  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 known 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.
