Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining

TL;DR

This work introduces a novel, parameter-adaptive AMPC architecture capable of online tuning without recomputing large datasets and retraining, and showcases generalization across system instances and variations through the parameter-adaptation method.

Abstract

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.

Figures (4)

• Figure 1: Parameter-adaptive AMPC. Approximate nominal MPC inputs are linearly adapted to true parameters $\theta$ by approximate sensitivities. The parameters can include parameters of the dynamics model ${\theta_\mathrm{dyn}}$ and other MPC parameters, like weights of the cost function.
• Figure 2: The cartpole inverted pendulum system (left) and the hardware pendulums used. The Quanser pendulum (center) and the self-made pendulum (right) have significantly different parameters $\theta$ from each other and from $\theta_{\mathrm{nom}}$. A video of our experiments is available at https://youtu.be/o1RdiYUH9uY.
• Figure 3: Approximate linear predictor effectiveness: Each cell indicates the fraction of closed-loop simulations from random initial states where the pendulum is stabilized upright, given a deviation in parameters (scaled to $\pm1$ in this plot). The use of approximate linear predictors enables the NN to stabilize the system across a broader parameter range.
• Figure 4: Closed-loop evaluation on Quanser and self-made cartpole pendulum hardware: The parameter-adaptive AMPC with true identified system parameters stabilizes both pendulums, Quanser (blue) and self-made (green), while no adaption (red) or parameters from the wrong system instance (orange) fail during the swing-up. Nominal, Quanser, and self-made system have significantly different parameters. The slow drift in the cart position for both systems is due to unmodeled stick-slip effects in the pendulum bearing near zero velocity. However, as our video shows on a long horizon, the cart slowly oscillates on its rail. Notably, with parameter-adaptive AMPC, the systems satisfy constraints.

Theorems & Definitions (3)

• theorem 1
• proof
• Remark 1