A Quantitative Framework for Navigating Controller Design Tradeoffs under Computational Constraints

Chris Verhoek and Nikolai Matni from the University of Pennsylvania have introduced a quantitative framework that explicitly incorporates computational constraints into the controller design process. Their paper, published on arXiv, addresses a long-standing gap: while approximations like model order reduction, temporal discretization, horizon truncation, and solver accuracy are ubiquitous in practice, their effects on stability and performance are rarely treated as tunable design parameters. The authors leverage incremental input-to-state stability to show that bounding the aggregate impact of these approximations reduces to verifying a design-dependent sector bound on the difference between the deployed policy and an idealized baseline, with stability guaranteed via a small-gain condition.

To operationalize these insights, Verhoek and Matni formulate a Design Meta-Problem that minimizes the performance gap subject to stability, real-time compute, and timing constraints. They demonstrate the framework on a receding horizon LQR case study, achieving a principled, near-optimal navigation of tradeoffs among sampling rate, model order, horizon length, and solver iterations. The work provides a systematic approach for engineers to explicitly balance performance and computational resources, making it highly relevant for embedded systems, robotics, and autonomous vehicles where compute budgets are critical.