Hinfinitykontroll

Hinfinitykontroll, or H∞ control, is a branch of robust control theory aimed at designing controllers that guarantee worst-case performance in the presence of disturbances and model uncertainties by constraining the H∞ norm of the closed-loop transfer function.

In standard setup, a linear time-invariant plant P(s) has inputs w (disturbances) and u (control), and outputs z (performance) and y (measurement). The task is to find a controller K(s) such that the closed-loop transfer from w to z has H∞ norm less than γ, for some γ > 0, thereby bounding energy amplification from disturbances to performance.

The design is typically carried out using state-space methods, via Riccati equations or linear matrix inequalities (LMIs). Existence conditions rely on the bounded real lemma.

History: The approach was developed in the 1980s by researchers including Doyle, Glover, Khargonekar, and Tannenbaum, and has since been documented in standard texts on robust control.

Applications: Hinfinitykontroll has been applied in aerospace, automotive, mechanical systems, process control, and robotics, among other fields, to achieve reliable performance under uncertainty and external disturbances.

Advantages and limitations: The framework provides robust guarantees for stability and performance under model errors and disturbances. It can be conservative and computationally intensive for large-scale systems, and practical design often involves trade-offs between performance, complexity, and model fidelity.

See also: H-infinity norm, robust control, Riccati equation, linear matrix inequalities.