Persistently Exciting Tube MPC

TL;DR

This paper introduces a novel control strategy combining robust MPC with persistent excitation for simultaneous system identification and regulation, using input decomposition and recursive least squares.

Contribution

It proposes a new control framework that separates regulation and excitation, ensuring persistent excitation for identification within a robust MPC setting.

Findings

Effective separation of regulation and excitation inputs.

Guarantees persistent excitation through non-convex constraints.

Successful recursive least squares identification during control.

Abstract

This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part.