Minimax Optimal Adaptive Control for Systems on Cones

TL;DR

This paper extends optimal control theory on positive cones to minimax adaptive control, providing explicit Bellman equation solutions for dual control and enabling better management of exploration-exploitation tradeoffs.

Contribution

It introduces a novel approach to minimax adaptive control on cones, offering explicit solutions to Bellman equations for dual control problems.

Findings

Explicit Bellman solutions for dual control

Enhanced optimization of exploration-exploitation tradeoff

Extension of control theory on positive cones

Abstract

The theory of optimal control on positive cones has recently identified several new problem classes where the Bellman equation can be solved explicitly, in analogy with classical linear quadratic control. In this paper, the idea is extended to minimax adaptive control, yielding exact solutions to instances of the Bellman equation for dual control. In particular, this allows for optimization of the fundamental tradeoff between exploration and exploitation.