Development of a velocity form for a class of RNNs, with application to offset-free nonlinear MPC design

TL;DR

This paper introduces a velocity form reformulation for RNNs to achieve offset-free tracking in nonlinear MPC, ensuring stability and constraint handling, validated through simulations on a benchmark process.

Contribution

A novel velocity form of RNNs is proposed for offset-free control, with stability conditions and an offset-free nonlinear MPC algorithm developed.

Findings

Effective offset-free tracking demonstrated in simulations

Stability conditions derived using LMIs

Successful handling of input/output constraints

Abstract

This paper addresses the offset-free tracking problem for nonlinear systems described by a class of recurrent neural networks (RNNs). To compensate for constant disturbances and guarantee offset-free tracking in the presence of model-plant mismatches, we propose a novel reformulation of the RNN model in velocity form. Conditions based on linear matrix inequalities are then derived for the design of a nonlinear state observer and a nonlinear state-feedback controller, ensuring global or regional closed-loop stability of the origin of the velocity form dynamics. Moreover, to handle input and output constraints, a theoretically sound offset-free nonlinear model predictive control algorithm is developed. The algorithm exploits the velocity form model as the prediction model and the static controller as an auxiliary law for the definition of the terminal ingredients. Simulations on a pH-neutralisation process benchmark demonstrate the effectiveness of the proposed approach.