Minimax Adaptive Control for State Matrix with Unknown Sign

TL;DR

This paper develops a minimax adaptive control strategy for linear systems with unknown sign in the state matrix, using a dynamic game approach and Riccati equations to optimize control performance.

Contribution

It introduces a novel adaptive control method that estimates the uncertain sign of the state matrix and applies an H-infinity control law once the sign is identified.

Findings

Explicit optimal control law derived via Riccati equation

Controller adapts based on sign estimation from past data

Performance matches standard H-infinity control after sign estimation

Abstract

For linear time-invariant systems having a state matrix with uncertain sign, we formulate a minimax adaptive control problem as a zero sum dynamic game. Explicit expressions for the optimal value function and the optimal control law are given in terms of a Riccati equation. The optimal control law is adaptive in the sense the past data is used to estimate the uncertain sign for prediction of future dynamics. Once the sign has been estimated, the controller behaves like standard H-infinity optimal state feedback.