Robust H2/H-infinity control under stochastic requirements: minimizing conditional value-at-risk instead of worst-case performance

TL;DR

This paper proposes a stochastic optimization approach for H2/H-infinity control that minimizes conditional value at risk, reducing conservatism compared to traditional worst-case methods.

Contribution

It introduces a new paradigm for robust control that leverages stochastic criteria like CVaR, with formulation and discussion of open challenges.

Findings

Significant performance improvement on a mechanical system.

Tolerates rare worst-case scenarios with some degradation.

Utilizes Monte Carlo sampling for controller optimization.

Abstract

Conventional robust H2/H-infinity control minimizes the worst-case performance, often leading to a conservative design driven by very rare parametric configurations. To reduce this conservatism while taking advantage of the stochastic properties of Monte Carlo sampling and its compatibility with parallel computing, we introduce an alternative paradigm that optimizes the controller with respect to a stochastic criterion, namely the conditional value at risk. We present the problem formulation and discuss several open challenges toward a general synthesis framework. The potential of this approach is illustrated on a mechanical system, where it significantly improves overall performance by tolerating some degradation in very rare worst-case scenarios.