MPC controller on a simulated inverted pendulum.
This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.