Stabilizing predictive control with persistence of excitation for constrained linear systems

TL;DR

This paper introduces a novel adaptive predictive control method for constrained linear systems that combines persistent excitation with tube MPC to ensure accurate parameter estimation, stability, and constraint satisfaction.

Contribution

It proposes a partitioned control scheme integrating persistent excitation with a tube MPC framework, enhancing parameter estimation and stability in constrained systems.

Findings

Guarantees constraint satisfaction and robust exponential stability.

Ensures convergence of parameter estimates.

Achieves optimal excitation for system identification.

Abstract

A new adaptive predictive controller for constrained linear systems is presented. The main feature of the proposed controller is the partition of the input in two components. The first part is used to persistently excite the system, in order to guarantee accurate and convergent parameter estimates in a deterministic framework. An MPC-inspired receding horizon optimization problem is developed to achieve the required excitation in a manner that is optimal for the plant. The remaining control action is employed by a conventional tube MPC controller to regulate the plant in the presence of parametric uncertainty and the excitation generated for estimation purposes. Constraint satisfaction, robust exponential stability, and convergence of the estimates are guaranteed under design conditions mildly more demanding than that of standard MPC implementations.