Output Feedback Minimax Adaptive Control

TL;DR

This paper introduces a minimax dual control framework for adaptive control that handles uncertainty in linear systems, providing finite-dimensional information states and controllers with guaranteed finite gain performance.

Contribution

It presents a unified approach for state and output feedback adaptive control using a minimax formulation with finite-dimensional information states.

Findings

Finite-dimensional information states exist for the minimax dual control problem.

Controllers designed via Bellman inequalities ensure finite gain stability.

Numerical example demonstrates the effectiveness of the proposed method.

Abstract

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.