A Quantitative Framework for Navigating Controller Design Tradeoffs under Computational Constraints

TL;DR

This paper introduces a quantitative framework for explicitly managing computational constraints in controller design, balancing performance and stability through tunable approximations.

Contribution

It formalizes the effects of design approximations on controller performance and stability, enabling systematic tradeoff navigation under computational limits.

Findings

Framework effectively captures tradeoffs among sampling rate, model order, horizon length, and solver iterations.

Stability is ensured via a sector bound and small-gain condition within the proposed approach.

Case study demonstrates near-optimal navigation of control design tradeoffs.

Abstract

Computational constraints permeate the controller design process, and yet are rarely treated as explicit design constraints. Towards addressing this gap, we propose a quantitative framework that captures the effects of common design approximations, such as model order reduction, temporal discretization, horizon truncation, and solver accuracy, on both controller performance and computational requirements. Our framework highlights that these approximations are tunable parameters within an overall controller design process. By leveraging incremental input-to-state stability, we show that bounding the aggregate effects of these approximations reduces to verifying a design-dependent sector bound on the difference between the deployed policy and an idealized baseline, with stability enforced via a small-gain condition. We operationalize these insights via a Design Meta-Problem in which the performance gap is minimized subject to stability, real-time compute, and timing constraints. Finally, we instantiate the framework on a receding horizon LQR case study, and demonstrate a principled near-optimal navigation of tradeoffs among sampling rate, model order, horizon length, and solver iterations.