Information-based complexity of uncertainty sets in feedback control

In this paper, a notion of information-based complexity is introduced to characterize complexities of plant uncertainty sets in feedback control settings, and to understand relationships between identification and feedback control in dealing with uncertainty. This new complexity measure extends the Kolmogorov entropy to problems involving information acquisition (identification) and processing (control), and provides a tangible measure of “difficulty” of an uncertainty set of plants. In the special cases of robust stabilization for systems with either gain uncertainty or unstructured additive uncertainty, the complexity measures are explicitly derived.