On Minimax Optimal Dual Control for Fully Actuated Systems

TL;DR

This paper derives an explicit minimax adaptive control strategy for fully actuated linear systems, balancing exploration and exploitation by solving a Bellman equation under specific assumptions.

Contribution

It introduces a novel explicit solution to a minimax dynamic game for adaptive control of fully actuated systems, addressing the exploration-exploitation tradeoff.

Findings

Explicit Bellman equation solution for specific system cases

Dual controller optimally balances exploration and exploitation

Provides a new approach for adaptive control in linear systems

Abstract

A multi-variable adaptive controller is derived as the explicit solution to a minimax dynamic game. The minimizing player selects the control action as a function of past state measurements and inputs. The maximizing player selects disturbances and model parameters for the underlying linear time-invariant dynamics. This leads to a Bellman equation that can be solved explicitly for the case with unitary B-matrix known up to a sign and no input penalty. The minimizing policy is a dual controller that optimizes the tradeoff between exploration and exploitation.