Volterra model-based control for nonlinear systems via Carleman linearization

TL;DR

This paper introduces a novel control approach for nonlinear systems by combining Carleman linearization with Volterra series, demonstrated on a benchmark reactor with promising simulation results.

Contribution

It develops a new Volterra model-based control method using Carleman linearization for nonlinear systems, enhancing control accuracy and practical applicability.

Findings

Effective control of a nonlinear reactor system

Superior performance in simulation results

Practical utility demonstrated on benchmark system

Abstract

This paper presents detailed insights of embedding Carleman linearization into nonlinear systems for designing Volterra model-based control technique. Volterra series method is a competent mathematical tool, which extends the convolution integral for linear systems to nonlinear systems. First, we utilize the Carleman linearization technique to arrive at the bilinear approximation of the nonlinear system. Secondly, the third-order Volterra model representation is computed from the Carleman bilinearized model. Then, Volterra model-based control strategy is developed. The proposed method is effectuated on the benchmark van de Vusse reactor exhibiting non-minimum phase response. The open and closed-loop simulation results are presented, demonstrating the superiority and practical utility of the proposed method.