Output Feedback Minimax Adaptive Control

This paper formulates adaptive controller design as a minimax dual control problem. The objective is to design a controller that minimizes the worst-case performance over a set of uncertain systems. The uncertainty is described by a set of linear time-invariant systems with unknown parameters. The main contribution is a common framework for both state feedback and output feedback control. We show that for finite uncertainty sets, the minimax dual control problem admits a finite-dimensional information state. This information state can be used to design adaptive controllers that ensure that the closed-loop has finite gain. The controllers are derived from a set of Bellman inequalities that are amenable to numerical solutions. The proposed framework is illustrated on a challenging numerical example.