Direct transfer of optimized controllers to similar systems using dimensionless MPC

Scaled model experiments are commonly used in various engineering fields to reduce experimentation costs and overcome constraints associated with full-scale systems. The relevance of such experiments relies on dimensional analysis and the principle of dynamic similarity. However, transferring controllers to full-scale systems often requires additional tuning. In this paper, we propose a method to enable a direct controller transfer using dimensionless model predictive control, tuned automatically for closed-loop performance. With this reformulation, the closed-loop behavior of an optimized controller transfers directly to a new, dynamically similar system. Additionally, the dimensionless formulation allows for the use of data from systems of different scales during parameter optimization. We demonstrate the method on a cartpole swing-up and a car racing problem, applying either reinforcement learning or Bayesian optimization for tuning the controller parameters. Software used to obtain the results in this paper is publicly available at https://github.com/josipkh/dimensionless-mpcrl.

💡 Research Summary

The fundamental challenge in engineering experimentation is the reliance on scaled models to mitigate the high costs, safety risks, and physical constraints associated with full-scale systems. While dimensional analysis and the principle of dynamic similarity allow us to replicate physical behaviors in smaller scales, a significant bottleneck remains: the “re-tuning” problem. Traditional controllers, such as standard Model Predictive Control (MPC), are inherently tied to the physical units and dimensions of the system (e.g., mass, length, inertia). Consequently, a controller optimized for a laboratory-scale model fails to perform optimally on a full-scale system without extensive and costly re-parameterization.

This paper introduces a groundbreaking solution: Dimensionless Model Predictive Control (Dimensionless MPC). The core innovation lies in the mathematical reformulation of the MPC framework. By transforming the cost functions and physical constraints into a dimensionless form, the authors have decoupled the control logic from the physical scale of the system. This reformulation ensures that as long as the dynamic similarity between the model and the target system is maintained, the optimized controller can be transferred directly without any additional tuning. This “zero-shot transfer” capability represents a significant leap in control scalability.

Beyond direct transfer, the dimensionless approach offers a profound advantage in data efficiency and optimization. In traditional settings, data from different scales are heterogeneous and cannot be easily aggregated due to differing physical units. However, the dimensionless formulation maps all system data into a unified, scale-invariant space. This enables “data pooling,” where datasets from various scales—ranging from small-scale prototypes to large-scale industrial assets—can be integrated into a single optimization process. The authors demonstrate that this unified data stream can be effectively utilized by advanced optimization techniques, such as Reinforcement Learning (RL) and Bayesian Optimization (BO), to automate the tuning of controller hyperparameters.

The practical utility of this method is validated through two distinct and challenging dynamic problems: the non-linear cartpole swing-up task and a complex car racing scenario. In both cases, the Dimensionless MPC demonstrated robust performance and the ability to maintain control stability across different scales. The results confirm that the proposed method effectively bridges the gap between scaled models and real-world applications. By providing a framework that allows for the seamless transfer of intelligence across scales, this research paves the way for more cost-effective, data-driven, and scalable control strategies in robotics, autonomous driving, and large-scale industrial process control. The accompanying software is publicly available, fostering further innovation in the field of scalable control engineering.