Fine-Tuning of Neural Network Approximate MPC without Retraining via Bayesian Optimization

Approximate model-predictive control (AMPC) aims to imitate an MPC's behavior with a neural network, removing the need to solve an expensive optimization problem at runtime. However, during deployment, the parameters of the underlying MPC must usually be fine-tuned. This often renders AMPC impractical as it requires repeatedly generating a new dataset and retraining the neural network. Recent work addresses this problem by adapting AMPC without retraining using approximated sensitivities of the MPC's optimization problem. Currently, this adaption must be done by hand, which is labor-intensive and can be unintuitive for high-dimensional systems. To solve this issue, we propose using Bayesian optimization to tune the parameters of AMPC policies based on experimental data. By combining model-based control with direct and local learning, our approach achieves superior performance to nominal AMPC on hardware, with minimal experimentation. This allows automatic and data-efficient adaptation of AMPC to new system instances and fine-tuning to cost functions that are difficult to directly implement in MPC. We demonstrate the proposed method in hardware experiments for the swing-up maneuver on an inverted cartpole and yaw control of an under-actuated balancing unicycle robot, a challenging control problem.

Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Re-Training

Model Predictive Control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address this limitation, enabling deployment on resource-constrained embedded systems. However, when tuning AMPCs for real-world systems, large datasets need to be regenerated and the NN needs to be retrained at every tuning step. This work introduces a novel, parameter-adaptive AMPC architecture capable of online tuning without recomputing large datasets and retraining. By incorporating local sensitivities of nonlinear programs, the proposed method not only mimics optimal MPC inputs but also adjusts to changes in physical parameters of the model using linear predictions while still guaranteeing stability. We showcase the effectiveness of parameter-adaptive AMPC by controlling the swing-ups of two different real cartpole systems with a severely resource-constrained microcontroller (MCU). We use the same NN across both system instances that have different parameters. This work not only represents the first experimental demonstration of AMPC for fast-moving systems on low-cost MCUs to the best of our knowledge, but also showcases generalization across system instances and variations through our parameter-adaptation method. Taken together, these contributions represent a marked step toward the practical application of AMPC in real-world systems.