Robust H2/H-infinity control under stochastic requirements: minimizing conditional value-at-risk instead of worst-case performance
This addresses the problem of overly conservative control designs for engineers and researchers in robust control, though it is an incremental shift in approach rather than a foundational breakthrough.
The paper tackles the conservatism of conventional robust H2/H-infinity control by introducing a new paradigm that optimizes controllers using conditional value-at-risk instead of worst-case performance, resulting in significant overall performance improvements in a mechanical system example.
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.