Recurrent neural network-based robust control systems with regional properties and application to MPC design

TL;DR

This paper develops robust control schemes for recurrent neural network systems using regional stability properties, enabling improved disturbance rejection and setpoint tracking, with applications to model predictive control.

Contribution

It introduces a novel observer and control design framework leveraging regional incremental ISS and tube-based NMPC for RNN systems.

Findings

The proposed methods ensure robustness to disturbances.

The control schemes enlarge the region of attraction.

Numerical simulations validate theoretical guarantees.

Abstract

This paper investigates the design of output-feedback schemes for systems described by a class of recurrent neural networks. We propose a procedure based on linear matrix inequalities for designing an observer and a static state-feedback controller. The algorithm leverages global and regional incremental input-to-state stability (incremental ISS) and enables the tracking of constant setpoints, ensuring robustness to disturbances and state estimation uncertainty. To address the potential limitations of regional incremental ISS, we introduce an alternative scheme in which the static law is replaced with a tube-based nonlinear model predictive controller (NMPC) that exploits regional incremental ISS properties. We show that these conditions enable the formulation of a robust NMPC law with guarantees of convergence and recursive feasibility, leading to an enlarged region of attraction. Theoretical results are validated through numerical simulations on the pH-neutralisation process benchmark.