Reduced Sample Complexity in Scenario-Based Control System Design via Constraint Scaling

TL;DR

This paper introduces a constraint scaling method inspired by large deviations theory that significantly reduces the sample size needed in scenario-based control design, enhancing computational efficiency for safety-critical applications.

Contribution

The paper presents a novel constraint scaling technique that achieves exponential reduction in sample complexity for low-violation control problems under mild distribution assumptions.

Findings

Exponential decrease in sample size requirements.

Supports low-violation safety-critical control applications.

Numerical experiments validate theoretical improvements.

Abstract

The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach can demand large sample sizes, making it intractable for safety-critical applications that require very low levels of constraint violation. To address this challenge, we propose a novel yet simple constraint scaling method, inspired by large deviations theory. Under mild nonparametric conditions on the underlying probability distribution, we show that our method yields an exponential reduction in sample size requirements for bilinear constraints with low violation levels compared to the classical approach, thereby significantly improving computational tractability. Numerical experiments on robust pole assignment problems support our theoretical findings.